Question

The graph between $1/\lambda$ and stopping potential (V) of three metals having work functions ${\oint }_1,{\oint }_{2}and{\oint }_3$ in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct ? (Here $\lambda$. is the wavelength of the incident ray).

• A. Ratio of work functions ${\oint }_1:{\oint }_2:{\oint }_3=1:2:4$
• B. Ratio of work functions ${\oint }_1:{\oint }_2:{\oint }_3=4:2:1$
• C. tan $\theta$ is directly proportional to hc/ e, where h is Planck's constant and c is the speed of light
• D. The violet colour light can eject photoelectrons from metals 2 and 3

Answer 1

Answer: (A), (C)

From the relation,
$eV=\frac{hc}{\lambda }-\oint$
or $V=\left(\frac{hc}{e}\right)\left(\frac{1}{\lambda }\right)-\frac{\oint }{e}$
This is equation of straight line.
Slope is tan $\theta =\frac{hc}{e}$
${\oint }_1:{\oint }_2:{\oint }_3=\frac{hc}{{\lambda }_{01}}:\frac{hc}{{\lambda }_{02}}:\frac{hc}{{\lambda }_{03}}$ $=\frac{1}{{\lambda }_{01}}:\frac{1}{{\lambda }_{02}}:\frac{1}{{\lambda }_{03}}=1:2:4$
$\frac{1}{{\lambda }_{01}}=0.001n{m}^{-1}$ or ${\lambda }_{01}=10000\mathring{A}$
$\frac{1}{{\lambda }_{02}}=0.002n{m}^{-1}$ or ${\lambda }_{02}=5000\mathring{A}$
$\frac{1}{{\lambda }_{03}}=0.004n{m}^{-1}$ or ${\lambda }_{03}=2500\mathring{A}$
Violet colour has wavelength $4000\mathring{A}.$
So, violet colour can eject photoelectrons from metal-1 and metal-2.