Search any question & find its solution
Question:
Answered & Verified by Expert
The graph between $1 / \lambda$ and stopping potential $(V)$ of three metals having work function $\phi_1, \phi_2$ 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].
Options:
Solution:
1474 Upvotes
Verified Answer
The correct answers are:
Ratio of work functions $\phi_1: \phi_2: \phi_3=1: 2: 4$.
,
$\tan \theta$ is directly proportional to $h c / e$, where $h$ is Planck's constant and $c$ is the speed of light.
Ratio of work functions $\phi_1: \phi_2: \phi_3=1: 2: 4$.
,
$\tan \theta$ is directly proportional to $h c / e$, where $h$ is Planck's constant and $c$ is the speed of light.
From the relation, $e V=\frac{h c}{\lambda}-\phi$ or $V=\left(\frac{h c}{e}\right)\left(\frac{1}{\lambda}\right)-\frac{\phi}{e}$ This is equation of straight line.
Slope is $\tan \theta=\frac{h c}{e}$
$$
\begin{aligned}
\phi_1: \phi_2: \phi_3 & =\frac{h c}{\lambda_{01}}: \frac{h c}{\lambda_{02}}: \frac{h c}{\lambda_{03}}=\frac{1}{\lambda_{01}}: \frac{1}{\lambda_{02}}: \frac{1}{\lambda_{03}}=1: 2: 4 \\
\frac{1}{\lambda_{01}} & =0.001 \mathrm{~nm}^{-1} \text { or } \lambda_{01}=10000 Å \\
\frac{1}{\lambda_{02}} & =0.002 \mathrm{~nm}^{-1} \text { or } \lambda_{02}=5000 Å \\
\frac{1}{\lambda_{03}} & =0.004 \mathrm{~nm}^{-1} \text { or } \lambda_{03}=25000 Å
\end{aligned}
$$
Violet colour has wavelength $4000 Å$.
So, violet colour can eject photoelectrons from metal-1 and metal-2.
Slope is $\tan \theta=\frac{h c}{e}$
$$
\begin{aligned}
\phi_1: \phi_2: \phi_3 & =\frac{h c}{\lambda_{01}}: \frac{h c}{\lambda_{02}}: \frac{h c}{\lambda_{03}}=\frac{1}{\lambda_{01}}: \frac{1}{\lambda_{02}}: \frac{1}{\lambda_{03}}=1: 2: 4 \\
\frac{1}{\lambda_{01}} & =0.001 \mathrm{~nm}^{-1} \text { or } \lambda_{01}=10000 Å \\
\frac{1}{\lambda_{02}} & =0.002 \mathrm{~nm}^{-1} \text { or } \lambda_{02}=5000 Å \\
\frac{1}{\lambda_{03}} & =0.004 \mathrm{~nm}^{-1} \text { or } \lambda_{03}=25000 Å
\end{aligned}
$$
Violet colour has wavelength $4000 Å$.
So, violet colour can eject photoelectrons from metal-1 and metal-2.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.