Ratio of radii of second and first Bohr orbits of H atom

Options

A. 2
B. 4
C. 3
D. 5

Explanation

To find the ratio of the radii of the second and first Bohr orbits of a hydrogen atom (H atom), we can use the formula for the radius of the nth Bohr orbit:

\[ r_n = 0.529 \times \frac{n^2}{Z} \]

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),
- \( Z \) is the atomic number (1 for hydrogen).

### Step-by-Step Solution:

1. **Identify the values for the first and second orbits:**
- For the first orbit (n = 1):
\[ r_1 = 0.529 \times \frac{1^2}{1} = 0.529 \, \text{Å} \]
- For the second orbit (n = 2):
\[ r_2 = 0.529 \times \frac{2^2}{1} = 0.529 \times 4 = 2.116 \, \text{Å} \]

2. **Set up the ratio of the radii:**
- The ratio of the radius of the second orbit to the first orbit is given by:
\[ \text{Ratio} = \frac{r_2}{r_1} = \frac{0.529 \times 4}{0.529} = 4 \]

3. **Conclusion:**
- The ratio of the radii of the second and first Bohr orbits of the hydrogen atom is:
\[ \text{Ratio} = 4 \]

### Final Answer:
The ratio of the radii of the second and first Bohr orbits of the H atom is **4**.