The radius of `n^th` orbit `r_n` in the terms of Bohr radius `(a_0)` for a hydrogen atom is given by the relation

Options

A. `na_0`
B. `sqrt(na_0)`
C. `n^2a_0`
D. `n^3a_0`

Explanation

To determine the radius of the \( n^{th} \) orbit \( r_n \) in terms of the Bohr radius \( a_0 \) for a hydrogen atom, we can use the formula derived from Bohr's model of the atom.

### Step-by-Step Solution:

1. **Understanding Bohr's Model**:
- According to Bohr's model, the radius of the \( n^{th} \) orbit for an electron in a hydrogen atom is quantized and can be expressed in terms of the Bohr radius \( a_0 \).

2. **Bohr Radius**:
- The Bohr radius \( a_0 \) is defined as the radius of the first orbit (ground state) of the hydrogen atom. Its value is approximately \( 5.29 \times 10^{-11} \) meters.

3. **Formula for the Radius of the \( n^{th} \) Orbit**:
- The radius of the \( n^{th} \) orbit is given by the formula:
\[ r_n = n^2 a_0 \]
- Here, \( n \) is the principal quantum number, which can take positive integer values (1, 2, 3,...).

4. **Conclusion**:
- Therefore, the radius of the \( n^{th} \) orbit in terms of the Bohr radius is:
\[ r_n = n^2 a_0 \]

### Final Answer:
The radius of the \( n^{th} \) orbit \( r_n \) in terms of the Bohr radius \( a_0 \) for a hydrogen atom is given by:
\[ r_n = n^2 a_0 \]