A gas of identical H-like atom has some atoms in the lowest (ground) energy level A and some atoms in a particular upper (excited) energy level B and there are no atoms in any other energy level. The atoms of the gas make transition to a higher energy level by aborbing monochromatic light of photon energy `2.7eV`. Subsequently, the atoms emit radiation of only six different photons energies. Some of the emitted photons have energy `2.7eV`. Some have more and some have less than `2.7eV`. (a) Find the principal quantum number of initially excitied level B. (b) Find the ionisation energy for the gas atoms. (c ) Find the maximum and the minimum energies of the emitted photons.

A gas of identical H-like atom has some atoms in the lowest (ground) e

1.	A gas of identical H-like atom has some atoms in the lowest (ground) energy level A and some atoms in a particular upper (excited) energy level B and there are no atoms in any other energy level. The atoms of the gas make transition to a higher energy level by aborbing monochromatic light of photon energy `2.7eV`. Subsequently, the atoms emit radiation of only six different photons energies. Some of the emitted photons have energy `2.7eV`. Some have more and some have less than `2.7eV`. (a) Find the principal quantum number of initially excitied level B. (b) Find the ionisation energy for the gas atoms. (c ) Find the maximum and the minimum energies of the emitted photons.
Answer» Correct Answer - `(a) n=2,(b)14.4eV, (c )13.5eV,0.7eV` Since we obtain 6 emission lines, it means electron comes from 4th orbit energy emitted is equal to less than and more than `2.7eV`. So it can be like this `E_(4)-E_(2)=2.7eV," "E_(4)-E_(3)lt2.7eV`, `E_(4)-E_(1)gt2.7eV` (a) `n=2` `(E_(4)-E_(2))^("atom")=(E_(4)-E_(2))^(H)xxZ^(2)` `2.7=2.55xxZ^(2)=1.029` (b) `IP=13.6Z^(2)=13.6xx(1.029)^(2)=14.4eV` (c ) Maximum energy emitted `=E_(4)-E_(1)=(E_(4)-E_(1))^(H)xxZ^(2)` `=12.75xx(1.029)^(2)` `13.5eV` Minimum energy emitted `=E_(4)-E_(3)=(E_(4)-E_(3))^(H)xxZ^(2)` `=66xx(1.029)^(2)=0.7eV`

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