Question

Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive materials having work Functions ${\omega{1}}$ and ${\omega{2}}$ ${(\omega{1}>\omega{2})}$. On what factors does the (i) Slope and (ii) intercept of the lines depends?​

Answer 1

We know By Einstein's Photoelectric Equation:

${:\implies \quad \sf h\nu =h\nu_{0}+\dfrac{1}{2}m{v^{2}}_{max}}$

${:\implies \quad \sf h\nu =h\nu_{0}+eV_{0}}$

${:\implies \quad \sf eV_{0}=h\nu -h\nu_{0}}$

${:\implies \quad \sf V_{0}=\dfrac{h\nu}{e}-\dfrac{h\nu_{0}}{e}}$

Since ${\nu}$ is plotted along X-axis and ${V_0}$ along Y-axis, it represents a straight line

(i) The slope of ${V_{0}}$ versus ${\nu}$ graph= (h/e) i.e it is a constant quantity and does not depend on the nature of the metal surface

(ii) The intercept on the ${\nu}$-axis = ${(h\nu_{0}/e)}$ i.e it depends on the work function of the metal surface

Refer to the attachment for the graph