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 $V=\bigg(\frac{hc}{e}\bigg)\bigg(\frac{1}{\lambda}\bigg)-\frac{\oint}{e}$
This is equation of straight line.
Slope is tan $\theta=\frac{hc}{e}$
$\oint_1:\oint_2:\oint_3=\frac{hc}{\lambda_{01}}:\frac{hc}{\lambda_{02}}:\frac{hc}{\lambda_{03}}$ $=\frac{1}{\lambda_{01}}:\frac{1}{\lambda_{02}}:\frac{1}{\lambda_{03}}=1:2:4$
$\frac{1}{\lambda_{01}}=0.001 nm^{-1}$ or $\lambda_{01}=10000\mathring{A}$
$\frac{1}{\lambda_{02}}=0.002 nm^{-1}$ or $\lambda_{02}=5000\mathring{A}$
$\frac{1}{\lambda_{03}}=0.004 nm^{-1}$ 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.