question_answer 38)

The electron energy in hydrogen atom is given by \[{{E}_{n}}=-\frac{2.18\times {{10}^{-18}}}{{{n}^{2}}}J.\]. Calculate the energy required to remove an electron completely from the \[n=2\] orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Answer:

Given that, \[{{E}_{n}}=-\frac{2.18\times {{10}^{-18}}}{{{n}^{2}}}\] \[\therefore \] \[{{E}_{2}}=-\frac{2.18\times {{10}^{-18}}}{{{2}^{2}}}\] \[=-5.45\times {{10}^{-19}}\text{J}\] Energy required to remove electron from \[n=2\] orbit i.e., \[\Delta E={{E}_{\infty }}-{{E}_{2}}\] \[=0-(-5.45\times {{10}^{-19}})\] \[=5.45\times {{10}^{-19}}\text{J}\] Wavelength of light required to cause above transition can be calculated as, \[\Delta E=h,\frac{c}{\lambda }\] \[\therefore \] \[\lambda =\frac{hc}{\Delta E}=\frac{6.626\times {{10}^{-34}}\times 3\times {{10}^{8}}}{5.45\times {{10}^{-19}}}\] \[=3647\times {{10}^{-10}}m\] \[=3647\times {{10}^{-8}}cm\]