The nth state energy of a hydrogen atom is given by Eₙ = − (symbols carry their usual meanings). Let in an ensemble, all H-atoms be in the ground state and a radiation having energy equal to E₂ − E₁ falls on it. In this situation which of the following statements could be true?
a) The radiation will not be absorbed at all.
b) Some of the atoms will move to the first excited state.
c) All atoms will be excited to n = 2 state.
d) No atoms will make a transition to n = 3 state.

Correct option is A

Correct answer is A
Explanation:
The radiation energy matches the energy difference (ΔE = E2 - E1), which means that transitions are possible from the ground state (n = 1) to the first excited state (n = 2).
Since the radiation energy does not match the energy difference for transitions to n = 3 (E3 - E1), no atoms will transition to the n = 3 state.