Some radionuclides decay by capturing one of their own atomic electrons, a K-electron, say. An example is

(a) We have to show that the disintegration energy for this process is given by

where and are the atomic masses of , respectively, and is the binding energy of the vanadium K-electron.

(b) We have to find the disintegration energy for the decay of by K-electron capture. The needed data are , , and .

Solution:             Click For PDF Version

We have to find the disintegration energy for the decay of by K-electron capture. The beta decay process is

We denote by and the atomic masses of , respectively, and let be the binding energy of the vanadium K-electron. We denote by the mass of the nucleus, and by the mass of the nucleus.

The value for the beta decay of nucleus by electron capture will therefore be

We have used the result that atom has 23 electrons and atom has 22 electrons. We have ignored the differences in the binding energies of the atomic electrons in atom and those in atom, except by taking into account that the extra electron in atom has less energy by an amount , as the energy in the K-shell is .

(b)

We use the data for calculating the for the beta decay of by K-electron capture. We have