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In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

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

Correct answer: 9/4

Solution

The longest wavelength in a series corresponds to the transition to the lowest energy level of that series. For the Lyman series, this is n=2 to n=1, and for the Balmer series, it is n=3 to n=2. Using the Rydberg formula, the ratio of wavelengths is (n₁²/n₂²) = (2²/3²) = 4/9.

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