A photon is emitted from a hydrogen atom during the electronic transition corresponding to the series limit of the Paschen series. This photon immediately strikes a second hydrogen atom, which is alre

Question

A photon is emitted from a hydrogen atom during the electronic transition corresponding to the series limit of the Paschen series. This photon immediately strikes a second hydrogen atom, which is already in its first excited state. After this interaction, what is the principal quantum number (n) of the electron in the second hydrogen atom?

TestHub · Accepted Answer

Paschen series limit = transition from n = ∞ to n = 3: E photon ​ = E ∞ ​ − E 3 ​ = 0 − ( − 13.6 eV / 3 2 ) ≈ 1.51 eV Target atom is at n = 2; minimum energy it can absorb is for the n = 2 → n = 3 transition: E e x p ​ = E 3 ​ − E 2 ​ = ( − 13.6/ 3 2 ) − ( − 13.6/ 2 2 ) = 1.89 eV Since 1.51 eV < 1.89 eV, the photon cannot be absorbed; no interaction occurs, so the electron remains at n = 2 Answer: 2

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