Modern Physics Ques 84
- The graph between $1 / \lambda$ and stopping potential $(V)$ of three metals having work functions $\phi _1, \phi _2$ and $\phi _3$ 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 $\phi _1: \phi _2: \phi _3=1: 2: 4$
(b) Ratio of work functions $\phi _1: \phi _2: \phi _3=4: 2: 1$
(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
Answer:
Correct Answer: 84.(a,c)
Solution:
Formula:
- From the relation,
$ \begin{aligned} e V & =\frac{h c}{\lambda}-\phi \\ \text { or } \quad V & =(\frac{h c}{e})( \frac{1}{\lambda})-\frac{\phi}{e} \end{aligned} $
This is equation of straight line.
Slope is $\tan \theta=\frac{h c}{e}$
$\phi _1: \phi _2: \phi _3=\frac{h c}{\lambda _{01}}: \frac{h c}{\lambda _{02}}: \frac{h c}{\lambda _{03}}$
$ =\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.
BETA
