If the radius of the first Bohr orbit of the H atom is r then for the `Li^(2+)` ion it will be:

Options

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

Explanation

To solve the problem of finding the radius of the first Bohr orbit of the `Li^(2+)` ion given that the radius of the first Bohr orbit of the hydrogen atom (H) is \( r \), we will use Bohr's formula for the radius of the nth orbit:

### Step-by-Step Solution:

1. **Understand the Formula**:
The radius of the nth Bohr orbit is given by the formula:
\[ R_n = \frac{0.53 \, n^2}{Z} \, \text{Å} \]
where \( R_n \) is the radius of the nth orbit, \( n \) is the principal quantum number, and \( Z \) is the atomic number.

2. **Identify the Parameters for Hydrogen (H)**:
For hydrogen (H), which has an atomic number \( Z = 1 \) and for the first orbit \( n = 1 \):
\[ R_1(H) = \frac{0.53 \times 1^2}{1} = 0.53 \, \text{Å} \]
This is given as \( r \).

3. **Identify the Parameters for Lithium Ion (Li²⁺)**:
For the lithium ion \( Li^{2+} \), it has an atomic number \( Z = 3 \) and for the first orbit \( n = 1 \):
\[ R_1(Li^{2+}) = \frac{0.53 \times 1^2}{3} = \frac{0.53}{3} \, \text{Å} \]

4. **Relate the Radius of Li²⁺ to r**:
Since we know that the radius of the first Bohr orbit of hydrogen is \( r \), we can express the radius of the Li²⁺ ion in terms of \( r \):
\[ R_1(Li^{2+}) = \frac{r}{3} \]

5. **Final Answer**:
Therefore, the radius of the first Bohr orbit of the `Li^(2+)` ion is:
\[ \frac{r}{3} \]