Derive an expression for the radius of `n^(th)` Bohr’s orbit in Hydrogen atom.

Explanation

To derive the expression for the radius of the \( n^{th} \) Bohr orbit in a hydrogen atom, we will follow a systematic approach based on classical mechanics and electrostatics.

### Step-by-Step Solution:

1. **Understanding the System**:
- In the Bohr model, an electron moves in a circular orbit around a positively charged nucleus (proton in the case of hydrogen). Let the radius of the \( n^{th} \) orbit be \( R_n \).

2. **Centripetal Force Requirement**:
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