The radius of 2nd Bohr.s orbit of hydrogen atom is :

Options

A. 0.053 nm
B. 0.106 nm
C. 0.2116 nm
D. 0.4256 nm

Explanation

To find the radius of the second Bohr orbit of a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Formula for the Radius of Bohr's Orbit:**
The radius of the nth orbit in a hydrogen atom is given by the formula:
\[ r_n = \frac{0.529 \, n^2}{Z} \text{ (in angstroms)} \]
where \( r_n \) is the radius of the nth orbit, \( n \) is the principal quantum number, and \( Z \) is the atomic number of the element.

2. **Determine the Values:**
For hydrogen (H), the atomic number \( Z = 1 \). We are interested in the second orbit, so \( n = 2 \).

3. **Substitute the Values into the Formula:**
Substitute \( n = 2 \) and \( Z = 1 \) into the formula:
\[ r_2 = \frac{0.529 \times 2^2}{1} \]

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

5. **Calculate the Radius:**
Now substitute \( 4 \) back into the equation:
\[ r_2 = 0.529 \times 4 = 2.116 \text{ angstroms} \]

6. **Convert Angstroms to Nanometers:**
Since 1 angstrom = \( 10^{-10} \) meters and 1 nanometer = \( 10^{-9} \) meters, we convert angstroms to nanometers:
\[ 2.116 \text{ angstroms} = 2.116 \times 10^{-10} \text{ meters} = 0.2116 \text{ nanometers} \]

7. **Final Answer:**
Therefore, the radius of the second Bohr orbit of the hydrogen atom is:
\[ \boxed{0.2116 \text{ nanometers}} \]