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The wavelengths of the first Lyman transition lines for hydrogen (H), He+ ion, and Li²+ ion are lambda1, lambda2, and lambda3 respectively. What is the ratio lambda1: lambda2: lambda3?

1. 1: 4: 9
2. 9: 4: 1
3. 36: 9: 4
4. 6: 3: 2

Correct answer: 36: 9: 4

Solution

Since wavelength for the first Lyman line scales as 1/Z², with Z=1,2,3 the ratio is 1:1/4:1/9 = 36:9:4.

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