Light described at a place by the equation \ $E=(100 \mathrm{~V} / \mathrm{m})\left[\sin \left(5

Question

Light described at a place by the equation \ $E=(100 \mathrm{~V} / \mathrm{m})\left[\sin \left(5 \times 10^{15} \mathrm{~s}^{-1}\right) t\right. \left.+\sin \left(8 \times 10^{15} \mathrm{~s}^{-1}\right) t\right]$ \ falls on a metal surface having work \ function 2.0 eV . The maximum kinetic energy \(in eV ) of the photoelectrons will be $\_\_\_\_$ .

Professor PC Thomas Classes · Answer

(3.27): The light contains two different frequencies. The one with larger frequency will cause photoelectrons with largest kinetic energy. \ This larger frequency is \ $ v=\frac{\omega}{2 \pi}=\frac{8 	imes 10^{15} \mathrm{~s}^{-1}}{2 \pi} $ \  The maximum kinetic energy of the photoelectrons is $ \begin{aligned} & K_{\max }=h v-\phi \ & =\left(4.14 	imes 10^{-15} \mathrm{eVs}ight) 	imes\left(\frac{8 	imes 10^{15}}{2 \pi} \mathrm{~s}^{-1}ight)-2.0 \mathrm{eV} \ & =5.27 \mathrm{eV}-2.0 \mathrm{eV}=3.27 \mathrm{eV} \end{aligned} $