Radioactive decay

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Alpha decay is one example type of radioactive decay, in which an atomic nucleus emits an alpha particle, and thereby transforms (or "decays") into an atom with a mass number decreased by 4 and atomic number decreased by 2. Many other types of decays are possible.


Radioactive decay is a stochastic (i.e. random) process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay.[1] However, the chance that a given atom will decay never changes, that is, it does not matter how long the atom has existed. For a large number of atoms however, the decay rate for the collection can be calculated from the measured decay constants, and the half-lives of the nuclides calculated. These numbers have no known limits for shortness or length of duration, and range over 55 orders of magnitude in time.

There are many types of radioactive decay (see table below). A decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide (or parent radioisotope[note 1]), transforms into an atom with a nucleus in a different state, or with a nucleus containing a different number of protons and neutrons. The product is called the daughter nuclide. In some decays, the parent and the daughter nuclides are different chemical elements, and thus the decay process results in the creation of an atom of a different element. This is known as a nuclear transmutation.

The first decay processes to be discovered were alpha decay, beta decay, and gamma decay. Alpha decay occurs when the nucleus ejects an alpha particle (helium nucleus). This is the most common process of emitting nucleons, but in rarer types of decays, nuclei can eject protons, or specific nuclei of other elements in a process called cluster decay. Beta decay occurs when the nucleus emits an electron or positron and a neutrino, in a process that changes a proton to a neutron or the other way about. The nucleus may capture an orbiting electron, causing a proton to convert into a neutron in a process called electron capture. All of these processes result in a nuclear transmutation.

By contrast, there are radioactive decay processes that do not result in a transmutation. The energy of an excited nucleus may be emitted as a gamma ray in a process called gamma decay, or be used to eject an orbital electron by its interaction with the excited nucleus, in a process called internal conversion. Highly excited neutron-rich nuclei, formed as the product of other types of decay, occasionally lose energy by way of neutron emission, resulting in a change of an element from one isotope to another. Another type of radioactive decay results in products that are not defined, but appear in a range of "pieces" of the original nucleus. This decay, called spontaneous fission, happens when a large unstable nucleus spontaneously splits into two (and occasionally three) smaller daughter nuclei, and generally leads to the emission of gamma rays, neutrons, or other particles from those.

For a summary table showing the number of stable and radioactive nuclides in each category, see radionuclide. There exist twenty-eight chemical elements on Earth that are radioactive. They are those that contain thirty-four radionuclides that date before the time of formation of the solar system. Well-known examples are uranium and thorium, but also included are naturally occurring long-lived radioisotopes such as potassium-40. Another fifty or so shorter-lived radionuclides, such as radium and radon, found on Earth, are the products of decay chains that began with the primordial nuclides, and ongoing cosmogenic processes, such as the production of carbon-14 from nitrogen-14 by cosmic rays. Radionuclides may also be produced artificially in particle accelerators or nuclear reactors, resulting in 650 of these with half-lives over an hour, and several thousand more with even shorter half-lives. See this list of nuclides for a list by half life.

History of discovery[edit]

Pierre and Marie Curie in their Paris laboratory, before 1907

Radioactivity was discovered in 1896 by the French scientist Henri Becquerel, while working on phosphorescent materials.[2] These materials glow in the dark after exposure to light, and he suspected that the glow produced in cathode ray tubes by X-rays might be associated with phosphorescence. He wrapped a photographic plate in black paper and placed various phosphorescent salts on it. All results were negative until he used uranium salts. The result with these compounds was to cause a blackening of the plate in spite of the plate being wrapped in black paper. These radiations were given the name "Becquerel Rays".

It soon became clear that the blackening of the plate had nothing to do with phosphorescence, as the plate recorded the presence of the mineral while wrapped and non-phosphorescent salts of uranium and metallic uranium also blackened the plate. It was clear that there was a form of invisible radiation that could pass through paper and was causing the plate to react as if exposed to light and so become black.

