17 3.3 Development of Quantum Theory
Learning Objectives
By the end of this section, you will be able to:
- Extend the concept of wave–particle duality that was observed in electromagnetic radiation to matter as well
- Understand the general idea of the quantum mechanical description of electrons in orbitals
- Relate the 3D shape of an orbital and how electrons are arranged within the atom to the radial distribution function
- List and describe traits of the four quantum numbers that describe orbitals and specify the location of an electron in an atom
Bohr’s model explained the experimental data for the hydrogen atom and was widely accepted, but it also raised many questions. Why did electrons orbit at only fixed distances defined by a single quantum number n = 1, 2, 3, and so on, but never in between? Why did the model work so well describing hydrogen and one-electron ions, but could not correctly predict the emission spectrum for helium or any larger atoms? To answer these questions, scientists needed to completely revise the way they thought about matter.
Behavior in the Microscopic World
We know how matter behaves in the macroscopic world—objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle: It will continue in a straight line unless it collides with another ball or the table cushion, or is acted on by some other force (such as friction). The ball has a well-defined position and velocity (or a well-defined momentum, p = mv, defined by mass m and velocity v) at any given moment. In other words, the ball is moving in a classical trajectory. This is the typical behavior of a classical object.
When waves interact with each other, they show interference patterns that are not displayed by macroscopic particles such as the billiard ball. For example, interacting waves on the surface of water can produce interference patters similar to those shown on Figure 1. This is a case of wave behavior on the macroscopic scale, and it is clear that particles and waves are very different phenomena in the macroscopic realm.
As technological improvements allowed scientists to probe the microscopic world in greater detail, it became increasingly clear by the 1920s that very small pieces of matter follow a different set of rules from those we observe for large objects. The unquestionable separation of waves and particles was no longer the case for the microscopic world.
One of the first people to pay attention to the special behavior of the microscopic world was Louis de Broglie. He asked the question: If electromagnetic radiation can have particle-like character, can electrons and other submicroscopic particles exhibit wavelike character? In his 1925 doctoral dissertation, de Broglie extended the wave–particle duality of light that Einstein used to resolve the photoelectric-effect paradox to material particles. He predicted that a particle with mass m and velocity v (that is, with linear momentum p) should also exhibit the behavior of a wave with a wavelength value λ, given by this expression in which h is the familiar Planck’s constant:
This is called the de Broglie wavelength. Unlike the other values of λ discussed in this chapter, the de Broglie wavelength is a characteristic of particles and other bodies, not electromagnetic radiation (note that this equation involves velocity [v, m/s], not frequency [ν, Hz]. Although these two symbols are identical, they mean very different things). Where Bohr had postulated the electron as being a particle orbiting the nucleus in quantized orbits, de Broglie argued that Bohr’s assumption of quantization can be explained if the electron is considered not as a particle, but rather as a circular standing wave such that only an integer number of wavelengths could fit exactly within the orbit (Figure 2).
For a circular orbit of radius r, the circumference is 2πr, and so de Broglie’s condition is:
Since the de Broglie expression relates the wavelength to the momentum and, hence, velocity, this implies:
This expression can be rearranged to give Bohr’s formula for the quantization of the angular momentum:
Classical angular momentum L for a circular motion is equal to the product of the radius of the circle and the momentum of the moving particle p.
Shortly after de Broglie proposed the wave nature of matter, two scientists at Bell Laboratories, C. J. Davisson and L. H. Germer, demonstrated experimentally that electrons can exhibit wavelike behavior by showing an interference pattern for electrons travelling through a regular atomic pattern in a crystal. The regularly spaced atomic layers served as slits, as used in other interference experiments. Since the spacing between the layers serving as slits needs to be similar in size to the wavelength of the tested wave for an interference pattern to form, Davisson and Germer used a crystalline nickel target for their “slits,” since the spacing of the atoms within the lattice was approximately the same as the de Broglie wavelengths of the electrons that they used. Figure 4 shows an interference pattern. It is strikingly similar to the interference patterns for light shown in Figure 5 in Chapter 6.1 Electromagnetic Energy. The wave–particle duality of matter can be seen in Figure 4 by observing what happens if electron collisions are recorded over a long period of time. Initially, when only a few electrons have been recorded, they show clear particle-like behavior, having arrived in small localized packets that appear to be random. As more and more electrons arrived and were recorded, a clear interference pattern that is the hallmark of wavelike behavior emerged. Thus, it appears that while electrons are small localized particles, their motion does not follow the equations of motion implied by classical mechanics, but instead it is governed by some type of a wave equation that governs a probability distribution even for a single electron’s motion. Thus the wave–particle duality first observed with photons is actually a fundamental behavior intrinsic to all quantum particles.
View the Dr. Quantum – Double Slit Experiment cartoon for an easy-to-understand description of wave–particle duality and the associated experiments.
Example 1
Calculating the Wavelength of a Particle
If an electron travels at a velocity of 1.000 × 107 m s–1 and has a mass of 9.109 × 10–28 g, what is its wavelength?
Solution
We can use de Broglie’s equation to solve this problem, but we first must do a unit conversion of Planck’s constant. You learned earlier that 1 J = 1 kg m2/s2. Thus, we can write h = 6.626 × 10–34 J s as 6.626 × 10–34 kg m2/s.
This is a small value, but it is significantly larger than the size of an electron in the classical (particle) view. This size is the same order of magnitude as the size of an atom. This means that electron wavelike behavior is going to be noticeable in an atom.
Check Your Learning
Calculate the wavelength of a softball with a mass of 100 g traveling at a velocity of 35 m s–1, assuming that it can be modeled as a single particle.
Answer:
1.9 × 10–34 m.
We never think of a thrown softball having a wavelength, since this wavelength is so small it is impossible for our senses or any known instrument to detect (strictly speaking, the wavelength of a real baseball would correspond to the wavelengths of its constituent atoms and molecules, which, while much larger than this value, would still be microscopically tiny). The de Broglie wavelength is only appreciable for matter that has a very small mass and/or a very high velocity.
Werner Heisenberg considered the limits of how accurately we can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurately we measure the momentum of a particle, the less accurately we can determine its position at that time, and vice versa. This is summed up in what we now call the Heisenberg uncertainty principle: It is fundamentally impossible to determine simultaneously and exactly both the momentum and the position of a particle. For a particle of mass m moving with velocity vx in the x direction (or equivalently with momentum px), the product of the uncertainty in the position, Δx, and the uncertainty in the momentum, Δpx , must be greater than or equal to [latex]\frac{\hbar}{2}[/latex] (recall that [latex]\hbar = \frac{h}{2 \pi}[/latex], the value of Planck’s constant divided by 2π).
This equation allows us to calculate the limit to how precisely we can know both the simultaneous position of an object and its momentum. For example, if we improve our measurement of an electron’s position so that the uncertainty in the position (Δx) has a value of, say, 1 pm (10–12 m, about 1% of the diameter of a hydrogen atom), then our determination of its momentum must have an uncertainty with a value of at least
The value of ħ is not large, so the uncertainty in the position or momentum of a macroscopic object like a baseball is too insignificant to observe. However, the mass of a microscopic object such as an electron is small enough that the uncertainty can be large and significant.
It should be noted that Heisenberg’s uncertainty principle is not just limited to uncertainties in position and momentum, but it also links other dynamical variables. For example, when an atom absorbs a photon and makes a transition from one energy state to another, the uncertainty in the energy and the uncertainty in the time required for the transition are similarly related, as ΔE Δt ≥ [latex]\Delta E \; \Delta t \ge \frac{\hbar}{2}[/latex]. As will be discussed later, even the vector components of angular momentum cannot all be specified exactly simultaneously.
Heisenberg’s principle imposes ultimate limits on what is knowable in science. The uncertainty principle can be shown to be a consequence of wave–particle duality, which lies at the heart of what distinguishes modern quantum theory from classical mechanics. Recall that the equations of motion obtained from classical mechanics are trajectories where, at any given instant in time, both the position and the momentum of a particle can be determined exactly. Heisenberg’s uncertainty principle implies that such a view is untenable in the microscopic domain and that there are fundamental limitations governing the motion of quantum particles. This does not mean that microscopic particles do not move in trajectories, it is just that measurements of trajectories are limited in their precision. In the realm of quantum mechanics, measurements introduce changes into the system that is being observed.
Read this article that describes a recent macroscopic demonstration of the uncertainty principle applied to microscopic objects.
The Quantum–Mechanical Model of an Atom
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, as Bohr had argued, Erwin Schrödinger extended de Broglie’s work by incorporating the de Broglie relation into a wave equation, deriving what is today known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra, and he did so without having to invoke Bohr’s assumptions of stationary states and quantized orbits, angular momenta, and energies; quantization in Schrödinger’s theory was a natural consequence of the underlying mathematics of the wave equation. Like de Broglie, Schrödinger initially viewed the electron in hydrogen as being a physical wave instead of a particle, but where de Broglie thought of the electron in terms of circular stationary waves, Schrödinger properly thought in terms of three-dimensional stationary waves, or wavefunctions, represented by the Greek letter psi, ψ. A few years later, Max Born proposed an interpretation of the wavefunction ψ that is still accepted today: Electrons are still particles, and so the waves represented by ψ are not physical waves but, instead, are complex probability amplitudes. The square of the magnitude of a wavefunction [latex]|\psi|^2[/latex] describes the probability of the quantum particle being present near a certain location in space. This means that wavefunctions can be used to determine the distribution of the electron’s density with respect to the nucleus in an atom. In the most general form, the Schrödinger equation can be written as:
[latex]\hat{\mathcal{H}}[/latex] is the Hamiltonian operator, a set of mathematical operations representing the total energy of the quantum particle (such as an electron in an atom), ψ is the wavefunction of this particle that can be used to find the special distribution of the probability of finding the particle, and [latex]E[/latex] is the actual value of the total energy of the particle.
