Question

The product of angular speed and tangential speed of electron in $n^{\text {th }}$ orbit of hydrogen atom is

• A. Directly proportional to $n^{2}$
• B. Directly proportional to $n^{3}$
• C. Inversely proportional to $n^{4}$
• D. Independent of $n$

Answer 1

Answer: (C)

Angular velocity $=\frac{v_{n}}{r_{n}}$
Product of angular velocity and tangential velocity
$=\frac{v_{n}}{r_{n}} \times v_{n}$
or $\frac{v_{n}^{2}}{r_{n}}$
or $\frac{v_{0}}{r_{0} n^{4}}$
$\left(\because v_{n}=\frac{v_{0}}{n}\right.$ and $\left.r _{n}=n^{2} r_{0}\right)$
Hence product $\propto \frac{1}{n^{4}}$