Question

The time taken by the electron in one complete revolution in the $n^{th}$ Bohr's orbit of the hydrogen atom is

• A. Inversely proportional to $n^2$
• B. Directly proportional to $n^3$
• C. Directly proportional to $\frac{h}{2\pi }$
• D. Inversely proportional to $\frac{n}{h}$

Answer 1

The correct option is B Directly proportional to $n^3$

Period $\left(T\right)=\frac{\text{Circumference}}{\text{Velocity}}$
$T=\frac{2\pi r}{v}$
$r=\frac{0.529n^2}{Z}$
$v=\frac{2.19\times {10}^6\times \text{Z}}{n}$
$T=\frac{2\pi \frac{0.529\times n^2}{Z}}{\frac{2.19\times {10}^6}{n}Z}$
$\therefore T\propto n^3$