Schrödinger’s work, as well as that of Heisenberg and many other scientists following in their footsteps, is generally referred to as quantum mechanics.
You may also have heard of Schrödinger because of his famous thought experiment. This story explains the concepts of superposition and entanglement as related to a cat in a box with poison.
Understanding Quantum Theory of Electrons in Atoms
The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding.
As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principle quantum number. The principle quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 5). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has.
This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom:
The values nf and ni are the final and initial energy states of the electron. Example 2 in Chapter 6.2 The Bohr Model in the previous section of the chapter demonstrates calculations of such energy changes.
The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principle quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located.
Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital.
Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider.
There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1.
Consider the examples in Figure 6. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals.
The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found.
If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principle quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 7.
Figure 8 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principle quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principle quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies, as shown on Figure 8. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy.
While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms.
The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates.
The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number [latex]m_s = \frac{1}{2}[/latex]. The other is called the β state, with the z component of the spin being negative and [latex]m_s = -\frac{1}{2}[/latex]. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having [latex]m_s = - \frac{1}{2}[/latex] and [latex]m_s = \frac{1}{2}[/latex] are different if an external magnetic field is applied.
Figure 9 illustrates this phenomenon.  Its moment is directed up (in the positive direction of the z axis) for the [latex]\frac{1}{2}[/latex] spin quantum number and down (in the negative z direction) for the spin quantum number of [latex]- \frac{1}{2}[/latex]. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron on Figure 9) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with [latex]m_s = \frac{1}{2}[/latex] has a slightly lower energy in an external field in the positive z direction, and an electron with [latex]m_s = -\frac{1}{2}[/latex] has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting.
The Pauli Exclusion Principle
An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values ([latex]\pm \frac{1}{2}[/latex]), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons.
The properties and meaning of the quantum numbers of electrons in atoms are briefly summarized in Table 1.
| Name | Symbol | Allowed values | Physical meaning |
|---|---|---|---|
| principle quantum number | n | 1, 2, 3, 4, …. | shell, the general region for the value of energy for an electron on the orbital |
| angular momentum or azimuthal quantum number | l | 0 ≤ l ≤ n – 1 | subshell, the shape of the orbital |
| magnetic quantum number | ml | – l ≤ ml ≤ l | orientation of the orbital |
| spin quantum number | ms | 12,−1212,−12 | direction of the intrinsic quantum “spinning” of the electron |
| Table 1. Quantum Numbers, Their Properties, and Significance |
Example 2
Working with Shells and Subshells
Indicate the number of subshells, the number of orbitals in each subshell, and the values of l and ml for the orbitals in the n = 4 shell of an atom.
Solution
For n = 4, l can have values of 0, 1, 2, and 3. Thus, s, p, d, and f subshells are found in the n = 4 shell of an atom. For l = 0 (the s subshell), ml can only be 0. Thus, there is only one 4s orbital. For l = 1 (p-type orbitals), m can have values of –1, 0, +1, so we find three 4p orbitals. For l = 2 (d-type orbitals), ml can have values of –2, –1, 0, +1, +2, so we have five 4d orbitals. When l = 3 (f-type orbitals), ml can have values of –3, –2, –1, 0, +1, +2, +3, and we can have seven 4f orbitals. Thus, we find a total of 16 orbitals in the n = 4 shell of an atom.
Check Your Learning
Identify the subshell in which electrons with the following quantum numbers are found: (a) n = 3, l = 1; (b) n = 5, l = 3; (c) n = 2, l = 0.
Answer:
(a) 3p (b) 5f (c) 2s
Example 3
Maximum Number of Electrons
Calculate the maximum number of electrons that can occupy a shell with (a) n = 2, (b) n = 5, and (c) n as a variable. Note you are only looking at the orbitals with the specified n value, not those at lower energies.
Solution
(a) When n = 2, there are four orbitals (a single 2s orbital, and three orbitals labeled 2p). These four orbitals can contain eight electrons.
(b) When n = 5, there are five subshells of orbitals that we need to sum:
Again, each orbital holds two electrons, so 50 electrons can fit in this shell.
(c) The number of orbitals in any shell n will equal n2. There can be up to two electrons in each orbital, so the maximum number of electrons will be 2 × n2
Check Your Learning
If a shell contains a maximum of 32 electrons, what is the principal quantum number, n?
Answer:
n = 4
Example 4
Working with Quantum Numbers
Complete the following table for atomic orbitals:
| Orbital | n | l | ml degeneracy | Radial nodes (no.) |
|---|---|---|---|---|
| 4f | ||||
| 4 | 1 | |||
| 7 | 7 | 3 | ||
| 5d | ||||
| Table 2. |
Solution
The table can be completed using the following rules:
- The orbital designation is nl, where l = 0, 1, 2, 3, 4, 5, … is mapped to the letter sequence s, p, d, f, g, h, …,
- The ml degeneracy is the number of orbitals within an l subshell, and so is 2l + 1 (there is one s orbital, three p orbitals, five d orbitals, seven f orbitals, and so forth).
- The number of radial nodes is equal to n – l – 1.
| Orbital | n | l | ml degeneracy | Radial nodes (no.) |
|---|---|---|---|---|
| 4f | 4 | 3 | 7 | 0 |
| 4p | 4 | 1 | 3 | 2 |
| 7f | 7 | 3 | 7 | 3 |
| 5d | 5 | 2 | 5 | 2 |
| Table 3. |
Check Your Learning
How many orbitals have l = 2 and n = 3?
Answer:
The five degenerate 3d orbitals
Key Concepts and Summary
Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. Their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the three-dimensional position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. Atomic wavefunctions are also called orbitals. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in space. Therefore, atomic orbitals describe the areas in an atom where electrons are most likely to be found.
An atomic orbital is characterized by three quantum numbers. The principal quantum number, n, can be any positive integer. The general region for value of energy of the orbital and the average distance of an electron from the nucleus are related to n. Orbitals having the same value of n are said to be in the same shell. The angular momentum quantum number, l, can have any integer value from 0 to n – 1. This quantum number describes the shape or type of the orbital. Orbitals with the same principle quantum number and the same l value belong to the same subshell. The magnetic quantum number, ml, with 2l + 1 values ranging from –l to +l, describes the orientation of the orbital in space. In addition, each electron has a spin quantum number, ms, that can be equal to ±12.±12. No two electrons in the same atom can have the same set of values for all the four quantum numbers.
Chemistry End of Chapter Exercises
- How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different?
- What are the allowed values for each of the four quantum numbers: n, l, ml, and ms?
- Describe the properties of an electron associated with each of the following four quantum numbers: n, l, ml, and ms.
- Answer the following questions:
(a) Without using quantum numbers, describe the differences between the shells, subshells, and orbitals of an atom.
(b) How do the quantum numbers of the shells, subshells, and orbitals of an atom differ?
- Identify the subshell in which electrons with the following quantum numbers are found:
(a) n = 2, l = 1
(b) n = 4, l = 2
(c) n = 6, l = 0
- Which of the subshells described in the previous question contain degenerate orbitals? How many degenerate orbitals are in each?
- Identify the subshell in which electrons with the following quantum numbers are found:
(a) n = 3, l = 2
(b) n = 1, l = 0
(c) n = 4, l = 3
- Which of the subshells described in the previous question contain degenerate orbitals? How many degenerate orbitals are in each?
- Sketch the boundary surface of a [latex]d_{x^2 - y^2}[/latex] and a py orbital. Be sure to show and label the axes.
- Sketch the px and dxz orbitals. Be sure to show and label the coordinates.
- Consider the orbitals shown here in outline.
(a) What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)?
(b) How many orbitals of type (x) are found in a shell with n = 2? How many of type (y)? How many of type (z)?
(c) Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n = 4. Of an orbital of type (y) in a shell with n = 2. Of an orbital of type (z) in a shell with n = 3.
(d) What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)?
(e) What are the possible l and ml values for an orbital of type (x)? Of type (y)? Of type (z)?
- State the Heisenberg uncertainty principle. Describe briefly what the principle implies.
- How many electrons could be held in the second shell of an atom if the spin quantum number ms could have three values instead of just two? (Hint: Consider the Pauli exclusion principle.)
- Which of the following equations describe particle-like behavior? Which describe wavelike behavior? Do any involve both types of behavior? Describe the reasons for your choices.
(a) [latex]c = \lambda\nu[/latex]
(b) [latex]E = \frac{m\nu^2}{2}[/latex]
(c) [latex]r = \frac{n^2a_0}{Z}[/latex]
(d) [latex]E = h\nu[/latex]
(e) [latex]\lambda = \frac{h}{m\nu}[/latex]
- Write a set of quantum numbers for each of the electrons with an n of 4 in a Se atom.
