The radius of the first Bohr orbit of hydrogen atom is `0.529Å`. The radius of the third orbit of H will be:

Options

A. `8.46Å`
B. `0.705Å`
C. `1.59Å`
D. `4.76Å`

Explanation

To find the radius of the third orbit of a hydrogen atom, we will use the formula for the radius of the nth orbit in a hydrogen atom, which is given by:

\[ r_n = r_0 \cdot \frac{n^2}{Z} \]

Where:
- \( r_n \) is the radius of the nth orbit,
- \( r_0 \) is the radius of the first orbit (which is given as \( 0.529 \, \text{Å} \)),
- \( n \) is the principal quantum number (which is 3 for the third orbit),
- \( Z \) is the atomic number (which is 1 for hydrogen).

### Step-by-Step Solution:

1. **Identify the values:**
- \( r_0 = 0.529 \, \text{Å} \)
- \( n = 3 \)
- \( Z = 1 \)

2. **Substitute the values into the formula:**
\[ r_3 = r_0 \cdot \frac{n^2}{Z} \]
\[ r_3 = 0.529 \cdot \frac{3^2}{1} \]

3. **Calculate \( n^2 \):**
\[ n^2 = 3^2 = 9 \]

4. **Substitute \( n^2 \) back into the equation:**
\[ r_3 = 0.529 \cdot 9 \]

5. **Perform the multiplication:**
\[ r_3 = 4.761 \, \text{Å} \]

### Final Answer:
The radius of the third orbit of the hydrogen atom is approximately \( 4.76 \, \text{Å} \).

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