The radius of the first orbit of hydrogen atom is `0.52xx10^(-8)cm`. The radius of the first orbit of helium atom is

Options

A. `0.26xx10^(-8)cm`
B. `0.52xx10^(-8)cm`
C. `1.04xx10^(-8)cm`
D. `2.08xx10^(-8)cm`

Answer

To find the radius of the first orbit of the helium atom, we can use the formula for the radius of the nth Bohr orbit, which is given by:

\[ r_n = \frac{n^2 \cdot a_0}{Z} \]

Where:
- \( r_n \) is the radius of the nth orbit,
- \( a_0 \) is the radius of the first orbit of hydrogen (which is given as \( 0.52 \times 10^{-8} \) cm),
- \( n \) is the principal quantum number (which is 1 for the first orbit),
- \( Z \) is the atomic number (which is 2 for helium).

### Step-by-step Solution:

1. **Identify the values:**
- For hydrogen, \( a_0 = 0.52 \times 10^{-8} \) cm.
- For helium, \( Z = 2 \).
- For the first orbit, \( n = 1 \).

2. **Substitute the values into the formula:**
\[ r_1 = \frac{1^2 \cdot (0.52 \times 10^{-8})}{2} \]

3. **Calculate \( 1^2 \):**
\[ 1^2 = 1 \]

4. **Substitute \( 1 \) back into the equation:**
\[ r_1 = \frac{1 \cdot (0.52 \times 10^{-8})}{2} \]

5. **Perform the division:**
\[ r_1 = \frac{0.52 \times 10^{-8}}{2} = 0.26 \times 10^{-8} \text{ cm} \]

6. **Final result:**
The radius of the first orbit of the helium atom is:
\[ r_1 = 0.26 \times 10^{-8} \text{ cm} \]

### Conclusion:
The radius of the first orbit of the helium atom is \( 0.26 \times 10^{-8} \) cm.