For hydrogen atom, Rydberg constant `(R_(H))` is `xm^(-1)`. Then for `He^(+)` ion, the corresponding value of this constant will be

Options

A. `x cm^(-1)`
B. `400 x cm^(-1)`
C. `4x cm^(-1)`
D. `0.04 x cm^(-1)`

Explanation

To find the Rydberg constant for the He\(^+\) ion, we start with the known relationship between the Rydberg constant for hydrogen (R\(_H\)) and the atomic number (Z) of the element.

### Step-by-Step Solution:

1. **Understanding the Rydberg Constant**:
The Rydberg constant for hydrogen (R\(_H\)) is given as \(x \, m^{-1}\). The Rydberg constant is proportional to the square of the atomic number (Z) of the element:
\[ R = R_H \cdot Z^2 \]

2. **Identify the Atomic Number**:
For hydrogen (H), the atomic number \(Z_H = 1\). For the helium ion (He\(^+\)), the atomic number \(Z_{He} = 2\).

3. **Calculate the Rydberg Constant for He\(^+\)**:
Using the formula for the Rydberg constant:
\[ R_{He^+} = R_H \cdot Z_{He}^2 = R_H \cdot 2^2 = R_H \cdot 4 \]
Substituting \(R_H = x \, m^{-1}\):
\[ R_{He^+} = 4x \, m^{-1} \]

4. **Convert to Centimeter Inverse**:
Since the question may require the answer in centimeters, we convert \(m^{-1}\) to \(cm^{-1}\):
\[ 1 \, m^{-1} = 100 \, cm^{-1} \]
Thus,
\[ R_{He^+} = 4x \cdot 100 \, cm^{-1} = 400x \, cm^{-1} \]

5. **Final Answer**:
Therefore, the Rydberg constant for the He\(^+\) ion is:
\[ R_{He^+} = 400x \, cm^{-1} \]