Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is -1.3 volt, estimate the work function of the metal. How would the photo-cell respond to a high intensity (~ 10⁵Wm^–2) red light of wavelength 6328 Å produced by He-Ne laser?

Here,
Sopping potential,  ${\mathrm{V}}_0 = 1.3 \mathrm{V}$ 
$$\begin{gathered} \mathrm{Wavelength} \mathrm{of} \mathrm{ultraviolet} \mathrm{light}, \mathrm{\lambda } = 2271 \mathrm{\AA } \\ = 2271 \times {10}^{-10}\mathrm{m} \end{gathered}$$

Now, using Einstein's photoelectric equation, 

        $\boxed{\mathrm{hv} = {\mathrm{hv}}_0+\frac{1}{2}{{\mathrm{mv}}^2}_{\max } = {\mathrm{\varphi }}_0+{\mathrm{eV}}_0}$  

$\Rightarrow$   ${\mathrm{\varphi }}_0 = \frac{\mathrm{hc}}{\mathrm{\lambda }}-{\mathrm{eV}}_0$ 
where, ${\mathrm{\varphi }}_{\mathrm{o}} \mathrm{is} \mathrm{the} \mathrm{work} \mathrm{function} \mathrm{of} \mathrm{the} \mathrm{metal}.$ 

Taking,      $\mathrm{h} = 6.62 \times {10}^{-34} \mathrm{Js}$
                 $\mathrm{e} = 1.6 \times {10}^{-19}\mathrm{C}$
                 $\mathrm{c} = 3 \times {10}^8 {\mathrm{ms}}^{-1}$ 
We have,

${\mathrm{\varphi }}_0 = \frac{6.62 \times {10}^{-34}\times 3 \times {10}^8}{2271 \times {10}^{-10}}-1.6 \times {10}^{-19} \times 1.3$

$\Rightarrow$    $$\begin{gathered} {\mathrm{\varphi }}_0 = 8.745 \times {10}^{-19}-2.08 \times {10}^{-19} \\ = 6.665 \times {10}^{-19}\mathrm{J} \end{gathered}$$   

i.e.,  ${\mathrm{\varphi }}_0 = \frac{6.665 \times {10}^{-19}}{1.6 \times {10}^{-19}} = 4.166 \mathrm{eV}.$ 

Threshold wavelength is given by, 

      $$\begin{gathered} \boxed{{\mathrm{\lambda }}_0 = \frac{{\mathrm{h}}_{\mathrm{c}}}{{\mathrm{\varphi }}_0}} \\ = \frac{6.62 \times {10}^{-34} \times 3 \times {10}^8}{6.665 \times {10}^{-19}} \\ = 2.98 \times {10}^{-7}\mathrm{m} \end{gathered}$$ 

i.e., ${\mathrm{\lambda }}_0 = 2980 \mathrm{\AA }$ 

As calculated above, wavelength of red light is greater than threshold wavelength λ_0. Therefore_, photocell will not respond when red light of wavelength 6328 A produced by He-Ne laser is incident on the photocell.