For hydrogen, the ratio of the largest wavelength in the Lyman series to the largest wavelength in the Balmer series is:
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Question

For hydrogen, the ratio of the largest wavelength in the Lyman series to the largest wavelength in the Balmer series is:

G1 Physics · Accepted Answer

The largest wavelength in a spectral series corresponds to the smallest energy gap in that series. Lyman series: transition 2→1. 1/λ_L = R(1 - 1/4) = 3R/4. Thus, λ_L = 4/(3R). Balmer series: transition 3→2. 1/λ_B = R(1/4 - 1/9) = 5R/36. Thus, λ_B = 36/(5R). Therefore, λ_L/λ_B = [4/(3R)]/[36/(5R)] = 20/108 = 5/27. Correct option: B.