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 n²
• B. Directly proportional to n³
• C. Directly proportional to h/2π
• D. Inversely proportional to n/h

Answer 1

The correct option is B

Directly proportional to n³

mvr=$\frac{nh}{2\pi }$

$2\pi r$=$\frac{nh}{mv}$...............(i)

Equation (i) is divided by v

$\frac{2\pi r}{v}=\frac{nh}{m{v}^2}$

$\frac{2\pi r}{v}$ is the time taken in one revolution and v $\alpha$ $\frac{1}{n}$ so,

$v^2$ $\alpha$ $\frac{1}{n^2}$ $\alpha$ $n^3$