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For any given series of spectral lines of atomic hydrogen, let Δν = νmax − νmin be the difference in maximum and minimum frequencies in cm−1. The ratio ΔνLyman / ΔνBalmer is:

1. 4: 1
2. 9: 4
3. 27: 5
4. 5: 4

Correct answer: 9: 4

Solution

For Lyman (n1=1): nu_max = R, nu_min = R(1-1/4) = 3R/4, so delta = R/4. For Balmer (n1=2): nu_max = R/4, nu_min = R(1/4-1/9) = 5R/36, so delta = R/9. Ratio = (R/4)/(R/9) = 9:4.

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