The key feature of Bohr's spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid.The rule to be applied is Bohr's quantization condition.
A diatomic molecule has moment of inertia `I`. By Bohr's quantization condition its rotational energy in the `n^(th)` level (`n = 0` is not allowed ) is

Options

A. `(1)/(n^(2)) ((h^(2))/(8 pi^(2) I))`
B. `(1)/(n) ((h^(2))/(8 pi^(2) I))`
C. `n ((h^(2))/(8 pi^(2) I))`
D. `n^(2) ((h^(2))/(8 pi^(2) I))`

Explanation

To find the quantized rotational energy of a diatomic molecule using Bohr's quantization condition, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Moment of Inertia**:
- For a diatomic molecule, the moment of inertia \( I \) can be expressed as:
\[
I = 2mr^2
...