Question

The average current due to an electron orbiting the proton in the $n^{th}$ Bohr orbit of the hydrogen atom is

• A. $\propto n$
• B. $\propto n^3$
• C. $\propto n^{-3}$
• D. none of these

Answer 1

Answer: (C)

$\propto n^{-3}$

We know,

$r_n\propto \frac{1}{n^2}$

$v_n\propto \frac{Z}{n}$

$\omega =\frac{2\pi r_n}{v_n}$

$\omega \propto \frac{Z}{n^3}$

$I\propto \omega \propto \frac{1}{n^{-3}}$

$L\propto n^{-3}$

Hence option $\text{C}$ is correct.