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 =E3−E1=−13.6×Z2(1n22−1n21)=−13.6×Z2(19−11)=48.35eV 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=−13.6eV