Glossary
- angular momentum quantum number (l)
- quantum number distinguishing the different shapes of orbitals; it is also a measure of the orbital angular momentum
- atomic orbital
- mathematical function that describes the behavior of an electron in an atom (also called the wavefunction), it can be used to find the probability of locating an electron in a specific region around the nucleus, as well as other dynamical variables
- d orbital
- region of space with high electron density that is either four lobed or contains a dumbbell and torus shape; describes orbitals with l = 2. An electron in this orbital is called a d electron
- electron density
- a measure of the probability of locating an electron in a particular region of space, it is equal to the squared absolute value of the wave function ψ
- f orbital
- multilobed region of space with high electron density, describes orbitals with l = 3. An electron in this orbital is called an f electron
- Heisenberg uncertainty principle
- rule stating that it is impossible to exactly determine both certain conjugate dynamical properties such as the momentum and the position of a particle at the same time. The uncertainty principle is a consequence of quantum particles exhibiting wave–particle duality
- magnetic quantum number (ml)
- quantum number signifying the orientation of an atomic orbital around the nucleus; orbitals having different values of ml but the same subshell value of l have the same energy (are degenerate), but this degeneracy can be removed by application of an external magnetic field
- p orbital
- dumbbell-shaped region of space with high electron density, describes orbitals with l = 1. An electron in this orbital is called a p electron
- Pauli exclusion principle
- specifies that no two electrons in an atom can have the same value for all four quantum numbers
- principal quantum number (n)
- quantum number specifying the shell an electron occupies in an atom
- quantum mechanics
- field of study that includes quantization of energy, wave-particle duality, and the Heisenberg uncertainty principle to describe matter
- s orbital
- spherical region of space with high electron density, describes orbitals with l = 0. An electron in this orbital is called an s electron
- shell
- set of orbitals with the same principal quantum number, n
- spin quantum number (ms)
- number specifying the electron spin direction, either [latex]+\frac{1}{2}[/latex] or [latex]-\frac{1}{2}[/latex]
- subshell
- set of orbitals in an atom with the same values of n and l
- wavefunction (ψ)
- mathematical description of an atomic orbital that describes the shape of the orbital; it can be used to calculate the probability of finding the electron at any given location in the orbital, as well as dynamical variables such as the energy and the angular momentum
Solutions
Answers to Chemistry End of Chapter Exercises
1. Both models have a central positively charged nucleus with electrons moving about the nucleus in accordance with the Coulomb electrostatic potential. The Bohr model assumes that the electrons move in circular orbits that have quantized energies, angular momentum, and radii that are specified by a single quantum number, n = 1, 2, 3, …, but this quantization is an ad hoc assumption made by Bohr to incorporate quantization into an essentially classical mechanics description of the atom. Bohr also assumed that electrons orbiting the nucleus normally do not emit or absorb electromagnetic radiation, but do so when the electron switches to a different orbit. In the quantum mechanical model, the electrons do not move in precise orbits (such orbits violate the Heisenberg uncertainty principle) and, instead, a probabilistic interpretation of the electron’s position at any given instant is used, with a mathematical function ψ called a wavefunction that can be used to determine the electron’s spatial probability distribution. These wavefunctions, or orbitals, are three-dimensional stationary waves that can be specified by three quantum numbers that arise naturally from their underlying mathematics (no ad hoc assumptions required): the principal quantum number, n (the same one used by Bohr), which specifies shells such that orbitals having the same n all have the same energy and approximately the same spatial extent; the angular momentum quantum number l, which is a measure of the orbital’s angular momentum and corresponds to the orbitals’ general shapes, as well as specifying subshells such that orbitals having the same l (and n) all have the same energy; and the orientation quantum number m, which is a measure of the z component of the angular momentum and corresponds to the orientations of the orbitals. The Bohr model gives the same expression for the energy as the quantum mechanical expression and, hence, both properly account for hydrogen’s discrete spectrum (an example of getting the right answers for the wrong reasons, something that many chemistry students can sympathize with), but gives the wrong expression for the angular momentum (Bohr orbits necessarily all have non-zero angular momentum, but some quantum orbitals [s orbitals] can have zero angular momentum).
3. n determines the general range for the value of energy and the probable distances that the electron can be from the nucleus. l determines the shape of the orbital. m1 determines the orientation of the orbitals of the same l value with respect to one another. ms determines the spin of an electron.
5. (a) 2p; (b) 4d; (c) 6s
7. (a) 3d; (b) 1s; (c) 4f
9.
11. (a) x. 2, y. 2, z. 2; (b) x. 1, y. 3, z. 0; (c) x. 4 0 0 12,12, y. 2 1 0 12,12, z. 3 2 0 12;12; (d) x. 1, y. 2, z. 3; (e) x. l = 0, ml = 0, y. l = 1, ml = –1, 0, or +1, z. l = 2, ml = –2, –1, 0, +1, +2
13. 12
15.
| n | l | ml | s |
|---|---|---|---|
| 4 | 0 | 0 | [latex]+\frac{1}{2}[/latex] |
| 4 | 0 | 0 | [latex]-\frac{1}{2}[/latex] |
| 4 | 1 | −1 | [latex]+\frac{1}{2}[/latex] |
| 4 | 1 | 0 | [latex]+\frac{1}{2}[/latex] |
| 4 | 1 | +1 | [latex]+\frac{1}{2}[/latex] |
| 4 | 1 | −1 | [latex]-\frac{1}{2}[/latex] |
| Table 4. |


Medical Language Related to the Body as a Whole
Learning Objectives
- Connect medical language learning to the context of anatomy and physiology
- Introduce the basic architecture and levels of organization of the human body
- Evaluate the anatomical position, regional terms, directional terms, body planes, and body quadrants for anatomical positioning
- Describe body cavities and the functions of associated membranes
Body Planes
Use the anatomic reference system to identify the body planes below:
Body Planes (Text Version)
- Sagittal Plane
- Frontal (coronal) Plane
- Transverse Plane
Body Planes Diagram (Text Version)
This illustration activity shows the human body standing upright in the anatomical position. Three anatomical planes are illustrated with transparent lines identifying the location of the three planes: the _______[Blank 1] which divides the left and right side of the body, the _______[Blank 2] dividing front and back portions of the body, and the _______[Blank 3] dividing top and bottom portion of the body.
Check your answers: [1]
Activity source: Medical language with the Context of Anatomy and Physiology Body by Tiffany Hunt, illustration from Anatomy and Physiology (OpenStax) licensed under CC BY 4.0./ Text version added.
Body Cavities
Use the anatomic reference system to identify the body cavities:
Body Cavities (Text Version)
- Abdominopelvic
- Abdominal
- Thoracic
- Pelvic
- Cranial
- Ventral
- Vertebral
- Diaphragm
- Dorsal
- Cranial
- Vertebral
Body Cavities Diagram (Text Version)
This diagram activity shows two views of the human head and torso. The right image shows the lateral view, and the left image shows an anterior view of the human head and torso. The image is highlighting the several cavities or hollowed out spaces where organs and structures are positioned. The lateral view show four cavities: the head cavity known as the _______[Blank 1], the upper back cavity known as the _______[Blank 2], the lower back area known as the _______[Blank 3], and the chest cavity known as the ______[Blank 4] cavity. Adjoining lines for both views identify the ________[Blank 5] which is a muscular partition dividing the lungs from the location below it known as the _________[Blank 6] and followed by the lower _______[Blank 7]. The anterior view identifies the _______[Blank 8], _____[Blank 9], ________[Blank 10],________[Blank 11] cavities, and sections.
Check your answers: [2]
Activity source: Medical language with the Context of Anatomy and Physiology Dorsal by Tiffany Hunt, illustration from Anatomy and Physiology (OpenStax) licensed under CC BY 4.0./Text version added.
Directional Terms
Practice pronouncing and defining the following directional terms:
Medical Language with the Context of Anatomy and Physiology Directional Terms (Text version)
- Cranial Cavity
- KRĀ-nē-ăl kah-vi-tē
- The space formed inside the skull that the brain occupies.
- Homeostasis
- HŌ-mē-ō-STĀ-sĭs
- Biological process that results in stable equilibrium
- Posterior (or Dorsal)
- pŏs-TĒ-rē-or(Original Term)
- Describes the back or direction toward the back of the body.
- Anterior (or Ventral)
- an-TĒR-ē-ŏr (Original Term)
- Describes the front or direction toward the front of the body.
- Deep
- DĒP (Original Term)
- Describes a position farther from the surface of the body.
- Distal
- DIS-tăl (Original Term)
- Describes a position in a limb that is farther from the point of attachment or the trunk of the body.
- Inferior (or Caudal)
- in-FĒR-ē-ŏr (Original Term)
- Describes a position below or lower than another part of the body proper; near or toward the tail.
- Lateral
- LĂT-ĕr- ăl (Original Term)
- Describes the side or direction toward the side of the body.
- Medial
- MĒD-ē-ăl (Original Term)
- Describes the side or direction toward the side of the body.
- Peritoneum
- (per-it-ŏ-NĒ-ŭm)
- Serous membrane surrounding several organs in the abdominopelvic cavity. This reduces friction between the abdominal and pelvic organs and the body wall.
- Proximal
- PROK-sĭ-măl (Original Term)
- Describes a position in a limb that is nearer to the point of attachment or the trunk of the body.
- Superficial
- SOO-pĕr-FISH-ăl (Original Term)
- Describes a position in a limb that is nearer to the point of attachment or the trunk of the body.
- Superior (or Cranial)
- soo-PĒ-rē-or(Original Term)
- Describes a position above or higher than another part of the body proper.
