A sample of monatomic hydrogen gas contains 100 atoms and all the atoms are in `n^(th)` excited state.
As the atoms come down to the ground state following various transitions, they release a total energy of = `(4800)/49` Rch (where 1 Rhc = 13.6 eV). Find the value of N, where maximum possible number of photons emitted in the process is `7N xx 100.`

Answer

3

Explanation

As all of atoms are in same nth state, they release energy (but number of transitions may be different for each.)
Released energy = `4800/49 xx"Rch"`
Energy re leased per atom = `48/49 "Rch" = 48/49 xx13.6eV = ((49-1)/(49))xx13.6 = (1/12-1/7^2)xx13.6`
So the atom is in the `7^(th)` excited state initially, so each atom must underog a maximum of `(n(n-1))/2=( 7xx6)/2 =21` transition (per atom).
`= 21 xx100 =2100= 7 xx 3 xx 100 " " :. n = 3`