The electron in a hydrogen atom rises from its n = 1 state to n = 4 state by absorbing energy. The energy of the electron in the n = 1 state is -13.6 eV. How much energy is absorbed by the electron in transition?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12.75 eV
In the Bohr model of hydrogen the energy of level \( n \) is \( E_n = -13.6/n^{2}\,\mathrm{eV} \). The energy absorbed in a jump up is the difference between the final and the initial energy.
\( \displaystyle E_4 = -\frac{13.6}{4^{2}}\,\mathrm{eV} = -0.85\,\mathrm{eV} \)
\( \Delta E = E_4 - E_1 = -0.85\,\mathrm{eV} - (-13.6\,\mathrm{eV}) = 12.75\,\mathrm{eV} \)
The energy absorbed is positive, because the electron moves to a higher (less negative) level.