At first, it seemed as though the new radiation was similar to the then recently discovered X-rays. Further research by Becquerel, Ernest Rutherford, Paul Villard, Pierre Curie, Marie Curie, and others showed that this form of radioactivity was significantly more complicated. Rutherford was the first to realize that they all decay in accordance with the same mathematical exponential formula, and Rutherford and his student Frederick Soddy were the first to realize that many decay processes resulted in the transmutation of one element to another. Subsequently, the radioactive displacement law of Fajans and Soddy was formulated to describe the products of alpha and beta decay.[3][4]


Early dangers[edit]


The dangers of radioactivity and radiation were not immediately recognized. The discovery of x‑rays in 1895 led to widespread experimentation by scientists, physicians, and inventors. Many people began recounting stories of burns, hair loss and worse in technical journals as early as 1896. In February of that year, Professor Daniel and Dr. Dudley of Vanderbilt University performed an experiment involving x-raying Dudley's head that resulted in his hair loss. A report by Dr. H.D. Hawks, a graduate of Columbia College, of his suffering severe hand and chest burns in an x-ray demonstration, was the first of many other reports in Electrical Review.[5] Many experimenters including Elihu Thomson at Thomas Edison's lab, William J. Morton, and Nikola Tesla also reported burns. Elihu Thomson deliberately exposed a finger to an x-ray tube over a period of time and suffered pain, swelling, and blistering.[6] Other effects, including ultraviolet rays and ozone were sometimes blamed for the damage.[7] Many physicians claimed that there were no effects from x-ray exposure at all.[6]


Radiation protection[edit]

Main article: Radiation protection


The second ICR was held in Stockholm in 1928 and proposed the adoption of the rontgen unit, and the 'International X-ray and Radium Protection Committee' (IXRPC) was formed. Rolf Sievert was named Chairman, but a driving force was George Kaye of the British National Physical Laboratory. The committee met at each of the ICR meetings in Paris in 1931, Zurich in 1934, and Chicago in 1937. The first post-war ICR convened in London in 1950, and adopted the present name, the International Commission on Radiological Protection (ICRP).[8] The ICRP has developed the present international system of radiation protection.

Units of radioactivity[edit]

Graphic showing relationships between radioactivity and detected ionizing radiation


An older unit of radioactivity is the curie, Ci, which was originally defined as the amount of radium emanation (radon-222) in equilibrium with one gram of pure radium, isotope Ra-226. Today, it is defined as the activity of any radionuclide decaying with a rate of 3.7×1010 Bq, so that 1 curie (Ci) = 3.7×1010 Bq. For radiological protection purposes, although the United States Nuclear Regulatory Commission permits the use of the unit curie alongside SI units,[9] the European Union European units of measurement directives required that its use for "public health ... purposes" be phased out by 31 December 1985.[10]

Types of decay[edit]


Early researchers found that an electric or magnetic field could split radioactive emissions into three types of beams. The rays were given the alphabetic names alpha, beta, and gamma, in order of their ability to penetrate matter. While alpha decay was seen only in heavier elements of atomic number 52, tellurium, and greater, the other two types of decay were seen in all of the elements. Lead, atomic number 82, is the heaviest element to have any isotopes stable (to the limit of measurement) to radioactive decay. Radioactive decay is seen in all isotopes of all elements of atomic number 83 (bismuth) or greater. Bismuth, however, is only very slightly radioactive.

Types of radioactive decay related to N and Z numbers

In analysing the nature of the decay products, it was obvious from the direction of the electromagnetic forces applied to the radiations by external magnetic and electric fields that alpha particles from decay carried a positive charge, beta particles carried a negative charge, and gamma rays were neutral. From the magnitude of deflection, it was clear that alpha particles were much more massive than beta particles. Passing alpha particles through a very thin glass window and trapping them in a discharge tube allowed researchers to study the emission spectrum of the captured gas, and ultimately proved that alpha particles are helium nuclei. Other experiments showed the similarity between beta radiation resulting from decay and cathode rays: They are both streams of high-speed electrons. Likewise, gamma radiation and X-rays were found to be similar high-energy electromagnetic radiation.


Although alpha, beta, and gamma radiations were most commonly found, other types of decay were eventually discovered. Shortly after the discovery of the positron in cosmic ray products, it was realized that the same process that operates in classical beta decay can also produce positrons (positron emission). In an analogous process, instead of emitting positrons and neutrinos, some proton-rich nuclides were found to capture their own atomic electrons, a process called electron capture, and emit only a neutrino and usually also a gamma ray. Each of these types of decay involves the capture or emission of nuclear electrons or positrons, and acts to move a nucleus toward the ratio of neutrons to protons that has the least energy for a given total number of nucleons, producing a more stable nucleus.

A theoretical process of positron capture, analogous to electron capture, is possible in antimatter atoms, but has not been observed since the antimatter atoms are not available.[11] This would require antimatter atoms at least as complex as beryllium-7, which is the lightest known isotope of normal matter to undergo decay by electron capture.


