Question:
Ratio of wavelengths for \(2\to1\) transition in Li\(^+\), He\(^+\), and H is
Ratio of wavelengths for \(2\to1\) transition in Li\(^+\), He\(^+\), and H is
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Hydrogen-like atoms $\Rightarrow$ wavelength inversely proportional to \(Z^2\).
Updated On: Apr 23, 2026
- \(1:2:3\)
- \(1:4:9\)
- \(4:9:36\)
- \(3:2:1\)
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The Correct Option is C
Solution and Explanation
Concept:
\[
\lambda \propto \frac{1}{Z^2}
\]
Step 1: Atomic numbers \[ Li^+ = 3,\quad He^+ = 2,\quad H = 1 \]
Step 2: Ratio \[ \lambda \propto \frac{1}{9} : \frac{1}{4} : 1 \] Multiply by 36: \[ 4 : 9 : 36 \]
Step 1: Atomic numbers \[ Li^+ = 3,\quad He^+ = 2,\quad H = 1 \]
Step 2: Ratio \[ \lambda \propto \frac{1}{9} : \frac{1}{4} : 1 \] Multiply by 36: \[ 4 : 9 : 36 \]
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