If an electron is moving in the
Question:

If an electron is moving in the $\mathrm{n}^{\text {th }}$ orbit of the hydrogen atom, then its

velocity $\left(\mathrm{v}_{\mathrm{n}}\right)$ for the $n^{\text {th }}$

orbit is given as:

1. (1) $\mathrm{v}_{\mathrm{n}} \propto \mathrm{n}$

2. (2) $v_{n} \propto \frac{1}{n}$

3. (3) $v_{n} \propto n^{2}$

4. (4) $v_{n} \propto \frac{1}{n^{2}}$

Correct Option: , 2

Solution:

$(2)$

We know velocity of electron in $\mathrm{n}^{\text {th }}$ shell of

hydrogen atom is given by

$v=\frac{2 \pi k Z e^{2}}{n h}$

$\therefore \mathrm{v} \propto \frac{1}{\mathrm{n}}$