The radius of the second Bohr orbit for hydrogen atom is [Planck's constant `(h)=6.6262xx10^(-34)* Js`, mass of electron=`9.1091xx10^(-31)kg`, charge of electron `=1.60210xx10^(-19)C`, permittivity of vacuum `(in_(0))=8.854185xx10^(-12)kg^(-1)*m^(-3)*A^(2)`]-

Options

A. 4.76Å
B. 0.529Å
C. 2.12Å
D. 1.65Å

Answer

To find the radius of the second Bohr orbit for a hydrogen atom, we can use the formula derived from Bohr's theory. The radius of the nth orbit (Rn) is given by:

\[ R_n = n^2 \cdot a_0 \]

where:
- \( n \) is the principal quantum number (for the second orbit, \( n = 2 \)),
- \( a_0 \) is the Bohr radius, which is approximately \( 0.53 \, \text{Å} \) (angstroms) or \( 0.53 \times 10^{-10} \, \text{m} \).

### Step-by-Step Solution:

1. **Identify the values**:
- For the hydrogen atom, the atomic number \( Z = 1 \).
- The principal quantum number for the second orbit \( n = 2 \).
- The Bohr radius \( a_0 = 0.53 \, \text{Å} \).

2. **Use the formula for the radius of the nth orbit**:
\[ R_n = n^2 \cdot a_0 \]

3. **Substitute the values into the formula**:
\[ R_2 = 2^2 \cdot 0.53 \, \text{Å} \]

4. **Calculate \( R_2 \)**:
\[ R_2 = 4 \cdot 0.53 \, \text{Å} = 2.12 \, \text{Å} \]

5. **Final Result**:
The radius of the second Bohr orbit for the hydrogen atom is \( 2.12 \, \text{Å} \).