if an electron is revolving in its bohr orbit having bohr radius of `0.529Å`, then the radius of third orbit is

Options

A. `4234Å`
B. `4496Å`
C. `4.761Å`
D. `5125nm`

Explanation

To find the radius of the third orbit of an electron in a Bohr model, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Bohr Model**: In the Bohr model of the atom, the radius of the nth orbit is given by the formula:
\[ r_n = r_0 \cdot n^2 \]
where \( r_n \) is the radius of the nth orbit, \( r_0 \) is the Bohr radius, and \( n \) is the principal quantum number (orbit number).

2. **Identify Given Values**: We are given:
- The Bohr radius \( r_0 = 0.529 \, \text{Å} \)
- The principal quantum number for the third orbit \( n = 3 \)

3. **Calculate \( n^2 \)**: For the third orbit:
\[ n^2 = 3^2 = 9 \]

4. **Substitute Values into the Formula**: Now, substitute the values into the formula for the radius of the third orbit:
\[ r_3 = r_0 \cdot n^2 = 0.529 \, \text{Å} \cdot 9 \]

5. **Perform the Multiplication**:
\[ r_3 = 0.529 \times 9 = 4.761 \, \text{Å} \]

6. **Conclusion**: The radius of the third orbit is:
\[ r_3 = 4.761 \, \text{Å} \]

### Final Answer:
The radius of the third orbit is \( 4.761 \, \text{Å} \).

---