Consider a hydrogen-like atom whose energy in nth excited state is given by `E_(n) = (13.6 Z^(2))/(n^(2))` When this excited makes a transition from excited state to ground state , most energetic photons have energy `E_(max) = 52.224 eV`. and least energetic photons have energy `E_(max) = 1.224 eV` Find the atomic number of atom and the intial state or excitation.
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`Max ^(n) ` energy is liberated for transition `E _(n) rarr E_(1)` and minimum energy for `E_(n) rarr E _(n-1)`. Hence, `(E_(1))/(n^(2))-(E_(1))/(12) =52.224eV `and `(E_(1))/(n^(2))-(E_(1))/((n-1)^(2)) =1.224eV`, Solving, we get, `E_(1) =-54.4eV `and n=5 hence, `E_(1)=-(13.6 Z^(2))/(12)=-54.4, Z=2`
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