Question

You learned in Chapter 36 that mass has an equivalent amount of energy. What are the energy equivalents in $\mathrm{MeV}$of the rest masses of an electron and a proton?

Short answer

For electron mass is, $m_e=5.12\times {10}^5\mathrm{eV}$ and for proton mass is, $m_p=9.39\times {10}^8\mathrm{eV}$

Step-by-step solution

Given Information

We know, mass has an equivalent amount of energy.

Calculation

The rest mass energy equivalent is $E=m{c}^2$in jule and in $\mathrm{eV}$it will be $\frac{m{c}^2}{1.6\times {10}^{-19}}\mathrm{eV}$. Where mass is taken in $\mathrm{kg}$and velocity of llght is $c=3\times {10}^8\mathrm{m}/\mathrm{s}$.
So for electron mass is $m_e=9.1\times {10}^{-31}\mathrm{kg}$. Therefore energy is
$E=\frac{9.1\times {10}^{-31}\times {\left(3\times {10}^8\right)}^2}{1.6\times {10}^{-19}}=5.12\times {10}^5\mathrm{eV}$
For proton mass is $m_p=1.67\times {10}^{-27}\mathrm{kg}$, So energy is
$E_p=\frac{1.67\times {10}^{-27}\times {\left(3\times {10}^8\right)}^2}{1.6\times {10}^{-19}}=9.39\times {10}^8\mathrm{eV}$