Decay energy

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

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

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

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:

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

or

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

or

${\displaystyle P=Q\times A.}$

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

• Q value (nuclear science)

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