Physics - Modern Physics Question with Solution | TestHub

Let $\varphi =$ work function of the metal, $\frac{\mathrm{hc}}{{\lambda }_1}=\varphi +{\mathrm{eV}}_1$ $\frac{\mathrm{hc}}{{\lambda }_2}=\varphi +{\mathrm{eV}}_2\dots \dots$ (ii) Sutracting (ii) from (i) we get $\mathrm{hc}\left(\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}\right)=\mathrm{e}\left({\mathrm{V}}_1-{\mathrm{V}}_2\right)$ $\Rightarrow V_1-V_2=\frac{hc}{e}\left(\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_1\cdot {\lambda }_2}\right)\left[\begin{array}{l}{\lambda }_1=300\mathrm{nm}\\ {\lambda }_2=400\mathrm{nm}\\ \frac{\mathrm{hc}}{\mathrm{e}}=1240\mathrm{nm}-\mathrm{V}\end{array}\right]$ $=(1240\mathrm{nm}-\mathrm{v})\left(\frac{100\mathrm{nm}}{300\mathrm{nm}\times 400\mathrm{nm}}\right)$ $=1,03\mathrm{V}\approx 1\mathrm{V}$