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 $\frac{v_0}{r_0{n}^4}$
$(\because v_n=\frac{v_0}{n}$ and $r_n=n^2{r}_0)$
Hence product $\propto \frac{1}{n^4}$