If velocity of an electron in `I` orbit of `H` atom is `V`, what will be the velocity of electron in `3^(rd)` orbit of `Li^(2+)`

Options

A. `V`
B. `V//3`
C. `3V`
D. `9V`

Explanation

To find the velocity of an electron in the 3rd orbit of the Li²⁺ ion when the velocity of an electron in the 1st orbit of the H atom is given as V, we can use the formula for the velocity of an electron in a hydrogen-like atom.

### Step-by-Step Solution:

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

2. **Identify the Values for Hydrogen (H):**
For the hydrogen atom (H), which has \( Z = 1 \) and \( n = 1 \):
\[ V_1 = k \cdot \frac{1}{1} = k \]
Given that this velocity is \( V \), we can say:
\[ k = V \]

3. **Identify the Values for Lithium Ion (Li²⁺):**
For the lithium ion (Li²⁺), which has \( Z = 3 \) and we need to find the velocity for \( n = 3 \):
\[ V_3 = k \cdot \frac{3}{3} = k \]
Substituting \( k = V \):
\[ V_3 = V \cdot \frac{3}{3} = V \]

4. **Conclusion:**
The velocity of the electron in the 3rd orbit of the Li²⁺ ion is equal to \( V \).

### Final Answer:
The velocity of the electron in the 3rd orbit of Li²⁺ is \( V \).