What is the radius of the second orbit of helium atom , on the basis of Bohr's atom model ?

Options

A. 1.06 Å
B. 2.12 Å
C. 0.265 Å
D. 0.53 Å

Explanation

To find the radius of the second orbit of a helium atom based on Bohr's atomic model, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: According to Bohr's atomic model, the radius of the nth orbit (Rn) is given by the formula:
\[ R_n = \frac{n^2 R_0}{Z} \]
where:
- \( R_n \) = radius of the nth orbit
- \( n \) = principal quantum number (for the second orbit, \( n = 2 \))
- \( R_0 \) = Bohr's radius (approximately \( 0.53 \) Å)
- \( Z \) = atomic number of the element (for helium, \( Z = 2 \))

2. **Identify the Values**:
- For helium, \( Z = 2 \)
- \( R_0 = 0.53 \) Å
- For the second orbit, \( n = 2 \)

3. **Substitute the Values into the Formula**:
\[ R_2 = \frac{2^2 \times R_0}{Z} \]
Substituting the known values:
\[ R_2 = \frac{2^2 \times 0.53 \, \text{Å}}{2} \]

4. **Calculate**:
- First, calculate \( 2^2 = 4 \):
\[ R_2 = \frac{4 \times 0.53 \, \text{Å}}{2} \]
- Now, multiply \( 4 \times 0.53 \):
\[ 4 \times 0.53 = 2.12 \, \text{Å} \]
- Finally, divide by \( 2 \):
\[ R_2 = \frac{2.12 \, \text{Å}}{2} = 1.06 \, \text{Å} \]

5. **Conclusion**: Therefore, the radius of the second orbit of the helium atom is:
\[ R_2 = 1.06 \, \text{Å} \]

### Final Answer:
The radius of the second orbit of the helium atom is **1.06 Å**.