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

(a) The decay constant is $8.25 \times 10-4 s-1$. (b) In this process, the liberated energy is $782 \mathrm{keV}$

Explanation:

In the question, it is given:

Free neutron’s half-life period when beta is decayed to form proton,  

T1/2 = 14 minutes

Half-life period, T1/2 = 0.6931λ

where, λ is a constant for decay.

Therefore,$\lambda=0.69314 \times 60=8.25 \times 10-4 \mathrm{s}-1$

If proton’s mass is mp, let me and mn be the electron mass and neutron mass, respectively.

Therefore, the liberated energy is E = $\lambda=0.69314 \times 60=8.25 \times 10-4 \mathrm{s}-1$

$=[1.008665 u-1.007276+0.0005486 u] c 2$

$=782 \mathrm{keV}$