In a gas of identical hydrogen-like atoms, some atoms are in the ground state and the rest in one upper state. The atoms absorb photons of energy 1.89 eV, jump to higher states, and then emit three distinct photon energies. Find the principal quantum number of the initially excited level.
Physics · Atomic Structure and X-rays
JEE Mains Advanced

Question

In a gas of identical hydrogen-like atoms, some atoms are in the ground state and the rest in one upper state. The atoms absorb photons of energy 1.89 eV, jump to higher states, and then emit three distinct photon energies. Find the principal quantum number of the initially excited level.

Physics · Atomic Structure and X-rays

G1 Physics · Accepted Answer

Three distinct emitted photon energies correspond to three possible transitions among three participating levels. Using Eₙ∝−1/n² and the absorbed energy 1.89 eV gives the initially excited level n=2.