The radius of the second Bohr orbit for hydrogen atom is :
(Planck's constant, `h = 6.6262 xx 10^(-34) Js`, mass of electron = `9.1091 xx 10^(-31) kg`, charge of electron `e = 1.60210 xx 10^(-19) C`, permittivity of vaccum `in_0 = 8.854185 xx 10^(-12) kg^(-1) m^(-3) A^2)`

Options

A. `1.65 Å`
B. `4.76 Å`
C. `0.529 Å`
D. `2.12 Å`

Explanation

To find the radius of the second Bohr orbit for a hydrogen atom, we can use the formula derived from Bohr's model of the atom. The radius of the nth orbit for hydrogen-like atoms is given by:

\[ r_n = \frac{0.529 \, n^2}{Z} \, \text{Å} \]

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, \( Z = 1 \)),
- \( 0.529 \) is a constant in angstroms.

### Step-by-Step Solution:

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

2. **Substitute the values into the formula**:
\[ r_2 = \frac{0.529 \times n^2}{Z} \]
\[ r_2 = \frac{0.529 \times 2^2}{1} \]

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

4. **Substitute \( 4 \) back into the equation**:
\[ r_2 = \frac{0.529 \times 4}{1} \]
\[ r_2 = 0.529 \times 4 \]

5. **Perform the multiplication**:
\[ r_2 = 2.116 \, \text{Å} \]

6. **Round the result**:
- The radius can be approximated to \( 2.12 \, \text{Å} \).

### Final Answer:
The radius of the second Bohr orbit for the hydrogen atom is approximately \( 2.12 \, \text{Å} \).