Question

Assuming the validity of Bohr's atomic model for hydrogen-like ions, the radius of $ \text{Li}^{2+} $ ion in its ground state is given by $ \frac{1}{X} a_0 $, where $ a_0 $ is the first Bohr's radius.

• A. 2
• B. 1
• C. 3
• D. 9

Hint:

For hydrogen-like ions, the radius decreases as the atomic number increases, following the formula \( r = r_0 \frac{n^2}{z} \).

Answer 1

The Correct Option is C

The radius for a hydrogen-like ion is given by the formula: \[ r = r_0 \frac{n^2}{z} \] where \( r_0 \) is the radius for hydrogen, \( n \) is the principal quantum number, and \( z \) is the atomic number. For \( \text{Li}^{2+} \), we have \( n = 1 \) and \( z = 3 \), so the radius is: \[ r = r_0 \frac{1^2}{3} = \frac{r_0}{3} \] Thus, \( X = 3 \).