Question

The frequency of revolution of an electron in the $n^{\text{th}$ orbit of hydrogen atom is

• A. directly proportional to $n^2$
• B. inversely proportional to $n^2$
• C. directly proportional to $n^3$
• D. inversely proportional to $n^3$

Hint:

Radius $n^2$, Velocity $1/n$, Time Period $n^3$, Frequency $1/n^3$.

Answer 1

The Correct Option is D

Step 1: Concept
Frequency $f = v/2\pi r$. In Bohr's model, velocity $v \propto 1/n$ and radius $r \propto n^2$.

Step 2: Meaning
Frequency is the reciprocal of the time period ($f = 1/T$).

Step 3: Analysis
$f \propto \frac{1/n}{n^2} \propto \frac{1}{n^3}$.

Step 4: Conclusion
Frequency of revolution is inversely proportional to $n^3$. Final Answer: (D)