An electron in the ground state of a hydrogen atom absorbs \( 12.09\,\mathrm{eV} \) energy. The angular momentum of the electron increases by
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2(h/2\pi) \)
The energy levels of hydrogen are \( E_n = -13.6/n^{2}\,\mathrm{eV} \). The electron starts in the ground state, \( n = 1 \), with \( E_1 = -13.6\,\mathrm{eV} \). After absorbing \( 12.09\,\mathrm{eV} \):
\( \displaystyle E = -13.6 + 12.09 = -1.51\,\mathrm{eV} = -\frac{13.6}{n^{2}} \;\Rightarrow\; n^{2} = 9 \;\Rightarrow\; n = 3 \)
By Bohr's quantisation condition the angular momentum is \( L = n\,(h/2\pi) \).
\( \displaystyle \Delta L = (3 - 1)\,\frac{h}{2\pi} = 2\,\frac{h}{2\pi} \)