Radius of 3rd Bohr orbit is

Options

A. 6.529 Å
B. 2.116 Å
C. 4.761 Å
D. 8.464 Å

Answer

To find the radius of the 3rd Bohr orbit for a hydrogen atom, we can use the formula for the radius of the nth orbit in a hydrogen-like atom:

\[ R_n = n^2 \cdot z \cdot R_0 \]

Where:
- \( R_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (for the 3rd orbit, \( n = 3 \)),
- \( z \) is the atomic number (for hydrogen, \( z = 1 \)),
- \( R_0 \) is the Bohr radius, which is approximately \( 0.529 \, \text{Å} \) or \( 0.529 \times 10^{-10} \, \text{m} \).

### Step-by-step Solution:

1. **Identify the values**:
- For the 3rd orbit, \( n = 3 \).
- For hydrogen, \( z = 1 \).
- The Bohr radius \( R_0 = 0.529 \, \text{Å} = 0.529 \times 10^{-10} \, \text{m} \).

2. **Substitute the values into the formula**:
\[ R_3 = n^2 \cdot z \cdot R_0 \]
\[ R_3 = 3^2 \cdot 1 \cdot 0.529 \times 10^{-10} \, \text{m} \]

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

4. **Multiply the values**:
\[ R_3 = 9 \cdot 0.529 \times 10^{-10} \, \text{m} \]
\[ R_3 = 4.761 \times 10^{-10} \, \text{m} \]

5. **Convert to Angstroms**:
Since \( 1 \, \text{Å} = 10^{-10} \, \text{m} \):
\[ R_3 = 4.761 \, \text{Å} \]

### Final Answer:
The radius of the 3rd Bohr orbit is approximately \( 4.761 \, \text{Å} \).

---