A sample of monatomic hydrogen gas contains $$100$$ atoms and all the atoms are in nth excited state. As the atoms come down to the ground state following various transitions, they release a total energy of $$480049Rch$$ (where$$ $$1$$ Rch $$=$$ $$13.6eV) . Find the value of N, where maximum possible number of photons emitted in the process is $$7N$$ x $$100$$.

Question

A sample of monatomic hydrogen gas contains $$100$$ atoms and all the atoms are in nth excited state. As the atoms come down to the ground state following various transitions, they release a total energy of $$480049Rch$$ (where$$ $$1$$ Rch $$=$$ $$13.6eV) . Find the value of N, where maximum possible number of photons emitted in the process is $$7N$$ x $$100$$.

Infinity Learn · Accepted Answer

As all of atoms are in same nth state, they release equal energy (but$$ number of transitions may be different for $$each). Released energy $$=480049$$×Rch Energy released per atom $$=4849Rch=4849$$×$$13.6eV=49$$−$$149$$×$$13.6=112$$−$$172$$×$$13.6eVSo$$, atoms are in $$7th$$ excited state initially.So, each atom can undergoes a maximum $$ofn(n$$−$$1)2=7$$×$$62=21$$ transitions (per$$ $$atom). So, maximum possible number of photons emitted, by the sample of $$100$$ atoms. $$=21$$×$$100=2100=7$$×$$3$$×$$100$$∴ $$N=3$$

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