If velocity of an electron in 1st orbit of H atoms is V , what will be the velocity in 3rd orbit of `Li^(2+)` ?

Options

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

Explanation

To solve the problem, we need to find the velocity of an electron in the 3rd orbit of the lithium ion \( Li^{2+} \) given that the velocity of an electron in the 1st orbit of the hydrogen atom is \( V \).

### Step-by-Step Solution:

1. **Understanding the Formula for Velocity**:
The velocity of an electron in an orbit of a hydrogen-like atom can be expressed as:
\[ v \propto \frac{Z}{n} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number (the orbit number).

2. **Determine Values for Hydrogen**:
For the hydrogen atom (\( H \)):
- Atomic number \( Z_H = 1 \)
- Principal quantum number for the 1st orbit \( n_H = 1 \)

Thus, the velocity of the electron in the 1st orbit of hydrogen is:
\[ v_H \propto \frac{1}{1} = 1 \]
We denote this velocity as \( V \).

3. **Determine Values for Lithium Ion**:
For the lithium ion (\( Li^{2+} \)):
- Atomic number \( Z_{Li} = 3 \)
- Principal quantum number for the 3rd orbit \( n_{Li} = 3 \)

Thus, the velocity of the electron in the 3rd orbit of lithium is:
\[ v_{Li} \propto \frac{Z_{Li}}{n_{Li}} = \frac{3}{3} = 1 \]

4. **Comparing Velocities**:
Since both velocities are proportional to 1, we can conclude:
\[ v_{Li} = V \]
Therefore, the velocity of the electron in the 3rd orbit of \( Li^{2+} \) is equal to the velocity of the electron in the 1st orbit of hydrogen.

### Final Answer:
The velocity of the electron in the 3rd orbit of \( Li^{2+} \) is \( V \).

---