Activity Source: Medical Language with the Context of Anatomy and Physiology Directional Terms from Medical Terminology by Grimm et al., licensed under CC BY 4.0./Re-recording of some H5P audio by Tania Deane and David McCuaig and text version added.
Regions and Quadrants of the Body
Use the anatomic reference system to identify the regions and quadrants of the body pictured below:
Regions and Quadrants of the Body (Text Version)
- Umbilical
- Epigastric
- Left Hypochondriac
- Right Lumbar
- Right Lower Quadrant
- Right Hypochondriac
- Right Iliac
- Left Lower Quadrant
- Left Lumbar
- Right Upper Quadrant
- Left Upper Quadrant
- Hypogastric
- Left Iliac
- Diaphragm
Regions and Quadrants of the Body Diagram (Text version)
This diagram activity shows two views of the abdominopelvic region. Image A shows the abdominopelvic region divided in nine sections with nine boxes. Image B shows the abdominopelvic region divided in four sections known as quadrants with a line dividing the four sections for each quadrant. For image A at the top are three white boxes identified working from right to left labeled as _______[Blank 1], followed by ______[Blank 2], and ________[Blank 3] region. The middle three boxes working from right to left identified as _______[Blank 4], followed by the _______[Blank 5], and ________[Blank 6] region. The three lower boxes working from right to left is the_______[Blank 7], followed by ________[Blank 8], and _________[Blank 9] region. Image B shows two upper white boxes and are from right to left is the _________[Blank 10] followed by the _________[Blank 11]. The two lower boxes from right to left is the _________[Blank 12] followed by _______[Blank 13].
Check your answers: [3]
Activity source: Medical language with the Context of Anatomy and Physiology Dorsal by Tiffany Hunt, illustration from Anatomy and Physiology (OpenStax) licensed under CC BY 4.0./Text version added.
Test Your Knowledge
Test your knowledge by answering the questions below:
Test Your Knowledge (Text Version)
- The smallest unit of any of these pure substances (elements) is a(n) _________ [Blank 1].
- Cell
- Atom
- Organ
- Describes a position closer to the surface of the body.
- Superficial
- Anterior
- Superior
- The plane that divides the body or organ horizontally into upper and lower portions is called the ________ [Blank 2].
- Sagittal Plane
- Transverse Plane
- Frontal Place
- The cavity that includes the cranial cavity and spinal cavity is called the _________ [Blank 3].
- Posterior cavity
- Anterior cavity
- Ventral Cavity
- The name of the layer of the membrane that covers the organs is the ________ [Blank 4].
- Serous layer
- Visceral layer
- Parietal layer
Check your answers: [4]
Activity source: Medical language with the Context of Anatomy and Physiology Reinforcement Activity by Tiffany Hunt, licensed under CC BY 4.0./Text version added.
Attribution
Except where otherwise noted, this book is adapted from Medical Terminology by Grimm et al. (2022), Nicolet College, CC BY 4.0 International. / A derivative of Building a Medical Terminology Foundation by Carter & Rutherford (2020), and Anatomy and Physiology by Betts, et al., CC BY 4.0, which can be accessed for free at OpenStax Anatomy and Physiology.
-
↵
Check your answers: Body Planes Diagram
This illustration activity shows the human body standing upright in the anatomical position. Three anatomical planes are illustrated with transparent lines identifying the location of the three planes: the sagittal plane which divides the left and right side of the body, the frontal plane dividing front and back portions of the body, and the transverse plane dividing top and bottom portion of the body. -
↵
Check your answers: Body Cavities Diagram (Text Version)
This diagram activity shows two views of the human head and torso. The right image shows the lateral view, and the left image shows an anterior view of the human head and torso. The image is highlighting the several cavities or hollowed out spaces where organs and structures are positioned. The lateral view show four cavities: the head cavity known as the cranial, the upper back cavity known as the dorsal, the lower back area known as the vertebral, and the chest cavity known as the thoracic cavity. Adjoining lines for both views identify the diaphragm which is a muscular partition dividing the lungs from the location below it known as the abdominal cavity and followed by the lower pelvic cavity. The anterior view identifies the cranial, vertebral, ventral, abdominopelvic cavities, and sections. -
↵
Check your answers: Regions and Quadrants of the Body Diagram (Text Version)
This diagram activity shows two views of the abdominopelvic region. Image A shows the abdominopelvic region divided in nine sections with nine boxes. Image B shows the abdominopelvic region divided in four sections known as quadrants with a line dividing the four sections for each quadrant. For image A at the top are three white boxes identified working from right to left labeled as right hypochondriac, followed by epigastric, and left hypochondriac region. The middle three boxes working from right to left identified as right lumbar, followed by the umbilical, and left lumbar region. The three lower boxes working from right to left is the right iliac, followed by hypogastric, and left iliac region. Image B show two upper white boxes and are from right to left is the right upper quadrant followed by the left upper quadrant. The two lower boxes from right to left is the right lower quadrant followed by left lower quadrant. - 1. Atom, 2. Superficial, 3. Transverse plane, 4. Posterior cavity, 5. Visceral layer ↵


147 Juno and the Paycock: ACT II
Sean O'Casey
ACT II
The same, but the furniture is more plentiful, and of a vulgar nature. A glaringly upholstered armchair and lounge; cheap pictures and photos everywhere. Every available spot is ornamented with huge vases filled with artificial flowers. Crossed festoons of colored paper chains stretch from end to end of ceiling. On the table is an old attaché case. It is about six in the evening, and two days after the First Act. Boyle, in his shirt-sleeves, is voluptuously stretched on the sofa; he is smoking a clay pipe. He is half asleep. A lamp is lighting on the table. After a few moments’ pause the voice of Joxer is heard singing softly outside at the door –”Me pipe I’ll smoke as I dhrive me moke– are you there, Mor…ee…ar…i…teee!”[1]
Boyle: (leaping up, takes a pen in his hand and busies himself with papers). Come along, Joxer, me son, come along.
 Are you be yourself?
Boyle: Come on, come on; that doesn’t matther; I’m masther now, an’ I’m goin’ to remain masther.
[Joxer comes in.]
Joxer: How d’ye feel now, as a man of money?
Boyle: (solemnly). It’s a responsibility, Joxer, a great responsibility.
Joxer: I suppose ‘tis now, though you wouldn’t think it.
Boyle: Joxer, han’ me over that attackey case on the table there. (Joxer hands the case.)
Joxer: Well, I won’t disturb you; I’ll dhrop in when…
Boyle: It’s all right, Joxer, this is the last one to be signed to-day. Now, Joxer, you want to see me; I’m at your service — what can I do for you, me man?
Joxer: I’ve just dhropped in with the £3:5s.that Mrs. Madigan riz on the blankets an’ table for you, an’ she says you’re to be in no hurry payin’ it back.
Boyle: She won’t be long without it; I expect the first cheque for a couple o’ hundhred any day. There’s the five bob[2] for yourself — go on, take it, man; it’ll not be the last you’ll get from the Captain. Now an’ agen we have our differ, but we’re there together all the time.
Joxer: Me for you, an’ you for me, like the two Musketeers.
Boyle: Father Farrell stopped me to-day an’ tole me how glad he was I fell in for the money.
Joxer: He’ll be stoppin’ you ofen enough now; I suppose it was ‘Mr.’ Boyle with him?
Boyle: He shuk me be the han’…
Joxer: I met with Napper Tandy, an’ he shuk me be the han’![3]
Boyle: You’re seldom asthray, Joxer, but you’re wrong shipped this time. What you’re sayin’ of Father Farrell is very near to blasfeemey. I don’t like any one to talk disrespectful of Father Farrell.
Joxer: You’re takin’ me up wrong, Captain; I wouldn’t let a word be said agen Father Farrell — the heart o’ the rowl,[4] that’s what he is; I always said he was a darlin’ man, a daarlin’ man.
Boyle: Comin’ up the stairs who did I meet but that bummer, Nugent. “I seen you talkin’ to Father Farrell,” says he, with a grin on him. “He’ll be folleyin’ you,” says he, “like a Guardian Angel from this out” — all the time the oul’ grin on him, Joxer.
Joxer: I never seen him yet but he had that oul’ grin on him!
Boyle: “Mr. Nugent,” says I, “Father Farrell is a man o’ the people, an’, as far as I know the History o’ me country, the priests was always in the van of the fight for Irelan’s freedom.”
Joxer: (fervently) Who was it led the van, Soggart Aroon? Since the fight first began, Soggart Aroon?[5]
Boyle: “Who are you tellin’?” says he. “Didn’t they let down the Fenians, an’ didn’t they do in Parnell? An’ now — ” “You ought to be ashamed o’ yourself,” says I, interruptin’, him, “not to know the History o’ your country.” An’ I left him gawkin’ where he was.
Joxer: Where ignorance ‘s bliss ’tis folly to be wise; I wondher did he ever read the Story o’ Irelan’.[6]
Boyle: Be J.L. Sullivan? Don’t you know he didn’t.
Joxer: Ah, it’s a darlin’ buk, a daarlin’ buk!
Boyle: You’d betther be goin’, now, Joxer; his Majesty, Bentham, ‘ll be here any minute, now.
Joxer: Be the way things is lookin’, it’ll be a match between him an’ Mary. She’s thrun over Jerry altogether. Well, I hope it will, for he’s a darlin’ man.
Boyle: I’m glad you think so — I don’t. (Irritably) What’s darlin’ about him?
Joxer: (nonplussed) I only seen him twiced; if you want to know me, come an’ live with me.
