A) \[-16\times {{10}^{-22}}J\]
B) \[8\times {{10}^{-22}}J\]
C) \[16\times {{10}^{-22}}J\]
D) \[A\]
Correct Answer: D
Solution :
If the maximum kinetic energy of photoelectrons emitted from the surface of a metal is EK and W is the work function of the metal, then from Einstein?s photoelectric equation we have \[{{E}_{K}}=hv-W\] Where, \[hv\] is the energy of the photon absorbed by the electron in the metal. Also \[v=\frac{c}{\lambda }\] \[=\frac{\text{velocity}}{\text{wavelength}}\] \[\therefore \] \[{{E}_{K}}=\frac{hc}{\lambda }-\frac{hc}{{{\lambda }_{0}}}=hc\left( \frac{1}{\lambda }-\frac{1}{{{\lambda }_{0}}} \right)\] Given, \[\lambda =3\times {{10}^{-7}}\,m,\,{{\lambda }_{0}}=4\times {{10}^{-7}}\,m.\] \[\therefore \] \[{{E}_{K}}=6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}\times \left( \frac{1}{3\times {{10}^{-7}}}-\frac{1}{4\times {{10}^{-7}}} \right)J\] \[=\frac{19.8\times {{10}^{-19}}}{12\times 1.6\times {{10}^{-19}}}eV\] \[=1.03\approx 1\,eV\]
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