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.

Question

$Li^{+2} \longrightarrow Li^{+3} + e^-$ :
Energy required for this process.
Given ionisation energy for ground state of hydrogen atom is $2.17 \times 10^{-18} \text{ J}$.

Answer 1

The radius of a hydrogen-like ion is calculated using the formula:\[r = r_0 \frac{n^2}{z}\]Here, $ r_0 $ represents the radius of hydrogen, $ n $ is the principal quantum number, and $ z $ is the atomic number. For the ion $ \text{Li}^{2+} $, with $ n = 1 $ and $ z = 3 $, the radius is determined as follows:\[r = r_0 \frac{1^2}{3} = \frac{r_0}{3}\]Therefore, $ X = 3 $.

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.

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The Correct Option is C

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