JEE Mains · Chemistry · STD 11 - 2. structure of atom

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 \(6.54 \times 10^{-17}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1.962 \times 10^{-17}\)

Step-by-step Solution

Detailed explanation

The given process \(Li^{2+}(g) \rightarrow Li^{3+}(g) + e^-\) represents the ionization of the hydrogen-like ion \(Li^{2+}\) from its ground state. The ionization energy for a hydrogen-like species is given by the formula: \(IE = IE_{H} \times Z^2\) For \(Li^{2+}\), the atomic…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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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\(^{-1}\))

Step-by-step Solution

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\(^{-1}\))