Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He^+ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is

Correct option is B.
n=2→n=4
Energy released for transition n=2 to n=1 of hydrogen atom
E=13.6 Z^2(1/n1^2 - 1/n2^2)
Z=1, n1=1, n2=2
E=13.6 × 1 × (1/1^2 - 1/2^2)
E=13.6 × 3/4 eV
For He+ ion z=2
(1) n=1 to n=4
E=13.6 × 2^2 × (1/1^2 - 1/4^2) = 13.6 × 15/4 eV
(2) n=2 to n=4
E=13.6 × 2^2 × (1/2^2 - 1/4^2) = 13.6 × 3/4 eV
(3) n=2 to n=5
E=13.6 × 2^2 × (1/2^2 - 1/5^2) = 13.6 × 21/25 eV
(4) n=2 to n=3
E=13.6 × 2^2 × (1/2^2 - 1/3^2) = 13.6 × 5/9 eV
Energy required for transition of He+ for n=2 to n=4 matches exactly with energy released in transition of H for n=2 to n=1.