If the radius of first Bohr orbit be `a_0`, then the radius of the third orbit would be-

Options

A. `3 xx a_0`
B. `6 xx a_0`
C. `9 xx a_0`
D. `1//9 xx a_0`

Explanation

To find the radius of the third Bohr orbit given that the radius of the first Bohr orbit is \( a_0 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Radius of Bohr Orbits**:
The radius of the nth Bohr orbit is given by the formula:
\[ R_n = \frac{0.529 \, \text{Å} \cdot n^2}{Z} \]
where \( R_n \) is the radius of the nth orbit, \( n \) is the principal quantum number (1 for the first orbit, 2 for the second, etc.), and \( Z \) is the atomic number.

2. **Set the Atomic Number**:
For hydrogen, \( Z = 1 \). Therefore, the formula simplifies to:
\[ R_n = 0.529 \, \text{Å} \cdot n^2 \]

3. **Calculate the Radius of the First Orbit**:
For the first orbit (\( n = 1 \)):
\[ R_1 = 0.529 \, \text{Å} \cdot (1^2) = 0.529 \, \text{Å} \]
Given that this radius is equal to \( a_0 \), we have:
\[ a_0 = 0.529 \, \text{Å} \]

4. **Calculate the Radius of the Third Orbit**:
For the third orbit (\( n = 3 \)):
\[ R_3 = 0.529 \, \text{Å} \cdot (3^2) = 0.529 \, \text{Å} \cdot 9 = 4.761 \, \text{Å} \]
Since \( R_1 = a_0 \), we can express \( R_3 \) in terms of \( a_0 \):
\[ R_3 = 9 \cdot a_0 \]

5. **Conclusion**:
Therefore, the radius of the third Bohr orbit is:
\[ R_3 = 9a_0 \]

### Final Answer:
The radius of the third Bohr orbit is \( 9a_0 \).