The radius of first Bohr orbit in H-atom is 0.53 Å. The radius of third orbit is

Options

A. 7.44 Å
B. 7.47 Å
C. 47.7 Å
D. 4.77 Å

Explanation

To find the radius of the third Bohr orbit in a hydrogen atom, we can use the formula that relates the radius of the nth orbit to the radius of the first orbit. The formula is:

\[ R_n = R_1 \times n^2 \]

Where:
- \( R_n \) is the radius of the nth orbit.
- \( R_1 \) is the radius of the first orbit.
- \( n \) is the principal quantum number of the orbit.

### Step-by-Step Solution:

1. **Identify the given values:**
- The radius of the first Bohr orbit \( R_1 = 0.53 \, \text{Å} \).
- We need to find the radius of the third orbit, where \( n = 3 \).

2. **Use the formula for the radius of the nth orbit:**
\[ R_n = R_1 \times n^2 \]

3. **Substitute the known values into the formula:**
\[ R_3 = 0.53 \, \text{Å} \times (3^2) \]
\[ R_3 = 0.53 \, \text{Å} \times 9 \]

4. **Calculate the radius of the third orbit:**
\[ R_3 = 0.53 \, \text{Å} \times 9 = 4.77 \, \text{Å} \]

5. **Final Answer:**
The radius of the third Bohr orbit in the hydrogen atom is \( 4.77 \, \text{Å} \).