Boyle: He’s too dignified for me — to hear him talk you’d think he knew as much as a Boney’s Oraculum.[footnote]Napoleon’s Oraculum was a popular book in the 19th and early 20th centuries. See British Museum Catalogue v., 168, column 624, the Oraculum (1822) is described: “The book of fate, formerly in the possession of Napoleon…and now first rendered into English, from a German translation of an ancient Egyptian manuscript….” Described in The National Union Catalogue (V, 405, 173): “”Napoleon’s Oraculum and dream book (1884): containing the great oracle of human destiny. Also the true meaning of almost any kind of dreams….”[/footnote] He’s given up his job as teacher, an’ is goin’ to become a solicitor in Dublin — he’s been studyin’ law. I suppose he thinks I’ll set him up, but he’s wrong shipped. An’ th’ other fella — Jerry’s as bad. The two o’ them ud give you a pain in your face, listenin’ to them; Jerry believin’ in nothin’, an’ Bentham believin’ in everythin’. One that says all is God an’ no man; an’ th’ other says all is man an’ no God!
Joxer: Well, I’ll be off now.
Boyle: Don’t forget to dhrop down afther awhile; we’ll have a quiet jar, an’ a song or two.
Joxer: Never fear.
Boyle: An’ tell Mrs. Madigan that I hope we’ll have the pleasure of her organization at our little enthertainment.
Joxer: Righto; we’ll come down together.[He goes out.
[Johnny comes from room on left, and sits down moodily at the fire. Boyle looks at him for a few moments, and shakes his head. He fills his pipe.]
Voice of Juno at the door: Open the door, Jack; this thing has me nearly kilt with the weight.
[Boyle opens the door. Juno enters carrying the box of a gramophone,followed by Mary carrying the horn and some parcels. Juno leaves the box on the table and flops into a chair.]
Juno: Carryin’ that from Henry Street was no joke.
Boyle: U-u-ugh, that’s a grand-lookin’ insthrument — how much was it?
Juno: Pound down, an’ five to be paid at two shillin’s a week.
Boyle: That’s reasonable enough.
Juno: I’m afraid we’re runnin’ into too much debt; first the furniture, an’ now this.
Boyle: The whole lot won’t be much out of £2000.
Mary: I don’t know what you wanted a gramophone for — I know Charlie hates them; he says they’re destructive of real music.
Boyle: Desthructive of music — that fella ud give you a pain in your face. All a gramophone wants is to be properly played; its thrue wondher is only felt when everythin’s quiet — what a gramophone wants is dead silence!
Mary: But, father, Jerry says the same; afther all, you can only appreciate music when your ear is properly trained.
 Properly thrained! I suppose you couldn’t appreciate football unless your fut was properly thrained.
Mrs. Boyle: (to Mary). Go on in ower that an’ dress, or Charlie’ll be in on you, an’ tea nor nothin’ll be ready.
[Mary goes into the room left.]
Mrs. Boyle: (arranging table for tea). You didn’t look at our new gramophone, Johnny?
Johnny: ‘Tisn’t gramophones I’m thinking of.
Mrs. Boyle: An’ what is it you’re thinkin’ of, allanna?[7]
Johnny: Nothin’, nothin’, nothin’.
Mrs. Boyle: Sure, you must be thinkin’ of somethin’; it’s yourself that has yourself the way y’are; sleepin’ wan night in me sisther’s, an’ the nex’ in your father’s brother’s — you’ll get no rest goin’ on that way.
Johnny: I can rest nowhere, nowhere, nowhere.
Mrs. Boyle: Sure, you’re not thryin’ to rest anywhere.
Johnny: Let me alone, let me alone, let me alone, for God’s sake.
[A knock at street door]
Mrs. Boyle: (in a flutter). Here he is; here’s Mr. Bentham!
Boyle: Well, there’s room for him; it’s a pity there’s not a brass band to play him in.
Mrs. Boyle: We’ll han’ the tea round, an’ not be clusthered round the table, as if we never seen nothin’. [Steps are heard approaching, and Juno opening the door, allows Bentham to enter.]
Juno: Give your hat an’ stick to Jack, there — sit down, Mr. Bentham — no, not there — in th’ easy chair be the fire — there, that’s betther. Mary’ll be out to you in a minute.
Boyle: (solemnly). I seen be the paper this mornin’ that Consols[8] was down half per cent. That’s serious, min’ you, an’ shows the whole counthry’s in a state o’ chassis.
Mrs. Boyle: What’s Consols, Jack?
Boyle: Consols? Oh, Consols is — oh, there’s no use tellin’ women what Consols is — th’ wouldn’t undherstand.
Bentham: It’s just as you were saying, Mr. Boyle…
[Mary enters, charmingly dressed.]
Bentham: Oh, good evening, Mary; how pretty you’re looking!
Mary: (archly). Am I?
Boyle: We were just talkin’ when you kem in, Mary; I was tellin’ Mr. Bentham that the whole counthry’s in a state o’ chassis.
Mary: (to Bentham). Would you prefer the green or the blue ribbon round me hair, Charlie?
Mrs. Boyle: Mary, your father’s speakin’.
Boyle: (rapidly). I was jus’ tellin’ Mr. Bentham that the whole counthry’s in a state o’ chassis.
Mary: I’m sure you’re frettin’, da, whether it is or no.
Mrs. Boyle: With all our churches an’ religions, the worl’s not a bit the betther.
Boyle: (with a commanding gesture). Tay!
[Mary and Mrs. Boyle dispense the tea.]
Mrs. Boyle: An’ Irelan’s takin’ a leaf out o’ the worl’s buk; when we got the makin’ of our own laws I thought we’d never stop to look behind us, but instead of that we never stopped to look before us! If the people ud folley up their religion betther there’d be a betther chance for us — what do you think, Mr. Bentham?
Bentham: I’m afraid I can’t venture to express an opinion on that point, Mrs. Boyle; dogma has no attraction for me.
Mrs. Boyle: I forgot you didn’t hold with us: what’s this you said you were?
Bentham: A Theosophist,[9] Mrs. Boyle.
Mrs. Boyle: An’ what in the name o’ God’s a Theosophist?
Boyle: A Theosophist, Juno, ‘s a — tell her, Mr. Bentham, tell her.
Bentham: It’s hard to explain in a few words : Theosophy’s founded on The Vedas, the religious books of the East. Its central theme is the existence of an all-pervading Spirit — the Life-Breath. Nothing really exists but this one Universal Life-Breath. And whatever even seems to exist separately from this Life-Breath, doesn’t really exist at all. It is all vital force in man, in all animals, and in all vegetation. This Life-Breath is called the Prawna.
Mrs. Boyle: The Prawna! What a comical name!
Boyle: Prawna; yis, the Prawna. (Blowing gently through his lips) That’s the Prawna!
Mrs. Boyle: Whist, whist, Jack.
Bentham: The happiness of man depends upon his sympathy with this Spirit. Men who have reached a high state of excellence are called Yogi. Some men become Yogi in a short time, it may take others millions of years.
Boyle: Yogi! I seen hundhreds of them in the streets o’ San Francisco.
Bentham: It is said by these Yogi that if we practise certain mental exercises we would have powers denied to others — for instance, the faculty of seeing things that happen miles and miles away.
Mrs. Boyle: I wouldn’t care to meddle with that sort o’ belief; it’s a very curious religion, altogether.
Boyle: What’s curious about it? Isn’t all religions curious? — if they weren’t, you wouldn’t get any one to believe them. But religions is passin’ away — they’ve had their day like everything else. Take the real Dublin people, f’rinstance: they know more about Charlie Chaplin[10] an’ Tommy Mix[11] than they do about SS. Peter an’ Paul!
Mrs. Boyle: You don’t believe in ghosts, Mr. Bentham?
Mary: Don’t you know he doesn’t, mother?
Bentham: I don’t know that, Mary. Scientists are beginning to think that what we call ghosts are sometimes seen by person of a certain nature. They say that sensational actions, such as the killing of a person, demand great energy, and that energy lingers in the place where the action occurred. People may live in the place and see nothing, when someone may come along whose personality has some peculiar connection with the energy of the place, and, in a flash, the person sees the whole affair.
Johnny: (rising swiftly, pale and affected). What sort o’ talk is this to be goin’ on with? Is there nothin’ betther to be talkin’ about but the killin’ o’ people? My God, isn’t it bad enough for these things to happen without talkin’ about them! [He hurriedly goes into the room on left.
Bentham: Oh, I’m very sorry, Mrs. Boyle; I never thought.. .
Mrs. Boyle: (apologetically). Never mind, Mr. Bentham, he’s very touchy.
[A frightened scream is heard from Johnny inside.]
Mrs. Boyle: Mother of God, what’s that? [He rushes out again, his face pale, his lips twitching, his limbs trembling.]
 Great God, have mercy on me! Blessed Mother o’ God shelter me, shelter your son!
Mrs. Boyle: (catching him in her arms). What’s wrong with you? What ails you? Sit down, sit down, here, on the bed — there now — there now.
Mary: Johnny, Johnny, what ails you?
Johnny: I seen him, I seen him — kneelin’ in front o’ the statue — merciful Jesus, have pity on me!
Mrs.
[Boyle gets the whisky.]

Johnny: I seen him — I seen Robbie Tancred kneelin’ down before the statue — an’ the red light shinin’ on him — an’ when I went in — he turned an’ looked at me — an’ I seen the woun’s bleedin’ in his breast — Oh, why did he look at me like that? — it wasn’t my fault that he was done in — Mother o’ God, keep him away from me!
