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Q.

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

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a

2

b

5

c

4

d

none of these

answer is A.

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Detailed Solution

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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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