For any given series of spectral lines of atomic hydrogen, let Δv = v_max - v_min be the difference in maximum and minimum frequencies in cm⁻¹. The ratio of v_Lyman / v_Balmer is:

Correct option is D.

9:4

For Lyman
v_max = R_H(1/1² - 1/∞²) = R_H
v_min = R_H(1/1² - 1/2²) = 3/4 R_H
v_Lyman = R_H(1 - 3/4) = R_H/4

For Balmer
v_max = R_H(1/2² - 1/∞²) = R_H/4
v_min = R_H(1/2² - 1/3²) = 5/36 R_H
v_Balmer = R_H/4 - 5/36 R_H = R_H/4 - 5R_H/36 = (9R_H - 5R_H)/36 = 4R_H/36 = R_H/9

v_Lyman/v_Balmer = (R_H/4) / (R_H/9) = 9/4