Ultra-violet light of wavelength 200 nm from a source is incident on a metal surface. If the stopping potential is -2.5 V, (a) calculate the work…

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.