A sample of hydrogen gas has some atoms in one excited state. It emits three different photons. When the sample was irradiated with radiation of energy `2.85 eV`, it emits `10` different photon all having energy less than `13.6 eV`
a. Find the principal quantum number of initially excited electrons
b. Find the maximum and minimum energies of the initially emitted photons.

Explanation

Initially sample emit three different photons. It means for one of the excited states, n = 3.
For other excited state, n = 1 or n = 2
After irradiation it emits 10 different photons, it means for this excited state, n = 5
Energy of `5^(th)` energy level ` = ( - 13.6)/((5)^(2)) = - 0.544 eV`
Energy of `3^(rd)` energy level ` = ( - 13.6)/((3)^(2)) = - 1.51 eV`
Energy of `2^(nd)` energy level ` = ( 13.6)/((2)^(2)) = - 3.4 e V`
So , after absorption of 2.85eV energy, only electron from second energy level can jump to `5^(th)` energy level. Principal quantum number of initially excited state are 2 and 3 respectively.
Maximum energy of emitted photon `= 13.6 - 15.1 = 12.09eV`
Minimum energy of emitted photon = 3.4 - 1.51 = 1.89 eV