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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
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
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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)=48.35 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
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)=48.35 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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