Radius of first orbit of hydrogen is `0.53 Å`. The radius in fourth orbit is:

Options

A. 8.48 Å
B. 1.06 Å
C. 0.13 Å
D. 2.22 Å

Answer

To find the radius of the fourth orbit of hydrogen, we can use the formula that relates the radius of the orbits to the principal quantum number (n). The radius of the nth orbit is given by the formula:

\[ r_n = n^2 \cdot r_1 \]

where:
- \( r_n \) is the radius of the nth orbit,
- \( r_1 \) is the radius of the first orbit (which is given as 0.53 Å),
- \( n \) is the principal quantum number (1 for the first orbit, 2 for the second, and so on).

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius of the first orbit, \( r_1 = 0.53 \) Å.
- We need to find the radius of the fourth orbit, so \( n = 4 \).

2. **Use the formula for the radius of the nth orbit:**
\[ r_n = n^2 \cdot r_1 \]

3. **Substitute the values into the formula:**
\[ r_4 = 4^2 \cdot r_1 \]
\[ r_4 = 16 \cdot 0.53 \, \text{Å} \]

4. **Calculate \( r_4 \):**
\[ r_4 = 16 \cdot 0.53 = 8.48 \, \text{Å} \]

5. **Final answer:**
The radius of the fourth orbit of hydrogen is \( 8.48 \) Å.