For hydrogen atom, radius of first Bohr orbit would be

Options

A. `9.63xx10^(-10) m`
B. `0.43xx10^(-10)m`
C. `0.50xx10^(-10)m`
D. `0.53xx10^(-10)m`

Explanation

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

\[ r_n = \frac{n^2 h^2}{4 \pi^2 m e^2 z} \]

Where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (for the first orbit, \( n = 1 \)),
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( m \) is the mass of the electron (\( 9.1 \times 10^{-31} \, \text{kg} \)),
- \( e \) is the charge of the electron (\( 1.6 \times 10^{-19} \, \text{C} \)),
- \( z \) is the atomic number (for hydrogen, \( z = 1 \)).

### Step-by-Step Solution:

1. **Identify Constants**:
- Planck's constant, \( h = 6.626 \times 10^{-34} \, \text{J s} \)
- Mass of electron, \( m = 9.1 \times 10^{-31} \, \text{kg} \)
- Charge of electron, \( e = 1.6 \times 10^{-19} \, \text{C} \)
- For hydrogen, \( n = 1 \) and \( z = 1 \).

2. **Substitute Values into the Formula**:
\[ r_1 = \frac{1^2 \cdot (6.626 \times 10^{-34})^2}{4 \pi^2 \cdot (9.1 \times 10^{-31}) \cdot (1.6 \times 10^{-19})^2 \cdot 1} \]

3. **Calculate \( (6.626 \times 10^{-34})^2 \)**:
\[ (6.626 \times 10^{-34})^2 = 4.39 \times 10^{-67} \, \text{J}^2 \text{s}^2 \]

4. **Calculate \( (1.6 \times 10^{-19})^2 \)**:
\[ (1.6 \times 10^{-19})^2 = 2.56 \times 10^{-38} \, \text{C}^2 \]

5. **Calculate the Denominator**:
\[ 4 \pi^2 \cdot (9.1 \times 10^{-31}) \cdot (2.56 \times 10^{-38}) \]
- First, calculate \( 4 \pi^2 \approx 39.478 \).
- Then, \( 39.478 \cdot 9.1 \times 10^{-31} \cdot 2.56 \times 10^{-38} \approx 9.73 \times 10^{-67} \).

6. **Final Calculation of Radius**:
\[ r_1 = \frac{4.39 \times 10^{-67}}{9.73 \times 10^{-67}} \approx 0.451 \times 10^{-10} \, \text{m} \approx 0.53 \, \text{Å} \]

### Conclusion:
The radius of the first Bohr orbit for a hydrogen atom is approximately \( 0.53 \times 10^{-10} \, \text{m} \) or \( 0.53 \, \text{Å} \).