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Question

The energy gap between the first energy state and the second excited state of a hydrogen like atom is 48.35 eV. Then the energy of the first excited state is

A
-3.4 eV
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B
-13.6 eV
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C
6.4 eV
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D
13.6 eV
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Solution

The correct option is B -13.6 eV
we know, second excited state corresponds to n = 3
The energy gap between the second excited state and the first energy state =E3E1=13.6×Z2(1n221n21)=13.6×Z2(1911)=48.35 eV
Thus , Z= 2
First excited state corresponds to n = 2
We know that the energy of nth level in a hydrogen like atom is given by =13.6 (Z2n2)
Thus the energy of the first excited state =13.6×44=13.6 eV

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