The radius of 2nd Bohr 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. **Understand the Formula for Bohr Orbit Radius:**
The radius of the nth Bohr orbit (Rn) is given by the formula:
\[ R_n = \frac{n^2 \cdot 0.53}{Z} \text{ angstroms} \]
where:
- \( n \) is the principal quantum number (orbit number),
- \( Z \) is the atomic number of the element (for hydrogen, \( Z = 1 \)),
- \( 0.53 \) is a constant representing the radius of the first Bohr orbit in angstroms.

2. **Substituting the Values:**
For the second Bohr orbit, \( n = 2 \) and for hydrogen, \( Z = 1 \). We can substitute these values into the formula:
\[ R_2 = \frac{2^2 \cdot 0.53}{1} \]

3. **Calculating the Radius:**
Now calculate:
\[ R_2 = \frac{4 \cdot 0.53}{1} = 4 \cdot 0.53 = 2.12 \text{ angstroms} \]

4. **Converting Angstroms to Nanometers:**
Since the answer is required in nanometers, we need to convert angstroms to nanometers. We know that:
\[ 1 \text{ angstrom} = 10^{-10} \text{ meters} \]
and
\[ 1 \text{ nanometer} = 10^{-9} \text{ meters} \]
Therefore, to convert angstroms to nanometers, we can use the conversion:
\[ R_2 = 2.12 \text{ angstroms} = 2.12 \times 10^{-10} \text{ meters} \]
To convert to nanometers:
\[ R_2 = 2.12 \times 10^{-10} \text{ meters} \times \frac{1 \text{ nanometer}}{10^{-9} \text{ meters}} = 0.212 \text{ nanometers} \]

5. **Final Answer:**
Thus, the radius of the second Bohr orbit of the hydrogen atom is:
\[ R_2 = 0.212 \text{ nanometers} \]