Question

In a hydrogen atom, the electron and proton and bound at a distance of about 0.53 A.
Estimate the potential energy of the system in eV, taking the zero of potential energy at infinite separation of electron from proton.

Answer 1

$r=0.53A$

$=0.53\times {10}^{10}m$

Charge of electron $-e$

Charge of proton $=e$

$\therefore$ Potential energy $=\frac{1}{4\pi {\epsilon }_0}.\frac{e(-e)}{r}=\frac{-e^2}{4\pi {\epsilon }_{0}r}$

$V=\frac{-(1.6{)}^2\times {10}^{-38}\times 9\times {10}^9}{0.53\times {10}^{-10}}$

$=\frac{-(1.6{)}^2\times {10}^{-38}\times 9\times {10}^9}{0.53\times {10}^{-10}\times 1.6\times {10}^{-19}}eV$

$=\frac{-1.6\times 9}{0.53}eV=-27.2eV$