question_answer 140)

  Calculate the energy and frequency of the radiation emitted when an electron jumps from \[n=3\] to \[n=2\] in a hydrogen atom.

Answer:

  \[\Delta E=({{E}_{3}}-{{E}_{2}})\] \[=-\frac{2.18\times {{10}^{-18}}}{{{3}^{2}}}-\left( -\frac{2.18\times {{10}^{-18}}}{{{2}^{2}}} \right)\]\[=\left( \frac{1}{4}-\frac{1}{9} \right)\times 2.18\times {{10}^{-18}}\] \[=\frac{5}{36}\times 2.18\times {{10}^{-18}}J\] \[=3.027\times {{10}^{-19}}J\] \[hv=3.027\times {{10}^{-19}}\] \[v=\frac{3.027\times {{10}^{-19}}}{6.626\times {{10}^{-34}}}\] \[=4.6\times {{10}^{14}}Hz\]