Modern Physics 2 Question 22
21. The graph between $1 / \lambda$ and stopping potential $(V)$ of three metals having work functions $\varphi _1, \varphi _2$ and $\varphi _3$ 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).
$(2006,5$ M)
(a) Ratio of work functions $\varphi _1: \varphi _2: \varphi _3=1: 2: 4$
(b) Ratio of work functions $\varphi _1: \varphi _2: \varphi _3=4: 2: 1$
(c) $\tan \theta$ is directly proportional to $h c / e$, 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
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Solution:
- From the relation,
$$ \begin{aligned} e V & =\frac{h c}{\lambda}-\varphi \\ \text { or } \quad V & =\frac{h c}{e} \frac{1}{\lambda}-\frac{\varphi}{e} \end{aligned} $$
This is equation of straight line.
Slope is $\tan \theta=\frac{h c}{e}$
$\varphi _1: \varphi _2: \varphi _3=\frac{h c}{\lambda _{01}}: \frac{h c}{\lambda _{02}}: \frac{h c}{\lambda _{03}}$
$$ =\frac{1}{\lambda _{01}}: \frac{1}{\lambda _{02}}: \frac{1}{\lambda _{03}}=1: 2: 4 $$
$\frac{1}{\lambda _{01}}=0.001 nm^{-1}$ or $\lambda _{01}=10000 \AA$
$\frac{1}{\lambda _{02}}=0.002 nm^{-1}$ or $\lambda _{02}=5000 \AA$
$\frac{1}{\lambda _{03}}=0.004 nm^{-1}$ or $\lambda _{03}=2500 \AA$
Violet colour has wavelength $4000 \AA$.
So, violet colour can eject photoelectrons from metal-1 and metal-2.
