A hydrogen like atom (atomic number \( =Z \) ) is in higher excited state of quantum number \( n...

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A hydrogen like atom (atomic number \( =Z \) ) is in higher excited state of quantum number \( n \). This excited atom can make a transition to first excited state by successively emitting two photons of energy \( 22.94 \mathrm{eV} \) and \( 5.15 \mathrm{eV} \). The atom from the same state \( n \) can make transition to second excited state by successively emitting two photons of energies \( 2.4 \mathrm{eV} \) and \( 8.7 \mathrm{eV} \). Find values of \( n \) and \( Z \).
(a) \( n=6 ; Z=5 \)
(b) \( n=8 ; \mathrm{Z}=2 \)
(c) \( n=2 ; Z=4 \)
(d) \( n=7 ; \mathrm{Z}=3 \)
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