question_answer 37)

What is the energy in joules, required to shift the electron of a hydrogen atom from first Bohr orbit to fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is \[-2.18\times {{10}^{-11}}erg.\] erg.

Answer:

\[\Delta E={{E}_{5}}-{{E}_{1}}\] \[=\frac{-2.18\times {{10}^{-11}}}{{{5}^{2}}}-\left( \frac{-218\times {{10}^{-11}}}{{{1}^{2}}} \right)\] \[=\frac{24}{25}\times 2.18\times {{10}^{-11}}erg\] \[=2.0928\times {{10}^{-11}}erg=2.0928\times {{10}^{-18}}\text{J}\] \[\Delta E=\frac{hc}{\lambda }\] \[\lambda =\frac{hc}{\Delta E}=\frac{6.626\times {{10}^{-27}}\times 3\times {{10}^{10}}}{2.0928\times {{10}^{-11}}}\] \[=9.498\times {{10}^{-6}}cm=949.8\times {{10}^{-8}}cm\] \[=9.498\times {{10}^{-6}}m\] \[=949.8\overset{o}{\mathop{\text{A}}}\,\]