Physics
Physics
Problem
A gas of identical hydrogen-like atoms has some atoms in the lowest (ground) energy level and some atoms in a particular upper (excited) energy level and there are no atoms in any other energy level. The atoms of the gas make transition to a higher energy level by absorbing monochromatic light of photon energy 2.7 eV. Subsequently, the atoms emit radiation of only six different photon energies. Some of the emitted photons have energy 2.7 eV, some have energy more and some have less than 2.7 eV. a. Find the principal quantum number of the initially excited level . b. Find the ionization energy for the gas atoms. c. Find the maximum and the minimum energies of the emitted photons.Intuitive explanation
This problem hinges on understanding energy level diagrams and the transitions they allow. When atoms absorb a 2.7 eV photon and jump to a higher level, they can then cascade back down through intermediate levels in multiple pathways—each path emits a different photon energy. The key insight is that six distinct emission energies means there are exactly six possible transitions among the levels involved, which constrains how many levels must exist and their spacing. Work backwards: if you know the number of distinct transitions, you can deduce the level structure and use the constraint that one transition equals 2.7 eV to find all energy differences.
Intuitive explanation
This problem hinges on understanding energy level diagrams and the transitions they allow. When atoms absorb a 2.7 eV photon and jump to a higher level, they can then cascade back down through intermediate levels in multiple pathways—each path emits a different photon energy. The key insight is that six distinct emission energies means there are exactly six possible transitions among the levels involved, which constrains how many levels must exist and their spacing. Work backwards: if you know the number of distinct transitions, you can deduce the level structure and use the constraint that one transition equals 2.7 eV to find all energy differences.