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Question:

Taking the wavelength of the first Balmer line in hydrogen spectrum (n=3 to n=2) as 660nm, the wavelength of the 2nd Balmer line (n=4 to n=2) will be:

889.2nm

642.7nm

488.9nm

388.9nm

Solution:

Correct option is C. 488.9nm

1/660 = R(1/2² - 1/3²) = 5R/36 (1)
1/λ = R(1/2² - 1/4²) = 3R/16 (2)

dividing (1) with (2)
λ/660 = (5/36) * (16/3)
λ = (5 * 16 * 660) / (36 * 3)
λ = 44000/9
λ = 488.88
λ = 488.9nm