Question

A free neutron beta-decays to a proton with a half-life of 14 minutes. (a) What is the decay constant ? (b) Find the energy liberated in the process.

Answer 1

We know,

Half life period = $\frac{0.6931}{\lambda }$

[Where $\lambda \to$ decay constant]

$\lambda =\frac{0.6931}{14\times 60}$

= $8.25\times 10s^{-1}$

[As Half life = 14 min = $14\times 60sec$]

$\text{Energy}$

=$\left[\right(M_p+M_e\left)\right]u$

$\left[\right({<}_{nu}-M_{pu})-M{e}_u]c^2$

=$[0.00189u-511KeV/c^2]$

=$[1293159eV/c^2-51,1000eV/c^2]c^2$

= 782159 eV = 782 KeV