Question

In one model of the electron, the electron of mass $m_e$ is thought to be a uniformly charged shell of radius $R$ and total charge $e$, whose electrostatic energy $E$ is equivalent to its mass $m_e$ via Einstein's mass energy relation $E=m_e{c}^2$. In this model, $R$ is approximately ($m_e=9.1\times {10}^{-31}kg$, $c=3\times {10}^{8}m{s}^{-1}$, $1/4\pi {\epsilon }_0=9\times {10}^{9}Farads{m}^{-1}$, magnitude of the electron charge $=1.6\times {10}^{-19}C$)

• A. $1.4\times {10}^{-15}m$
• B. $2\times {10}^{-13}m$
• C. $5.3\times {10}^{-11}m$
• D. $2.8\times {10}^{-35}m$

Answer 1

The correct option is A $1.4\times {10}^{-15}m$

Comparing the electrostatic energy of a shell with radius R with $m{c}^2$

So we get $\frac{e^2}{8\pi ϵR}=m{c}^2$

on putting value we get $R=1.4\times {10}^{-15}m$