Question

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

• A. $19.53 \times 10^{-18} \text{ J}$
• B. $19.54 \times 10^{-18} \text{ J}$
• C. $19.56 \times 10^{-18} \text{ J}$
• D. $19.55 \times 10^{-18} \text{ J}$

Answer 1

The Correct Option is A

Step 1: Recall the energy formula for hydrogen-like atoms.
$E_n = -E_H \cdot \frac{Z^2}{n^2}$. Ionisation energy is the energy required to remove the electron: $IE = E_H \cdot \frac{Z^2}{n^2}$.

Step 2: Identify constants for Lithium.
$Z = 3$. For ground state $n = 1$.
$E_H = 2.17 \times 10^{-18} \text{ J}$.

Step 3: Calculate the energy required.
$E = 2.17 \times 10^{-18} \times \frac{3^2}{1^2} = 9 \times 2.17 \times 10^{-18} = 19.53 \times 10^{-18} \text{ J}$.

Final Answer: Option (1).