Determine Bohr's radius of `Li^(2+)` ion for n = 2. Given (Bohr's radius of H-atom = `a_0`)

Options

A. `(3a_0)/4`
B. `(4a_0)/3`
C. `(a_0)/3`
D. `(16a_0)/9`

Explanation

To determine the Bohr's radius of the `Li^(2+)` ion for n = 2, we can use the formula for the radius of the nth orbit in a hydrogen-like atom:

### Step-by-Step Solution:

1. **Understand the Formula**: The formula for the radius of the nth orbit in a hydrogen-like atom is given by:
\[ R_n = \frac{a_0 \cdot n^2}{Z} \]
where:
- \( R_n \) is the radius of the nth orbit,
- \( a_0 \) is the Bohr radius of the hydrogen atom (approximately 0.529 Å),
- \( n \) is the principal quantum number,
- \( Z \) is the atomic number of the ion.

2. **Identify the Values**: For the `Li^(2+)` ion:
- The atomic number \( Z \) of lithium (Li) is 3.
- We are calculating for \( n = 2 \).

3. **Substitute the Values into the Formula**:
\[ R_2 = \frac{a_0 \cdot (2^2)}{3} \]
\[ R_2 = \frac{a_0 \cdot 4}{3} \]

4. **Express in Terms of \( a_0 \)**:
Since \( a_0 \) is the Bohr radius of hydrogen, we can express the radius for `Li^(2+)` as:
\[ R_2 = \frac{4}{3} a_0 \]

5. **Final Result**: Therefore, the Bohr's radius of the `Li^(2+)` ion for \( n = 2 \) is:
\[ R_2 = \frac{4}{3} a_0 \]