Radius of Bohr's orbit of hydrogen atom is

Options

A. `0.24 Å`
B. `0.48 Å`
C. `0.53 Å`
D. `1.06 Å`

Answer

To find the radius of Bohr's orbit for a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The formula for the radius of Bohr's orbit is given by:
\[ r_n = \frac{0.529 \, \text{Å} \cdot n^2}{Z} \]
where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number,
- \( Z \) is the atomic number.

2. **Identify Values for Hydrogen Atom**: For a hydrogen atom:
- The principal quantum number \( n = 1 \).
- The atomic number \( Z = 1 \).

3. **Substitute Values into the Formula**: Now, substituting the values into the formula:
\[ r_1 = \frac{0.529 \, \text{Å} \cdot (1)^2}{1} \]

4. **Calculate the Radius**: Simplifying the equation:
\[ r_1 = 0.529 \, \text{Å} \]

5. **Compare with Given Options**: The calculated radius is approximately \( 0.529 \, \text{Å} \). Now, let's compare this with the given options:
- Option 1: \( 0.24 \, \text{Å} \) (No)
- Option 2: \( 0.48 \, \text{Å} \) (No)
- Option 3: \( 0.53 \, \text{Å} \) (Yes, approximately equal)
- Option 4: \( 5.29 \, \text{Å} \) (No)

6. **Conclusion**: Therefore, the correct answer is:
\[ \text{Radius of Bohr's orbit of hydrogen atom is } 0.53 \, \text{Å} \text{ (Option 3)} \]