Question

What is the energy (in J atom\(^{-1}\)) required for the following process?} \[ Li^{2+}(g) \rightarrow Li^{3+}(g) + e^{-} \] (Take the ionization energy for the H atom in the ground state as \(2.18 \times 10^{-18}\) J atom\(^{-1}\)).

• A. \(8.72 \times 10^{-18}\)
• B. \(1.962 \times 10^{-18}\)
• C. \(1.962 \times 10^{-17}\)
• D. \(6.54 \times 10^{-17}\)

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
\(Li^{2+}\) is a hydrogen-like species because it contains only one electron. The ionization energy for any hydrogen-like species (with atomic number Z) is related to the ionization energy of hydrogen through the square of its atomic number.
Step 2: Key Formula or Approach:
Ionization Energy (\(IE\)) = \(IE_H \times Z^2\)
For Lithium (\(Li\)), \(Z = 3\).
Step 3: Detailed Explanation:
The process \(Li^{2+}(g) \rightarrow Li^{3+}(g) + e^-\) corresponds to the 3rd ionization energy of Lithium.
Given ionization energy of Hydrogen \(IE_H = 2.18 \times 10^{-18} \text{ J atom}^{-1}\).
Atomic number of Lithium, \(Z = 3\).
Energy required = \(2.18 \times 10^{-18} \times (3)^2\)
\[ \text{Energy} = 2.18 \times 10^{-18} \times 9 \]
\[ \text{Energy} = 19.62 \times 10^{-18} \text{ J atom}^{-1} \]
\[ \text{Energy} = 1.962 \times 10^{-17} \text{ J atom}^{-1} \]
Step 4: Final Answer:
The energy required is \(1.962 \times 10^{-17} \text{ J atom}^{-1}\).