The radius of first orbit of hydrogen is `0.53 Å. The radius of second orbit would be :

Options

A. `1.06 Å`
B. `0.26 Å`
C. `0.53 Å`
D. `2.12 Å`

Explanation

To find the radius of the second orbit of hydrogen, we can use Bohr's model of the atom. According to this model, the radius of the nth orbit (Rn) is given by the formula:

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

where:
- \( R_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (1 for the first orbit, 2 for the second orbit, etc.),
- \( Z \) is the atomic number of the element (for hydrogen, \( Z = 1 \)).

### Step-by-Step Solution:

1. **Identify the values:**
- For hydrogen, the atomic number \( Z = 1 \).
- We want to find the radius of the second orbit, so \( n = 2 \).

2. **Substitute the values into the formula:**
\[ R_2 = \frac{0.529 \, \text{Å} \cdot (2^2)}{1} \]

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

4. **Substitute \( n^2 \) back into the equation:**
\[ R_2 = \frac{0.529 \, \text{Å} \cdot 4}{1} \]

5. **Perform the multiplication:**
\[ R_2 = 0.529 \, \text{Å} \cdot 4 = 2.116 \, \text{Å} \]

6. **Final result:**
The radius of the second orbit of hydrogen is \( 2.116 \, \text{Å} \).

### Summary:
The radius of the second orbit for hydrogen is \( 2.116 \, \text{Å} \).