Other types of radioactive decay that emit previously-seen particles were found, but by different mechanisms. An example is internal conversion, which results in electron and sometimes high-energy photon emission, even though it involves neither beta nor gamma decay. A neutrino is not emitted, and neither the electron nor photon originate in the nucleus. Internal conversion decay, like isomeric transition gamma decay and neutron emission, involves an excited nuclide releasing energy, without the transmutation of one element into another.

Rare events that involve a combination of two beta-decay type events happening simultaneously are known (see below). Any decay process that does not violate the conservation of energy or momentum laws (and perhaps other particle conservation laws) is permitted to happen, although not all have been detected. An interesting example discussed in a final section, is bound state beta decay of rhenium-187. In this process, an inverse of electron capture, beta electron-decay of the parent nuclide is not accompanied by beta electron emission, because the beta particle has been captured into the K-shell of the emitting atom. An antineutrino, however, is emitted.


If energy circumstances are favorable, a given radionuclide may undergo many competing types of decay, with some atoms decaying by one route, and others decaying by another. An example is copper-64, which has 29 protons, and 35 neutrons, which decays with a half-life of about 12.7 hours. This isotope has one unpaired proton and one unpaired neutron, so either the proton or the neutron can decay to the opposite particle. This particular nuclide (though not all nuclides in this situation) is almost equally likely to decay through proton decay by positron emission (18%) or electron capture (43%), as through neutron decay by electron emission (39%). The excited energy states produced by some of these decays, which fail to decay to the ground energy state, also produce later internal conversion and gamma decay in almost 0.5% of decays.

Mode of decay Participating particles Daughter nucleus
Decays with emission of nucleons:
Different modes of beta decay:
Transitions between states of the same nucleus:


Decay energy therefore remains associated with a certain measure of mass of the decay system, called invariant mass, which does not change in the decay, even though the energy of decay is distributed among decay particles. The energy of photons, the kinetic energy of emitted particles, and, later, the thermal energy of the surrounding matter, all contribute to the invariant mass of the system. Thus, while the sum of rest masses of the particles is not conserved in radioactive decay, the system mass and system invariant mass (and also the system total energy) is conserved throughout any decay process. This is a restatement of the equivalent laws of conservation of energy and conservation of mass.

Radioactive decay rates[edit]


Constant quantities:

  • The mean lifetimeτ, "tau" the average lifetime of a radioactive particle before decay.

Although these are constants, they are associated with statistically random behaviour of populations of atoms. In consequence, predictions using these constants are less accurate for small number of atoms.


Time-variable quantities:


These are related as follows:

 A = - \frac{\mathrm{d}N}{\mathrm{d}t} = \lambda N
 S_A a_0 = - \frac{\mathrm{d}N}{\mathrm{d}t}\bigg|_{t=0} = \lambda N_0


Mathematics of radioactive decay[edit]


Universal law of radioactive decay[edit]



One-decay process[edit]


-\frac{\mathrm{d}N}{\mathrm{d}t} \propto N.


 -\frac{\mathrm{d}N}{N} = \lambda \mathrm{d}t


N(t) = N_0\,e^{-{\lambda}t} = N_0\,e^{-t/ \tau}, \,\!

where N0 is the value of N at time t = 0.[12]

We have for all time t:

 N_A + N_B = N_\mathrm{total} = N_{A0},

where Ntotal is the constant number of particles throughout the decay process, which is clearly equal to the initial number of A nuclides since this is the initial substance.

If the number of non-decayed A nuclei is:

N_A = N_{A0}e^{-{\lambda}t} \,\!


 N_B = N_{A0} - N_A = N_{A0} - N_{A0}e^{-{\lambda}t} = N_{A0} \left ( 1 - e^{-{\lambda}t} \right ).


 P(N) = \frac{\langle N \rangle^N \exp(-\langle N\rangle)}{N!} .

Chain-decay processes[edit]

Chain of two decays


\frac{\mathrm{d}N_B}{\mathrm{d}t} = -\lambda_B N_B + \lambda_A N_A.


Re-writing using the previous results:

 \frac{\mathrm{d}N_B}{\mathrm{d}t} = - \lambda_B N_B + \lambda_A N_{A0} e^{-\lambda_A t}


 N_B = \frac{N_{A0}\lambda_A}{\lambda_B - \lambda_A} \left ( e^{-\lambda_A t} - e^{-\lambda_B t}\right ) .

