When a light of wavelength ${\mathrm{\lambda }}_1$ fall on metal sheet will eject electron with V₁ velocity and with ${\mathrm{\lambda }}_2$ light eject electron of V₂ velocity. What is ${\mathrm{V}}_2^2-{\mathrm{V}}_1^2$ value

When a light of wavelength ${\mathrm{\lambda }}_1$ fall on metal sheet, $\frac{\mathrm{hc}}{{\mathrm{\lambda }}_1}=\mathrm{W}+\frac{1}{2}{\mathrm{mV}}_1^2---\left(1\right)$

When a light of wavelength ${\mathrm{\lambda }}_1$ fall on metal sheet, $\frac{\mathrm{hc}}{{\mathrm{\lambda }}_2}=\mathrm{W}+\frac{1}{2}{\mathrm{mV}}_2^2---\left(2\right)$

Eq.(2)-Eq.(1) gives,

$$\begin{gathered} \frac{\mathrm{hc}}{{\mathrm{\lambda }}_2}-\frac{\mathrm{hc}}{{\mathrm{\lambda }}_1}=\frac{1}{2}{\mathrm{mV}}_2^2-\frac{1}{2}{\mathrm{mV}}_1^2 \\ \mathrm{hc}\left(\frac{1}{{\mathrm{\lambda }}_2}-\frac{1}{{\mathrm{\lambda }}_1}\right)=\frac{1}{2}\mathrm{m}\left({\mathrm{V}}_2^2-{\mathrm{V}}_1^2\right) \\ \left({\mathrm{V}}_2^2-{\mathrm{V}}_1^2\right)=\frac{2\mathrm{hc}}{\mathrm{m}}\left(\frac{1}{{\mathrm{\lambda }}_2}-\frac{1}{{\mathrm{\lambda }}_1}\right) \end{gathered}$$