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

Options

A. `(3xxx)` pm
B. `(6xxx)` pm
C. `(1/2xxx)` pm
D. `(9xxx)` pm

Explanation

To solve the problem of finding the radius of the third Bohr orbit given that the radius of the first Bohr orbit is \( a_0 \), we can use the formula for the radius of the nth Bohr orbit:

### Step-by-Step Solution:

1. **Understand the Formula**: The radius of the nth Bohr orbit is given by the formula:
\[ R_n = a_0 \cdot \frac{n^2}{Z} \]
where:
- \( R_n \) is the radius of the nth orbit,
- \( a_0 \) is the radius of the first orbit,
- \( n \) is the principal quantum number (orbit number),
- \( Z \) is the atomic number of the element.

2. **Identify Given Values**:
- For the first orbit (n = 1), we know that:
\[ R_1 = a_0 \cdot \frac{1^2}{Z} \]
Since it is given that \( R_1 = a_0 \), we can deduce:
\[ a_0 = a_0 \cdot \frac{1}{Z} \]
This implies that \( Z = 1 \).

3. **Calculate the Radius of the Third Orbit**: Now we need to find the radius of the third orbit (n = 3):
\[ R_3 = a_0 \cdot \frac{3^2}{Z} \]
Substituting \( Z = 1 \):
\[ R_3 = a_0 \cdot \frac{9}{1} \]
Therefore:
\[ R_3 = 9a_0 \]

4. **Conclusion**: The radius of the third Bohr orbit is:
\[ R_3 = 9a_0 \]

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

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