A sample of hydrogen atom gas contains `100 "atom"`. All the atoms are excited to the same `n^(th)` excited state. The total energy released by all the atoms is `(4800)/(49) Rch` ( where `Rch=13.6eV`), as they come to the ground state through various types of transitions, Find

Options

A. maximum energy of the emitted photon will be less than `(48)/(49)Rch`.
B. maximum energy of the emitted photon may be grater than `(48)/(49) Rch`
C. the value of `n=6`
D. maximum total number of photons that can be emitted by this sample may be less than 600.

Answer

C, D

Explanation

(i) Maximum energy from one atom
`=(4800)/(49)Rchxx(1)/(100)=(48)/(49)Rch`.
(ii) `DeltaE=13.6 (1-(1)/((n+1)^(2)))eV`
`(48)/(49)xx13.6xx(1-(1)/((n+1)^(2)))`
`rArr n=6`.
(iii) Since `n=6` is the excited state. An atom can emit a maximum transition of `6`.