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The ground state energy of hydrogen atom is $-13.6$ eV. When its electron is in the first excited state, its excitation energy is -
A
10.2 eV
B
zero
C
3.4 eV
D
6.8 eV
Detailed Solution
Energy of the $n$th level of hydrogen: $E_n = -\dfrac{13.6}{n^2}$ eV
Ground state ($n = 1$): $E_1 = -13.6$ eV
First excited state ($n = 2$): $E_2 = -\dfrac{13.6}{4} = -3.4$ eV
Excitation energy = energy needed to raise the electron from the ground state to the higher level
$\Delta E = E_2 - E_1 = -3.4 - (-13.6)$
$\Delta E = -3.4 + 13.6 = 10.2$ eV
Ground state ($n = 1$): $E_1 = -13.6$ eV
First excited state ($n = 2$): $E_2 = -\dfrac{13.6}{4} = -3.4$ eV
Excitation energy = energy needed to raise the electron from the ground state to the higher level
$\Delta E = E_2 - E_1 = -3.4 - (-13.6)$
$\Delta E = -3.4 + 13.6 = 10.2$ eV