The velocity of an electron in the first orbit of `H` atom is `v` . The velocity of an electron in the second orbit of `He^(+)` is

Options

A. `2 v`
B. v
C. `(v)/(2)`
D. `(v)/(4)`

Explanation

To find the velocity of an electron in the second orbit of the He\(^+\) ion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Velocity in Orbits**:
The velocity of an electron in the nth orbit of a hydrogen-like atom is given by the formula:
\[ V_n = V_0 \cdot \frac{Z}{n} \]
where:
- \(V_n\) is the velocity in the nth orbit,
- \(V_0\) is a constant for the atom,
- \(Z\) is the atomic number,
- \(n\) is the principal quantum number (orbit number).

2. **Determine Values for Hydrogen Atom**:
For the hydrogen atom (H):
- The atomic number \(Z = 1\).
- For the first orbit, \(n = 1\).
- Given that the velocity of the electron in the first orbit of hydrogen is \(V\), we can write:
\[ V_1 = V_0 \cdot \frac{1}{1} = V_0 \]
Thus, we have:
\[ V_0 = V \]

3. **Determine Values for Helium Ion (He\(^+\))**:
For the helium ion (He\(^+\)):
- The atomic number \(Z = 2\).
- We want to find the velocity in the second orbit, so \(n = 2\).

4. **Apply the Formula for He\(^+\)**:
Using the formula for the second orbit:
\[ V_2 = V_0 \cdot \frac{Z}{n} \]
Substituting the known values:
\[ V_2 = V \cdot \frac{2}{2} \]

5. **Simplify the Expression**:
\[ V_2 = V \cdot 1 = V \]

### Conclusion:
The velocity of an electron in the second orbit of He\(^+\) is \(V\).