question_answer

The work function, for a certain metal is 4 eV. Will this metal give photoelectric emission for incident radiation of wavelength 300 nm?

Answer:

Given, work function,      \[{{\phi }_{0}}=4eV=4\times 1.6\times {{10}^{-19}}\] \[{{\phi }_{0}}=6.4\times {{10}^{-19}}J\] Wavelength of radiation,  \[\lambda =300\,nm=300\times {{10}^{-9}}m\] If the energy of each photon is more than or equal to the work function, then only the photoelectric emission takes place. Energy of each photon, \[E=\frac{hc}{\lambda }=\frac{6.63\times {{10}^{-34}}\times 3\times {{10}^{8}}}{300\times {{10}^{-9}}}=6.63\times {{10}^{-19}}J\] Since \[E>{{\phi }_{0}},\] hence photoelectric emission takes place.