Decay energy

The decay energy is the energy released by a radioactive decay. Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide.

Decay calculation

The energy difference of the reactants is often written as Q:

$Q=\left({\text{Kinetic energy}}\right)_{\text{before}}-\left({\text{Kinetic energy}}\right)_{\text{after}},$

$Q=\left(\left({\text{Rest mass}}\right)_{\text{before}}\times c^{2}\right)-\left(\left({\text{Rest mass}}\right)_{\text{after}}\times c^{2}\right).$

Decay energy is usually quoted in terms of the energy units MeV (million electronvolts) or keV (thousand electronvolts).

Types of radioactive decay include

• gamma ray
• beta decay (decay energy is divided between the emitted electron and the neutrino which is emitted at the same time)
• alpha decay

The decay energy is the mass difference Δm between the parent and the daughter atom and particles. It is equal to the energy of radiation E. If A is the radioactive activity, i.e. the number of transforming atoms per time, M the molar mass, then the radiation power P is:

$P=\Delta {m}\times \left({\frac {A}{M}}\right).$

or

$P=E\times \left({\frac {A}{M}}\right).$

or

$P=Q\times A.$

Example: ⁶⁰Co decays into ⁶⁰Ni. The mass difference Δm is 0.003u. The radiated energy is approximately 2.8 MeV. The molar weight is 59.93. The half life T of 5.27 year corresponds to the activity A = N * [ ln(2) / T ], where N is the number of atoms per mol, and T is the half-life. Taking care of the units the radiation power for ⁶⁰Co is 17.9 W/g

Radiation power in W/g for several isotopes:

⁶⁰Co: 17.9

²³⁸Pu: 0.57

¹³⁷Cs: 0.6

²⁴¹Am: 0.1

²¹⁰Po: 140 (T=136 d)

⁹⁰Sr: 0.9

²²⁶Ra: 0.02

See also

• Q value (nuclear science)

References

Radioactivity Radionuclides Radiation by Joseph Magill and Jean Galy, Springer Verlag, 2005