Mrs. Boyle: There, there, child, you’ve imagined it all. There was nothin’ there at all — it was the red light you seen, an’ the talk we had put all the rest into your head. Here, dhrink, more o’ this — it’ll do you good — An’, now, stretch yourself down on the bed for a little. (To Boyle) Go in, Jack, an’ show him it was only in his own head it was.
Boyle: (making no move). E-e-e-eh; it’s all nonsense; it was only a shadda he saw.
Mary: Mother o’ God, he made me heart lep!
Bentham: It was simply due to an overwrought imagination — we all get that way at times.
Mrs. Boyle: There, dear, lie down in the bed, an’ I’ll put the quilt across you — e-e-e-eh, that’s it — you’ll be as right as the mail in a few minutes.
Johnny: Mother, go into the room an’ see if the light’s lightin’ before the statue.
Mrs. Boyle: (to Boyle). Jack, run in an’ see if the light’s lightin’ before the statue.
Boyle: (to Mary). Mary, slip in an’ see if the light’s lightin’ before the statue. [Mary hesitates to go in.]
Bentham: It’s all right; Mary, I’ll go. [He goes into the room, remains for a few moments, and returns.
Bentham: Everything’s just as it was — the light burning bravely before the statue. Boyle: Of course; I knew it was all nonsense.
[A knock at the door.]
Boyle: (going to open the door). E-e-e-e-eh. [He opens it, and Joxer, followed by Mrs. Madigan, enters. Mrs.  She is a woman who, in manner at least, can mourn with them that mourn, and rejoice with them that do rejoice. When she is feeling comfortable, she is inclined to be reminiscent; when others say anything, or following a statement made by herself, she has a habit of putting her head a little to one side, and nodding it rapidly several times in succession, like a bird pecking at a hard berry. Indeed, she has a good deal of the bird in her, but the bird instinct is by no means a melodious one. She is ignorant, vulgar and forward, but her heart is generous withal. For instance, she would help the neighbor’s sick child; she would probably kill the child, but her intention would be to cure it; she would be more at home helping a drayman to lift a fallen horse.   Boyle receives them effusively.]
Boyle: Come on in, Mrs. Madigan; come on in; I was afraid you weren’t comin’ – (Slyly) There’s some people able to dhress, ay, Joxer?
Joxer: Fair as the blossoms that bloom in the May, an’ sweet as the scent of the new-mown hay. — Ah, well she may wear them.
Mrs. Madigan: (Looking at Mary). I know some as are as sweet as the blossoms that bloom in the May — oh, no names, no pack dhrill!
Boyle: An’ now I’ll inthroduce the pair o’ yous to Mary’s intended: Mr. Bentham, this is Mrs. Madigan, an oul’ back-parlour neighbour, that, if she could help it at all, ud never see a body shuk!
Bentham: (rising, and tentatively shaking the hand of Mrs. Madigan). I’m sure, it’s a great pleasure to know you, Mrs. Madigan.
Mrs. Madigan: An’ I’m goin’ to tell you, Mr. Bentham, you’re goin’ to get as nice a bit o’ skirt in Mary, there, as ever you seen in your puff. Not like some of the dhressed-up dolls that’s knockin’ about lookin’ for men when it’s a skelpin’ they want. I remember, as well as I remember yestherday, the day she was born — of a Tuesday, the 25th o’ June, in the year 1901, at thirty-three minutes past wan in the day be Foley’s clock, the pub at the corner o’ the street. A cowld day it was too, for the season o’ the year, an’ I remember sayin’ to Joxer, there, who I met comin’ up th’ stairs, that the new arrival in Boyle’s ud grow up a hardy chiselur if it lived, an’ that she’d be somethin’ one o’ these days that nobody suspected, an’ so signs on it, here she is to-day, goin’ to be married to a young man lookin’ as if he’d be fit to commensurate in any position in life it ud please God to call him!
Boyle: (effusively). Sit down, Mrs. Madigan, sit down, me oul’ sport. This is Joxer Daly, Past Chief Ranger of the Dear Little Shamrock Branch of the Irish National Foresters, an oul’ front-top neighbour, that never despaired, even in the darkest days of Ireland’s sorra.
Joxer: Nil desperandum,[12] Captain, nil desperandum.
Boyle: Sit down, Joxer, sit down. The two of us was ofen in a tight corner.
Mrs. Boyle: Ay, in Foley’s snug!
Joxer: An’ we kem out of it flyin’, we kem out of it flyin’, Captain.
Boyle: An’ now for a dhrink — I know yous won’t refuse an oul’ friend.
Mrs. Madigan: Is Johnny not well, Mrs…
Mrs. Boyle: (warningly). S-s-s-sh.
Mrs. Madigan: Oh, the poor darlin’.
Boyle: Well, Mrs. Madigan, is it tea or what?
Mrs. Madigan: Well, speakin’ for meself, I jus’ had me tea a minute ago, an’ I’m afraid to dhrink any more — I’m never the same when I dhrink too much tay. Thanks, all the same, Mr. Boyle.
Boyle: Well, what about a bottle o’ stout or a dhrop o’ whisky?
Mrs. Madigan: A bottle o’ stout ud be a little too heavy for me stummock afther me tay — A-a-a-ah, I’ll thry the ball o’ malt.
[Boyle prepares the whisky.]
Mrs. Madigan: There’s nothin’ like a ball o’ malt occasional like — too much of it isn’t good. (To Boyle, who is adding water) Ah, God, Johnny, don’t put too much wather on it! (She drinks). I suppose yous’ll be lavin’ this place.
Boyle: I’m looking for a place near the sea; I’d like the place that you might say was me cradle, to be me grave as well. The sea is always callin’ me.
Joxer: She is callin’, callin’, callin’, in the win’ an’ on the sea.
Boyle: Another dhrop o’ whisky, Mrs. Madigan?
Mrs. Madigan: Well, now, it ud be hard to refuse seein’ the suspicious times that’s in it.
Boyle: (with a commanding gesture). Song! — Juno — Mary — Home to Our Mountains![13]
Mrs. Madigan: (enthusiastically). Hear, hear!
Joxer: Oh, tha’s a darlin’ song, a daarlin’ song!
Mary: (bashfully). Ah no, da; I’m not in a singin’ humour.
Mrs. Madigan: Gawn with you, child, an’ you only goin’ to be married; I remember as well as I remember yestherday, — it was on a lovely August evenin’, exactly, accordin’ to date, fifteen years ago, come the Tuesday folleyin’ the nex’ that’s comin’ on, when me own man — the Lord be good to him — an’ me was sittin’ shy together in a doty little nook on a counthry road, adjacent to The Stiles. ‘That’ll scratch your lovely, little white neck,’ says he, ketchin’ hould of a danglin’ bramble branch, holdin’ clusters of the lovliest flowers you ever seen, an’ breakin’ it off, so that his arm fell, accidental like, roun’ me waist, an’ as I felt it tightenin’, an’ tightenin’, an’ tightenin’, I thought me buzzom was every minute goin’ to burst out into a roystherin’ song about ‘The little green leaves that were shakin’ on the threes, The gallivantin’ buttherflies, an’ buzzin’ o’ the bees! ‘
Boyle: Ordher for the song!
Juno: Come on, Mary — we’ll do our best. [Juno and Mary stand up, and choosing a suitable position, sing simply ‘Home to Our Mountains’. [They bow to the company and return to their places.
Boyle: (emotionally, at the end of song). Lull — me — to — rest!
Joxer: (clapping his hands). Bravo, bravo! Darlin’ girulls, darlin’ girulls!
Mrs. Madigan: Juno, I never seen you in betther form.
Bentham: Very nicely rendered indeed.
Mrs. Madigan: A noble call, a noble call!
Mrs. Boyle: What about yourself, Mrs. Madigan?
[After some coaxing, Mrs. Madigan rises, and in a quavering voice, sings the following verse]:
Mrs. Madigan:
If I were a blackbird I’d whistle and sing;
I’d follow the ship that my thrue love was in;
An’ on the top riggin’, I’d there build me nest,
An’ at night I would sleep on me Willie’s white breast![14] [Becoming husky, amid applause, she sits down.]
Mrs. Madigan: Ah, me voice is too husky now, Juno; though I remember the time when Maisie Madigan could sing like a nightingale at matin’ time. I remember as well as I remember yestherday, at a party given to celebrate the comin’ of the first chiselur to Annie an’ Benny Jimeson — who was the barber, yous may remember, in Henrietta Street, that, afther Easter Week, hung out a green, white an’ orange pole an’ then, when the Tans[15] started their Jazz dancin’, whipped it in agen, an’ stuck out a red, white an’ blue wan instead, givin’ as an excuse that a barber’s pole was strictly non-political — singin’ ‘An’ You’ll Remember Me’ with the top notes quiverin’ in a dead hush of pethrified attention, folleyed be a clappin’ o’ han’s that shuk the tumblers on the table, an’ capped by Jimeson, the barber, sayin’ that it was the best rendherin’ of ‘You’ll Remember Me’ he ever heard in his natural!
Boyle: (peremptorily). Ordher for Joxer’s song!

Boyle: Joxer’s song, Joxer’s song — give us wan of your shut-eyed wans.
