Conceptual Question on Mass-Energy Equivalence. #3

Given:

• the rest masses of the proton is $1.6726\times 10^{ -27}\rm \ kg$,
• the rest masses of the electron is $9.11\times 10^{ -31}\rm \ kg$, and

• the rest masses of the anti-neutrino is $0$.

 To find:

• the total kinetic energy shared among the three particles when a neutron decays at rest.

We know the values:

• the rest masses for neutron is $1.6749 \times 10^{ -27}\rm \ kg$, and
• the unified atomic mass, $\rm u = 1.66054\times 10^{ -27}\rm \ kg$

The nuclear reaction of neutron-decay is

$\rm n \rightarrow p + e^{-1} + \bar{\nu}$

The mass defect of the above nuclear reaction is given by;

$\begin{aligned} \Delta m &= \text{Mass}(\rm neutron) – \text{Mass} (\rm protron)- \text{Mass} (\rm electron) -Mass (\rm anti-neutrino) \\ &=(1.674929\times 10^{ -27}\rm \ kg) – (1.6726\times 10^{ -27} \ kg)-(9.11\times 10^{ -31} \ kg)-0\\ &= 0.001418\rm \ kg\\ \end{aligned}$

Therefore, the total kinetic energy shared among the three particles when a neutron decays at rest is;

$\begin{aligned} K.E._{( p + e^{-1} + \bar{\nu})} &= \Delta m c^2\\ &=(0.001418\rm \ kg) \times (3\times 10^8 \ m/s)^2\\ &= 1.2762\times 10^6\rm \ J \\ \end{aligned}$