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 Bohr orbit of a hydrogen atom, we can use the formula for the radius of the nth Bohr orbit:

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

Where:
- \( R_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (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**:
- For hydrogen, \( Z = 1 \).
- For the third orbit, \( n = 3 \).

2. **Substitute the values into the formula**:
\[ R_3 = \frac{0.529 \, (3^2)}{1} \, \text{Å} \]

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

4. **Substitute \( n^2 \) back into the equation**:
\[ R_3 = 0.529 \times 9 \, \text{Å} \]

5. **Perform the multiplication**:
\[ R_3 = 4.761 \, \text{Å} \]

### Final Answer:
The radius of the third Bohr orbit of the hydrogen atom is **4.761 Å**.

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