[Solution from source] Longest wavelengths: Lyman (2 → 1): 1/λ = R(1 − 1/4) = 3R/4, λ = 4/(3R). Balmer (3 → 2): 1/λ = R(1/4 − 1/9) = 5R/36, λ = 36/(5R). Ratio = (4/3)/(36/5) = 20/108 = 5/27. Answer (1).
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