[Joxer settles himself in his chair; takes a drink; clears his throat; solemnly closes his eyes, and begins to sing in a very querulous voice]:
Joxer:
She is far from the lan’ where her young hero sleeps,
An’ lovers around her are sighing,
An’ lovers around her are sighin’ — sighin’ — sighin’…[16] [A pause].
Boyle: (imitating Joxer). And lovers around her are sighing! What’s the use of thryin’ to sing the song if you don’t know it?
Mary: Thry another one, Mr. Daly — maybe you’d be more fortunate.
Mrs. Madigan: Gawn, Joxer; thry another wan.
Joxer: (starting again).
I have heard the mavis singin’ his love song to the morn[17];
I have seen the dew-dhrop clingin’ to the rose jus’ newly born;
but — but – (frantically) To the rose jus’ newly born — newly born — born.
Johnny: Mother, put on the gramophone, for God’s sake, an’ stop Joxer’s bawlin’.
Boyle: (commandingly). Gramophone! — I hate to see fellas thryin’ to do what they’re not able to do. [Boyle arranges the gramophone, and is about to start it, when voices are heard of persons descending the stairs.]
Mrs. Boyle: (warningly). Whisht, Jack, don’t put it on, don’t put it on yet; this must be poor Mrs. Tancred comin’ down to go to the hospital — I forgot all about them bringin’ the body to the church to-night. Open the door, Mary, an’ give them a bit o’ light.
[Mary opens the door, and Mrs. Tancred—very old woman, obviously shaken by the death of her son — appears, accompanied by several neighbours. The first few phrases are spoken before they appear.]
First Neighbour: It’s a sad journey we’re goin’ on, but God’s good, an’ the Republicans won’t be always down.
Mrs. Tancred: Ah, what good is that to me now? Whether they’re up or down — it won’t bring me darlin’ boy from the grave.
Mrs. Boyle: Come in an’ have a hot cup o’ tay, Mrs. Tancred, before you go.
Mrs. Tancred: Ah, I can take nothin’ now, Mrs. Boyle — I won’t be long afther him.
 Ah, what’s the pains I suffered bringin’ him into the world to carry him to his cradle, to the pains I’m sufferin’ now, carryin’ him out o’ the world to bring him to his grave!
Mary: It would be better for you not to go at all, Mrs. Tancred, but to stay at home beside the fire with some o’ the neighbours.
Mrs. Tancred: I seen the first of him, an’ I’ll see the last of him.
Mrs. Boyle: You’d want a shawl, Mrs. Tancred; it’s a cowld night, an’ the win’s blowin’ sharp.
Mrs. Madigan: (rushing out).
Mrs. Tancred: Me home is gone now; he was me only child, an’ to think that he was lyin’ for a whole night stretched out on the side of a lonely counthry lane, with his head, his darlin’ head, that I ofen kissed an’ fondled, half hidden in the wather of a runnin’ brook. An’ I’m told he was the leadher of the ambush where me nex’ door neighbour, Mrs. Mannin’, lost her Free State soldier son. An’ now here’s the two of us oul’ women, standin’ one on each side of a scales o’ sorra, balanced be the bodies of our two dead darlin’ sons. (Mrs. Madigan returns, and wraps a shawl around her.) God bless you, Mrs. Madigan — (She moves slowly towards the door) Mother o’ God, Mother o’ God, have pity on the pair of us! — O Blessed Virgin, where were you when me darlin’ son was riddled with bullets, when me darlin’ son was riddled with bullets! — Sacred Heart of the Crucified Jesus, take away our hearts o’ stone — an’ give us hearts o’ flesh! — Take away this murdherin’ hate — an’ give us Thine own eternal love! [They pass out of the room].
Mrs. Boyle: (explanatorily to Bentham). That was Mrs. Tancred of the two-pair back; her son was found, e’er yestherday, lyin’ out beyant Finglas riddled with bullets. A Die-hard he was, be all accounts. He was a nice quiet boy, but lattherly he went to hell, with his Republic first, an’ his Republic last an’ Republic over all. He often took tea with us here, in the oul’ days, an’ Johnny, there, an’ him used to be always together.
Johnny: Am I always to be havin’ to tell you that he was no friend o’ mine? I never cared for him, an’ he could never stick me. It’s not because he was Commandant of the Battalion that I was Quarther-Masther of, that we were friends.
Mrs. Boyle: He’s gone now — the Lord be good to him! God help his poor oul’ creature of a mother, for no matther whose friend or enemy he was, he was her poor son.
Bentham: The whole thing is terrible, Mrs. Boyle; but the only way to deal with a mad dog is to destroy him.
Mrs. Boyle: An’ to think of me forgettin’ about him bein’ brought to the church to-night, an’ we singin’ an’ all, but it was well we hadn’t the gramophone goin’, anyhow.
Boyle: Even if we had aself. We’ve nothin’ to do with these things, one way or t’other. That’s the Government’s business, an’ let them do what we’re payin’ them for doin’.
Mrs. Boyle: I’d like to know how a body’s not to mind these things; look at the way they’re afther leavin’ the people in this very house. Hasn’t the whole house, nearly, been massacreed? There’s young Dougherty’s husband with his leg off; Mrs. Travers that had her son blew up be a mine in Inchegeela, in Co. Cork; Mrs. Mannin’ that lost wan of her sons in an ambush a few weeks ago, an’ now, poor Mrs. Tancred’s only child gone west with his body made a collandher of. Sure, if it’s not our business, I don’t know whose business it is.
 If they want a wake, well, let them have a wake. When I was a sailor, I was always resigned to meet with a wathery grave; an’ if they want to be soldiers, well, there’s no use o’ them squealin’ when they meet a soldier’s fate.
Joxer: Let me like a soldier fall — me breast expandin’ to th’ ball!
Mrs. Boyle: In wan way, she deserves all she got; for lately, she let th’ Die-hards make an open house of th’ place; an’ for th’ last couple of months, either when th’ sun was risin’ or when th’ sun was settin’, you had C.I.D.[18] men burstin’ into your room, assin’ you where were you born, where were you christened, where were you married, an’ where would you be buried!
Johnny: For God’s sake, let us have no more o’ this talk.
Mrs. Madigan: What about Mr. Boyle’s song before we start th’ gramophone?
Mary: [getting her hat, and putting it on]. Mother, Charlie and I are goin’ out for a little sthroll.
Mrs. Boyle: All right, darlin’.
Bentham: [Going out with Mary]. We won’t be long away, Mrs. Boyle.
Mrs. Madigan: Gwan, Captain, gwan.
Boyle: E-e-e-e-eh, I’d want to have a few more jars in me, before I’d be in fettle for singin’.
Joxer: Give us that poem you writ t’other day. (To the rest) Aw, it’s a darlin’ poem, a daarlin’ poem.
Mrs. Boyle: God bless us, is he startin’ to write poetry!
Boyle: (rising to his feet). E-e-e-e-eh. [He recites in an emotional, consequential manner the following verses]:
Shawn an’ I were friends, sir, to me he was all in all.
His work was very heavy and his wages were very small.
None betther on th’ beach as Docker, I’ll go bail,
‘Tis now I’m feelin’ lonely, for to-day he lies in jail.
He was not what some call pious — seldom at church or prayer;
For the greatest scoundrels I know, sir, goes every Sunday there.
Fond of his pint — well, rather, but hated the Boss by creed
But never refused a copper to comfort a pal in need. E-e-e-e-eh. [He sits down.]
Mrs. Madigan: Grand, grand; you should folly that up, you should folly that up.
Joxer: It’s a daarlin’ poem!
Boyle: (delightedly). E-e-e-e-eh.
Johnny: Are yous goin’ to put on th’ gramophone to-night, or are yous not?
Mrs. Boyle: Gwan, Jack, put on a record.
Mrs. Madigan: Gwan, Captain, gwan.
Boyle: Well, yous’ll want to keep a dead silence.
[He sets a record, starts the machine, and it begins to play “If you’re Irish, come into the Parlour”. As the tune is in full blare the door is suddenly opened by a brisk, little bald-headed man, dressed circumspectly in a black suit; He glares fiercely at all in the room; he is ‘Needle Nugent’, a tailor. He carries his hat in his hand.]
Nugent: (loudly, above the noise of the gramophone).
Are yous goin’ to have that thing bawlin’ an’ the funeral of Mrs. Tancred’s son passin’ the house? Have none of yous any respect for the Irish people’s National regard for the dead? [Boyle stops the gramophone.
Mrs. Boyle: Maybe, Needle Nugent, it’s nearly time we had a little less respect for the dead, an’ a little more regard for the livin’.
Mrs. Madigan: We don’t want you, Mr. Nugent, to teach us what we learned at our mother’s knee. Persons are heard running down to the street, some saying, “Here it is, here it is.” Nugent withdraws, and the rest, except Johnny, go to the window looking into the street, and look out. Sounds of a crowd coming nearer are heard; portion are singing]:
Crowd:
To Jesus’ Heart all burning
With fervent love for men,
My heart with fondest yearning
Shall raise its joyful strain.
While ages course along,
Blest be with loudest song
The Sacred Heart of Jesus
By every heart and tongue.
Mrs. Boyle: Here’s the hearse, here’s the hearse!
Boyle: There’s t’oul’ mother walkin’ behin’ the coffin.
Mrs. Madigan: You can hardly see the coffin with the wreaths.
Joxer: Oh, it’s a darlin’ funeral, a daarlin’ funeral!
Mrs. Madigan: W’d have a betther view from the street.
