Consider a hydrogen like atom whose energy in nth excited state is given by $$En=$$−$$13.6Z2n2$$ . When this excited atom, makes a transition from excited state to ground state, most energetic photons have energy $$Emax=52.224eV$$ and least energetic photons have energy $$Emin=1.224eV$$. The atomic number of atom is

Question

Consider a hydrogen like atom whose energy in nth excited state is given by $$En=$$−$$13.6Z2n2$$ . When this excited atom, makes a transition from excited state to ground state, most energetic photons have energy $$Emax=52.224eV$$ and least energetic photons have energy $$Emin=1.224eV$$. The atomic number of atom is

Infinity Learn · Accepted Answer

Maximum energy is liberated for transition En→$$1$$ and minimum energy for En→En−$$1$$ Hence  $$E1n2$$−$$E1=52.224eV$$.........(i)  and $$E1n2$$−$$E1(n$$−$$1)2=1.224eV$$..........(ii) Solving equations (i) and (ii) we $$getE1=$$−$$54.4eV$$ and $$n=5$$  Now $$E1=$$−$$13.6Z212=$$−$$54.4eV$$. Hence $$Z=2$$

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