An electron jumps from the fourth state to first state in a hydrogen atom. The energy released due to transition is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12.75 eV
The energy of the n-th level of hydrogen is \( E_n = -\frac{13.6}{n^{2}}\,\mathrm{eV} \). In a jump to a lower level, the energy released equals the difference between the two energy levels.
\( \displaystyle E_4 = -\frac{13.6}{16}\,\mathrm{eV} = -0.85\,\mathrm{eV} \)
\( \displaystyle E_1 = -13.6\,\mathrm{eV} \)
\( \displaystyle \Delta E = E_4 - E_1 = -0.85\,\mathrm{eV} - (-13.6\,\mathrm{eV}) = 12.75\,\mathrm{eV} \)