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:

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

Where:
- \( r_n \) is the radius of the nth orbit for the atom in question.
- \( r_H \) is the radius of the first orbit of the hydrogen atom.
- \( n \) is the principal quantum number (which is 1 for the first orbit).
- \( Z \) is the atomic number of the atom.

### Step-by-Step Solution:

1. **Identify Given Values**:
- The radius of the first orbit of hydrogen (\( r_H \)) is given as \( 0.52 \times 10^{-8} \) cm.
- For helium, the atomic number \( Z = 2 \).
- The principal quantum number for the first orbit \( n = 1 \).

2. **Substitute Values into the Formula**:
\[ r_1 = \frac{r_H \cdot n^2}{Z} \]
Substituting the known values:
\[ r_1 = \frac{0.52 \times 10^{-8} \, \text{cm} \cdot 1^2}{2} \]

3. **Calculate the Radius**:
\[ r_1 = \frac{0.52 \times 10^{-8} \, \text{cm}}{2} = 0.26 \times 10^{-8} \, \text{cm} \]

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

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