Question

In a hydrogen atom the total energy of electron is

• A. $\frac{e^2}{4\pi {\epsilon }_{0}r}$
• B. $\frac{-e^2}{4\pi {\epsilon }_{0}r}$
• C. $\frac{-e^2}{8\pi {\epsilon }_{0}r}$
• D. $\frac{e^2}{8\pi {\epsilon }_{0}r}$

Answer 1

Answer: (C)

The kinetic energy of the electron in hydrogen atom are
$K=\frac{1}{2}m{v}^2$
$=\frac{e^2}{8\pi {\epsilon }_{0}r}\left[\because v^2=\frac{e^2}{4\pi {\epsilon }_{0}mr}\right]$
Electrostatic potential energy,
$U=\frac{-e^2}{4\pi {\epsilon }_{0}r}$
The total energy $E$ of the electron in a hydrogen atom is
$E=K+U,E$
$=\frac{e^2}{8\pi {\epsilon }_{0}r}+\left(\frac{-e^2}{4\pi {\epsilon }_{0}r}\right)$
$=-\frac{e^2}{8\pi {\epsilon }_{0}r}$
here negative sign shows that electron is bound to the nucleus.