Naturally, in the case where B is a stable nuclide (λB = 0), this equation reduces to the previous solution, in the case :

 \lim_{\lambda_B\rightarrow 0} \left [ \frac{N_{A0}\lambda_A}{\lambda_B - \lambda_A} \left ( e^{-\lambda_A t} - e^{-\lambda_B t}\right ) \right ] = \frac{N_{A0}\lambda_A}{0 - \lambda_A} \left ( e^{-\lambda_A t} - 1 \right ) = N_{A0} \left ( 1- e^{-\lambda_A t} \right ),


Chain of any number of decays


 \frac{\mathrm{d}N_j}{\mathrm{d}t} = - \lambda_j N_j + \lambda_{j-1} N_{(j-1)0} e^{-\lambda_{j-1} t}.

The general solution to the recursive problem is given by Bateman's equations:[14]

Bateman's equations

 N_D = \frac{N_1(0)}{\lambda_D} \sum_{i=1}^D \lambda_i c_i e^{-\lambda_i t}

 c_i = \prod_{j=1, i\neq j}^D \frac{\lambda_j}{\lambda_j - \lambda_i}

Alternative decay modes[edit]


 N = N_A + N_B + N_C


\frac{\mathrm{d}N_A}{\mathrm{d}t} & = - \left(\frac{\mathrm{d}N_B}{\mathrm{d}t} + \frac{\mathrm{d}N_C}{\mathrm{d}t} \right) \\
- \lambda N_A & = - N_A \left ( \lambda_B + \lambda_C \right ) \\


 \lambda = \lambda_B + \lambda_C .

Notice that

 \frac{\mathrm{d}N_A}{\mathrm{d}t} < 0,\frac{\mathrm{d}N_B}{\mathrm{d}t} > 0, 
\frac{\mathrm{d}N_C}{\mathrm{d}t} > 0.

Solving this equation for NA:

 N_A = N_{A0} e^{-\lambda t} .


 N_B = \frac{\lambda_B}{\lambda} N_{A0} \left ( 1 - e^{-\lambda t} \right ),
 N_C = \frac{\lambda_C}{\lambda} N_{A0} \left ( 1 - e^{-\lambda t} \right ).


Corollaries of the decay laws[edit]



Decay timing: definitions and relations[edit]

Time constant and mean-life[edit]

For the one-decay solution A → B:






 \lambda = \lambda_B + \lambda_C \,

into the decay solution leads to:

\frac{1}{\tau} = \lambda = \lambda_B + \lambda_C = \frac{1}{\tau_B} + \frac{1}{\tau_C}\,
Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms (left) or 400 (right). The number at the top indicates how many half-lives have elapsed. Note the law of large numbers: with more atoms, the overall decay is less random.





t_{1/2} = \frac{\ln 2}{\lambda} = \tau \ln 2.



N(t) = N_0\,e^{-t/ \tau} =N_0\,2^{-t/t_{1/2}}. \,\!


Mathematically, the nth life for the above situation would be found in the same way as above—by setting N = N0/n, {{{1}}} and substituting into the decay solution to obtain

t_{1/n} = \frac{\ln n}{\lambda} = \tau \ln n.




 N = N_0\,e^{-t/ \tau},

where:  \frac{N}{ N_0} = 4/14 \approx 0.286,

 \tau = \frac{T_{1/2}}{\ln 2} \approx 8267 years,
 t = -\tau\,\ln\frac{N}{ N_0} \approx 10360 years.

Changing decay rates[edit]






Recent results suggest the possibility that decay rates might have a weak dependence on environmental factors. It has been suggested that measurements of decay rates of silicon-32, manganese-54, and radium-226 exhibit small seasonal variations (of the order of 0.1%),[21][22][23] while the decay of Radon-222 exhibit large 4% peak-to-peak seasonal variations,[24] proposed to be related to either solar flare activity or distance from the Sun. However, such measurements are highly susceptible to systematic errors, and a subsequent paper[25] has found no evidence for such correlations in seven other isotopes (22Na, 44Ti, 108Ag, 121Sn, 133Ba, 241Am, 238Pu), and sets upper limits on the size of any such effects.

Theoretical basis of decay phenomena[edit]





Occurrence and applications[edit]


Nuclides that are produced by radioactive decay are called radiogenic nuclides, whether they themselves are stable or not. There exist stable radiogenic nuclides that were formed from short-lived extinct radionuclides in the early solar system.[27][28] The extra presence of these stable radiogenic nuclides (such as Xe-129 from primordial I-129) against the background of primordial stable nuclides can be inferred by various means.



