Ultra-violet light of wavelength $\displaystyle 200$ nm from a source is incident on a metal surface. If the stopping potential is -$\displaystyle 2.5$ V, (a) calculate the work function of the metal, and (b) How would the surface respond to a high intensity red light of wavelength $\displaystyle 6328 \AA$ produced by a laser ?

a) $\displaystyle \lambda=200 \mathrm{~nm}$, stopping potential = -2.5V\begin{aligned} & \text { K.E. }=2.5 \times 1.6 \times 10^{-19} \mathrm{~J}=4 \times & \qquad \begin{aligned} E=h v & =h \frac{c}{\lambda} & =\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{200 \times 10^{-9}} & =9.945 \times 10^{-19} \mathrm{~J} \end{aligned} \end{aligned}Work function $\displaystyle =\mathrm{E}-\mathrm{eV}$\begin{aligned} = & \left(9.945 \times 10^{-19}-4 \times 10^{-19}\right) \mathrm{J} & =5.595 \times 10^{-19} \mathrm{~J} \end{aligned}b) Wavelength of red light $\displaystyle =6328 \AA$\begin{aligned} E= & h v=h \frac{c}{\lambda} & =\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{6328 \times 10^{-10}} & =0.00314 \times 10^{-16} \mathrm{~J} & =3.14 \times 10^{-19} \mathrm{~J} \end{aligned}Energy of red light < work function of metal surface ∴ No emission of photoelectrons takes place.