When a point light source of power P emitting monochromatic light of wavelength $\lambda$ is kept at a distance $\mathit{a}$ from a photo-sensitive surface of work-function W₀ and area A. which of the expressions is wrong.

The number of photons released per unit time is given by
$$\begin{gathered} \mathrm{n}=\frac{\text{ Power }}{\text{ energy of photon }}=\frac{\mathrm{P}}{(\mathrm{hc}/\mathrm{\lambda })} \\ \mathrm{These} \mathrm{photons} \mathrm{are} \mathrm{spread} \mathrm{out} \mathrm{in} \mathrm{all} \mathrm{directions} \mathrm{over} \mathrm{an} \mathrm{ar}ea 4{\mathrm{\pi a}}^2. \\ \mathrm{The} \mathrm{share} \mathrm{of} \mathrm{an} \mathrm{area} A \mathrm{is} \mathrm{a} \mathrm{fraction} \left( \mathrm{A}/4{\mathrm{\pi a}}^2\right) \mathrm{of} \mathrm{total} \mathrm{number} \mathrm{of} \mathrm{photonc} \mathrm{emitted} \\ \text{'}. \mathrm{number} \mathrm{of} \mathrm{photons} \mathrm{stri}ki\mathrm{ng} \mathrm{the} \mathrm{surface} \mathrm{per} \mathrm{unit} \mathrm{time} =\raisebox{1ex}{$\mathrm{PA\lambda }$}\!\left/ \!\raisebox{-1ex}{$\left(4{\mathrm{\pi hca}}^2\right)$}\right. \\ \mathrm{The} \mathrm{maximum} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{emitted} \mathrm{photo}-\mathrm{electron} \mathrm{is} \\ {\mathrm{E}}_{max}=\frac{\mathrm{hc}}{\mathrm{\lambda }}-{\mathrm{W}}_0 \\ =\frac{1}{\mathrm{\lambda }}\left[\mathrm{hc}-{\mathrm{\lambda W}}_0\right] \\ \mathrm{Further} {\mathrm{eV}}_{\mathrm{s}}={\mathrm{E}}_{max} \\ \mathrm{or} {\mathrm{V}}_{\mathrm{s}}=\frac{{\mathrm{E}}_{max}}{\mathrm{e}}=\frac{1}{\mathrm{\lambda e}}\left[\mathrm{hc}-{\mathrm{\lambda W}}_0\right] \\ \mathrm{where} {\mathrm{V}}_{\mathrm{s}} = \mathrm{stopping} \mathrm{potential}. \\ \mathrm{For} \mathrm{photo} e\mathrm{mission} \mathrm{to} \mathrm{be} \mathrm{possible}, \mathrm{we} \mathrm{must} \mathrm{have} \\ \frac{\mathrm{hc}}{\mathrm{\lambda }}\ge {\mathrm{W}}_0\text{ or }\mathrm{\lambda }\le \frac{\mathrm{hc}}{{\mathrm{W}}_0} \\ \text{ So, permitted range of values of }\mathrm{\lambda }\text{ is } \\ 0\le \mathrm{\lambda }\le \mathrm{hc}/{\mathrm{W}}_0 \end{gathered}$$