The radius of the first Bohr orbit for `H^(o+)` is

Options

A. `0.529 Å`
B. `0.264 Å`
C. `0.132 Å`
D. `0.176 Å`

Explanation

To find the radius of the first Bohr orbit for the hydrogen ion \( H^{o+} \), we can use the formula derived from the Bohr model of the atom:

### Step-by-Step Solution:

1. **Identify the Formula**: The radius \( r_n \) of the nth Bohr orbit is given by the formula:
\[ r_n = 0.529 \times \frac{n^2}{Z} \text{ angstroms} \]
where:
- \( n \) is the principal quantum number (orbital number),
- \( Z \) is the atomic number.

2. **Determine Values for Hydrogen**: For the hydrogen atom:
- The atomic number \( Z \) is 1 (since hydrogen has one proton).
- For the first orbit, the principal quantum number \( n \) is 1.

3. **Substitute the Values into the Formula**:
\[ r_1 = 0.529 \times \frac{1^2}{1} \]
This simplifies to:
\[ r_1 = 0.529 \times 1 = 0.529 \text{ angstroms} \]

4. **Conclusion**: Therefore, the radius of the first Bohr orbit for \( H^{o+} \) is:
\[ \boxed{0.529 \text{ angstroms}} \]