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Question

Hydrogen (H), deuterium (D), singly ionized helium (He+) and doubly ionized lithium (Li++) all have one electron around the nucleus. Consider n = 2 to n = 1 transition. The wavelengths of emitted radiations are λ1,λ2,λ3 and λ4 respectively. Then approximately

A
λ1=λ2=4λ3=9λ4
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B
4λ1=2λ2=2λ3=λ4
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C
λ1=2λ2=22λ3=32λ4
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D
λ1=λ2=2λ3=3λ4
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Solution

The correct option is A λ1=λ2=4λ3=9λ4
Using ΔEZ2 (n1 and n2 are same)
hcλZ2λZ2=constantλ1Z21=λ2Z22=λ3Z23=λ4Z4λ1×1=λ2×12=λ3×22=λ4×33
λ1=λ2=4λ3=9λ4

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