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 $\frac{n^3}{Z^2}$
• 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 $\frac{n^3}{Z^2}$

Time period of revolution 'T' of an electron in its orbit = 2πr/v
$v_n=2.18\times {10}^6\frac{Z}{n}m{s}^{-1}$ where $v_n$ is the velocity of the electron
$r_n=0.529\times \frac{n^2}{Z}$ $\stackrel{\circ }{A}$
where $r_n$ is the radius of $n^{th}$ orbit.
Z is the atomic number of the Hydrogen atom
On putting the values,
T = $\frac{2\pi \times 0.529\frac{n^2}{Z}}{2.18\times {10}^6\frac{Z}{n}}$
So, Time period T ∝ $\frac{n^3}{Z^2}$