Boyle: Yes — this place ud give you a crick in your neck. [They leave the room, and go down. Johnny sit smoothly by the fire. A young man enters; he looks at Johnny for a moment.]
The Young Man: Quarther-Masther Boyle.
Johnny: (with a start ). The Mobilizer!
The Young Man: You’re not at the funeral?
Johnny: I’m not well.
The Young Man: I’m glad I’ve found you; you were stoppin’ at your aunt’s; I called there but you’d gone. I’ve to give you an ordher to attend a Battalion Staff meetin’ the night afther to-morrow.
Johnny: Where?
The Young Man: I don’t know; you’re to meet me at the Pillar at eight o’clock; then we’re to go to a place I’ll be told of to-night; there we’ll meet a mothor that’ll bring us to the meeting. They think you might be able to know somethin’ about them that gave the bend where Commandment Tancred was shelterin’.
Johnny: I’m not goin’, then. I know nothing about Tancred.
The Young Man: (at the door). You’d betther come for your own sake — remember your oath.
Johnny: (passionately.
I won’t go! Haven’t I done enough for Ireland! I’ve lost me arm, an’ me hip’s desthroyed so that I’ll never be able to walk right agen! Good God, haven’t I done enough for Ireland?
The Young Man: Boyle, no man can do enough for Ireland! [He goes.
[Faintly in the distance the crowd is heard saying]:
Crowd: Hail, Mary, full of grace, the Lord is with Thee; Blessed art Thou amongst women, and blessed, etc.
- This song became popular through the patriotic singer Gerard Crofts in the internment camps set up after the Easter Rebellion of 1916. Moriarity is a member of the D.M.P. (Dublin Metropolitan Police). ↵
- Five shillings. ↵
- A line from the ballad “The Wearing of the Green.” James Napper Tandy (1740-1803) was an Irish patriot. ↵
- A good fellow. ↵
- Saggart Aroon. Gaelic. “Dear priest.” Joxer is probably referring to a variant of a patriotic poem by John Banim (1798-1842), “Soggarth Aroon”. ↵
- Story of Ireland (1867). A popular history by A.M. Sullivan (1830-1874), one of the founders of the Home Rule Party. Boyle confuses the author with Irish-American boxer John L. Sullivan (1858-1918). ↵
- Gaelic. “My baby.” ↵
- Government securities. ↵
- One who aims at the knowledge of God by means of intuition and contemplation. The Theosophical Society was founded in 1875 by Mme Helena Blavatsky. ↵
- Charles Chaplin (1889-1977). London-born Hollywood comic actor. ↵
- Thomas Edwin “Tom” Mix (1880-1940).The first major star of Hollywood westerns. ↵
- Never despair (Latin). ↵
- Aria from Verdi’s Il Trovatore (1853). ↵
- A traditional Irish song about a woman jilted by a sailor. ↵
- Black and Tans. A force of temporary constables recruited in Britain in 1919 to fight the Irish Republican Army. Their nickname referred to the colour of their khaki uniforms. They became infamous for their attacks on civilians. ↵
- Song composed by Irish poet Thomas Moore (1779-1852), best-known for “The Minstrel Boy.” ↵
- A popular love song (ca. 1850), by Charles Jefferys (1805-1867). ↵
- Criminal Investigation Department (CID) in the Irish Free State was an armed, plain-clothed counter-insurgency police unit that operated during the Irish Civil War. ↵
- Irish police force. ↵


29 Woo and Reeves, “Meaningful interaction in web-based learning: A social constructivist interpretation”
Reference
Background
Interaction is an essential ingredient of any learning environment (face-to-face classroom-based, synchronous/asynchronous online education, or blended models) (Woo & Reeves, 2007). As Web-based learning environments have continued to grow over the years maintaining interaction is more challenging than in the traditional face-to-face learning environments. This article takes a look at many different types of interaction that can happen in web-based instruction. Not every interaction will lead to increased learning. The authors of this article define meaningful interaction as having a direct influence on learners’ intellectual growth.
Woo and Reeves hope to improve and/or create design principles to increase the quality of Web-based learning environments by examining online interaction in terms of meaningful learning based on the learning theory known as social constructivism.
Key points
- One of the key components of good pedagogy, regardless of whether technology is involved, is interaction.
- Instructional designers still lack sound theoretical foundations for determining what is good quality or meaningful interaction
- Meaningful interactions are unlikely to occur without the provision of an instructional design model that fosters them.
- Defining online interaction
- Interaction in various forms of learning environments has been defined in a variety of ways.
- The nature of interaction is also dependent upon the context in which interaction occurs, in a face-to-face environment or at a distance.
- Moore’s (1989) classic definition of interaction within distance education is based upon a communication-based framework, defining the sender and receiver of three types of interaction: learner-content, learner-instructor, and learner-learner.
- Northrup (2001) proposed five interaction purposes: to interact with content, to collaborate, to converse, to help monitor and regulate learning (intrapersonal interaction), and to support performance.
- The meaning of meaningful
- Idle chatting, online surfing, or mindlessly clicking Web pages is unlikely to lead to substantive learning even though learners are interacting with other objects.
- Interaction must stimulate the learners’ intellectual curiosity, engage them in productive instructional activities, and directly influence their learning (Hirumi, 2002; Vrasidas & McIsaac, 1999).
- The meaning of meaningful interaction is strongly related to the learning theories underlying the development of particular learning environments.
- Learning is derived from rich conversation with other people who have similar or different perspectives based on their own life experiences (Jonassen, 1999; Jonassen et al., 1995). We call this theory social constructivism.
- Social Constructivist perspective
- Meaningful interaction
- Many educators have come to see the value of social constructivism as a foundation for the design of more effective learning environments.
- In an online learning environment designed on the principles of social constructivism, meaningful interaction should include responding, negotiating internally and socially, arguing against points, adding to evolving ideas, and offering alternative perspectives with one another while solving some real tasks (Jonassen et al., 1995; Lapadat, 2002; Lave & Wenger, 1991,: Vrasidas, 2000; Vygotsky, 1978).
- Authentic Tasks/Activities
- To accomplish an authentic task, students must interact through sharing what they are thinking, relating their ideas to past experiences, collaborating with their peers, actively constructing their own meaning, and incorporating the diverse perspectives of others (Barr & Tagg, 1995).
- Newmann and Wehlage (1993) outlined five standards for authentic activities:
- Meaningful interaction
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- Higher order thinking
- Depth of knowledge
- Connectedness to the world
- Substantive conversation
- Social support for students
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- Reeves, Herrington, and Oliver (2002) identified the following ten main characteristics of authentic activities:
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- Authentic activities have real-world relevance.
- Authentic activities are ill-defined, requiring students to define the tasks and sub-tasks needed to complete the activity.
- Authentic activities comprise complex tasks to be investigated by students over a sustained period of time.
- Authentic activities provide the opportunity for students to examine the task from different perspectives, using a variety of resources.
- Authentic activities provide the opportunity to collaborate.
- Authentic activities provide the opportunity to reflect.
- Authentic activities can be integrated and applied across different subject areas and lead beyond domain-specific outcomes.
- Authentic activities are seamlessly integrated with assessment.
- Authentic activities create polished products valuable in their own right rather than as preparation for something else.
- Authentic activities allow competing solutions and diversity of outcomes.
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Discussion
The main substance of this article is that to improve the learning effects of online interaction we first need to clearly understand the essence of interaction from a social constructivist learning theory. Once this is understood research can be developed and conducted to determine the proper principles of design to gain more effective interaction and activities for Web-based learning environments.
In order for the learning to be significant the interaction must be meaningful. This meaningful interaction will only happen if the instructional design does not foster them. Meaningful interaction should include arguing against points, adding to evolving ideas, and offering alternative perspectives with one another while solving some real/authentic tasks. Students should be sharing what they are thinking, relating their ideas to past experiences, collaborating with their peers, actively constructing their own meaning, and incorporating the diverse perspectives of others.
Discussion questions
- Of the multiple learning theories available, why is it that Web-based learning environments have seemingly gravitated toward a social constructivist mindset?
- Will the best principles of design differ depending on how the course is conducted over time. i.e. courses that are self-paced (MOOCs) versus courses that have weekly or regularly scheduled deadlines like a semester length college course?
- What is more important, the technology used or how the technology is used?
- Focus has been shifted from quantity of interaction to quality of interaction. Do you think that quantity can also be a part of quality?
Additional resources
- Bronack, S., Riedl, R., & Tashner, J. (2006). Learning in the zone: A social constructivist framework for distance education in a 3-dimensional virtual world. Interactive Learning Environments, 14(3), 219–232. https://doi.org/10.1080/10494820600909157.
- Berge, Z. (1999). Interaction in Post-Secondary Web-Based Learning. Educational Technology, 39(1), 5-11. Retrieved from http://www.jstor.org/stable/44429005
- Janette R. Hill, Liyan Song & Richard E. West (2009) Social Learning Theory and Web-Based Learning Environments: A Review of Research and Discussion of Implications, American Journal of Distance Education, 23(2), 88–103. https://doi.org/10.1080/08923640902857713.
References
- Barr, R. B., & Tagg, J. (1995). From teaching to learning: A new paradigm for undergraduate education. Change, 27(6), 12−25. https://doi.org/10.1080/00091383.1995.10544672.
- Hirumi, A. (2002). The design and sequencing of E-learning interactions: A grounded approach. International Journal on E-learning, 1(1), 19−27. https://www.learntechlib.org/primary/p/8390/.
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