The radius of second Bohr's orbit is

Options

A. `0.053 nm`
B. `0.053//4 nm`
C. `0.053 xx 4 nm`
D. `0.053 xx 20 nm`

Explanation

To find the radius of the second Bohr's orbit, we can use the formula for the radius of the nth orbit in a hydrogen-like atom:

\[ r_n = \frac{0.53 \, \text{Å} \times n^2}{Z} \]

Where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (for the second orbit, \( n = 2 \)),
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)),
- \( 0.53 \, \text{Å} \) is the radius of the first Bohr orbit.

### Step-by-Step Solution:

1. **Identify the values:**
- For the second Bohr orbit, \( n = 2 \).
- For hydrogen, \( Z = 1 \).

2. **Substitute the values into the formula:**
\[ r_2 = \frac{0.53 \, \text{Å} \times (2^2)}{1} \]

3. **Calculate \( n^2 \):**
\[ n^2 = 2^2 = 4 \]

4. **Calculate the radius:**
\[ r_2 = 0.53 \, \text{Å} \times 4 = 2.12 \, \text{Å} \]

5. **Convert angstroms to nanometers:**
- Since \( 1 \, \text{Å} = 0.1 \, \text{nm} \),
\[ r_2 = 2.12 \, \text{Å} \times 0.1 \, \text{nm/Å} = 0.212 \, \text{nm} \]

### Final Answer:
The radius of the second Bohr's orbit is \( 0.212 \, \text{nm} \).