The energy required to excite an electron in a hydrogen atom from the first excited state to the third state is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \sim 1.89 \) eV
In the Bohr model of hydrogen, \( E_{n} = -13.6/n^{2} \) eV. The first excited state is \( n = 2 \) and the third state is \( n = 3 \).
\( \displaystyle E_{2} = -\frac{13.6}{2^{2}}\,\mathrm{eV} = -3.40\,\mathrm{eV} \)
\( \displaystyle E_{3} = -\frac{13.6}{3^{2}}\,\mathrm{eV} = -1.51\,\mathrm{eV} \)
\( \Delta E = E_{3}-E_{2} = -1.51\,\mathrm{eV}-(-3.40\,\mathrm{eV}) \approx 1.89\,\mathrm{eV} \)