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

Show Answer

Solution:

  1. 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.



NCERT Chapter Video Solution

Dual Pane