1s orbital 2D
The ancient Greeks postulated that matter was made up of minute indivisible units or particles called atoms.
Scientific models of the atom: we shall look at four models of the atom. These are, in chronological order:
Atoms - Models of the Atom
J.J. Thomson’s model of the atom

It was known that metals, and possibly all matter, contained electrons. Thomson discovered the electron and measured its
charge/mass ratio and won the Nobel prize in physics in 1906. It was also known that electrons were negatively charged, but
that matter was usually electrically neutral, so it was inferred that the atom contained an equal number of positive charges.
This is the ‘plum pudding’ model of the atom.
Rutherford’s model of the atom

Rutherford fired a beam of alpha-particles (helium nuclei, quite heavy positively charged particles consisting of 2 neutrons
and 2 protons, He2+) at gold foil and measured how widely the alpha particles were scattered when they bounced off the
atoms in the gold:
Bohr’s model of the atom

  • Bohr extended Rutherford’s model by confining each electron to a specific orbit.
  • Now electrons could not fall inwards but were kept in their orbits (by a then unknown mechanism).
  • Each orbit has a specific energy – the further the orbit is from the nucleus, the more energy its electron has.
  • Each orbit (or the electron in that orbit) is assigned a quantum number, n. The orbit nearest the nucleus is n = 1, and
    has the least energy; n can take any value.
  • Bohr concentrated on the hydrogen atom, which has only one electron, this electron can move from n = 1 to a higher
    orbit, say n = 3, by gaining enough energy. If the energy of the electron in n = 1 is E1, and the energy of the electron in
    n = 3, E3, then to move from n = 1 out to n = 3, the electron must gain energy equal to E3 - E1. The electron can jump
    down from n = 3 to n = 1 by losing energy equal to E3 - E1.
  • An electron is not allowed to be between orbits except when rapidly jumping up or down between the orbits.
  • The main way an electron can gain energy to jump up, is to absorb a quantum of light energy of the exact amount
    needed. These packets of light energy are the particles of light, called photons.
  • When an electron jumps down, it can lose the energy needed to do this by emitting a photon of the exact energy it
    needs to shed.

  • Bohr’s model correctly predicts the energies of these orbits and the energies of the photons absorbed or emitted when
    an electron jumps between orbits.
  • These photons give rise to the absorption and emission spectra of the hydrogen atom.
Schrödinger’s model of the atom

Sometimes electrons behave as particles and sometimes as waves! This is wave-particle duality.
This means that the Bohr model of electrons moving around the atom in definite orbits, though useful, is a simplification –
electrons are more mysterious than that.

Schrödinger treated the electron as a wave and formultaed Schrödinger’s wave equation. The properties of electrons, such as
their position and velocity, are obtained from mathematical solutions to Schrödinger’s equation.

These solutions or orbitals are described by several quantum numbers:

  • The principal quantum number, n, is retained as the energy level.
  • The quantum number L, which is due to the angular momentum of the electron – that is momentum due to the
    asymmetry of the orbital around the nucleus.
Schrodinger's Model - wave-particle duality

Mathematical Plots of H Atom Wavefunctions
View more plots of Schrodinger's model of the hydrogen atom
Dirac's Model of the Atom

Schrodinger's model is not the end of the story. It does not take into account the intrinsic angular momentum of the
electron due to its own 'rotation about its axis' (or the quantum mechanical equivalent) and it does not take into account
relativistic effects. In atoms, the speed of electrons may reach a significant fraction of the speed of light, in which case the
relativistic energy should be used. This led to Dirac's relativistic model of the atom. This relativistic theory predicts
electron spin and spin-orbit coupling. Spin-orbital coupling changes the energy of the electron and is due to interacting
magnetic fields within the atom. The electron is electrically charged, and charges in motion create magnetic fields. The
magnetic field due to the spin of the electron (which is like a tiny bar magnet) interacts with the magnetic field generated
by the electron's orbit around the nucleus.


Quantum electrodynamics (QED) is a theory which deals with the quantisation of the electromagnetic field, rather than
focusing on individual particles in isolation, and this predicts several corrections to the electron energy. These include the
Darwin term - which is due to the apparent instant 'teleporting' of the electron from one location to another as the vacuum
randomly 'swallows' one electron and replaces it with another new electron, resulting in so-called jitter-motion of the
electron as it orbits the nucleus. Additionally, the electron can emit and reabsorb transient or virtual photons as it
appears to momentarily create new particles in apparent violation of energy conservation. However, no violation is
observed, since the electron will re-absorb these particles in the time permitted by the energy-time uncertainty principle.
Mathematical summary - a pdf summarising Schrodinger's theory of the hydrogen
atom and discussing relativistic and QED corrections.
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