Origins of radioactive nuclides[edit]

Main article: nucleosynthesis

Radioactive primordial nuclides found in the Earth are residues from ancient supernova explosions which occurred before the formation of the solar system. They are the long-lived fraction of radionuclides surviving in the primordial solar nebula through planet accretion until the present. The naturally occurring short-lived radiogenic radionuclides found in rocks are the daughters of these radioactive primordial nuclides. Another minor source of naturally occurring radioactive nuclides are cosmogenic nuclides, formed by cosmic ray bombardment of material in the Earth's atmosphere or crust. The radioactive decay of these radionuclides in rocks within Earth's mantle and crust contribute significantly to Earth's internal heat budget.

Decay chains and multiple modes[edit]

The daughter nuclide of a decay event may also be unstable (radioactive). In this case, it will also decay, producing radiation. The resulting second daughter nuclide may also be radioactive. This can lead to a sequence of several decay events. Eventually, a stable nuclide is produced. This is called a decay chain (see this article for specific details of important natural decay chains).


An example is the natural decay chain of 238U, which is as follows:



Associated hazard warning signs[edit]

See also[edit]





  2. ^ Mould, Richard F. (1995). A century of x-rays and radioactivity in medicine : with emphasis on photographic records of the early years (Reprint. with minor corr ed.). Bristol: Inst. of Physics Publ. p. 12. ISBN 9780750302241. 
  9. ^ 10 CFR 20.1004. US Nuclear Regulatory Commission. 2009. 
  11. ^ Radioactive Decay
  14. ^ Cetnar, Jerzy (May 2006). "General solution of Bateman equations for nuclear transmutations". Annals of Nuclear Energy 33 (7): 640–645. doi:10.1016/j.anucene.2006.02.004. 
  16. ^ Wang, B.; Yan, S.; Limata, B. et al. (2006). "Change of the 7Be electron capture half-life in metallic environments". The European Physical Journal A 28 (3): 375–377. doi:10.1140/epja/i2006-10068-x. ISSN 1434-6001. 
  17. ^ Jung, M.; Bosch, F.; Beckert, K. et al. (1992). "First observation of bound-state β decay". Physical Review Letters 69 (15): 2164–2167. doi:10.1103/PhysRevLett.69.2164. ISSN 0031-9007. PMID 10046415. 
  18. ^ Smoliar, M.I.; Walker, R.J.; Morgan, J.W. (1996). "Re-Os ages of group IIA, IIIA, IVA, and IVB iron meteorites". Science 271 (5252): 1099–1102. Bibcode:1996Sci...271.1099S. doi:10.1126/science.271.5252.1099. 
  20. ^ Emery, G.T. (1972). "Perturbation of Nuclear Decay Rates". Annual Review of Nuclear Science (ACS Publications) 22: 165–202. Bibcode:1972ARNPS..22..165E. doi:10.1146/annurev.ns.22.120172.001121. Retrieved 6 August 2012. 
  22. ^ Jenkins, Jere H.; Fischbach, Ephraim (2009). "Perturbation of Nuclear Decay Rates During the Solar Flare of 13 December 2006". Astroparticle Physics 31 (6): 407–411. arXiv:0808.3156. Bibcode:2009APh....31..407J. doi:10.1016/j.astropartphys.2009.04.005. 
  23. ^ Jenkins, J. H.; Buncher, John B.; Gruenwald, John T.; Krause, Dennis E.; Mattes, Joshua J. et al. (2009). "Evidence of correlations between nuclear decay rates and Earth–Sun distance". Astroparticle Physics 32 (1): 42–46. arXiv:0808.3283. Bibcode:2009APh....32...42J. doi:10.1016/j.astropartphys.2009.05.004. 
  25. ^ Norman, E. B.; Shugart, Howard A.; Joshi, Tenzing H.; Firestone, Richard B. et al. (2009). "Evidence against correlations between nuclear decay rates and Earth–Sun distance". Astroparticle Physics 31 (2): 135–137. arXiv:0810.3265. Bibcode:2009APh....31..135N. doi:10.1016/j.astropartphys.2008.12.004. 
  26. ^ NUBASE evaluation of nuclear and decay properties
  29. ^ IAEA news release Feb 2007


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