JEE Advanced · Physics · 26. Dual Nature
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].

- 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.
Answer & Solution
Correct Answer
(C) \(\tan \theta\) is directly proportional to \(h c / e\), where \(h\) is Planck's constant and \(c\) is the speed of light.
Step-by-step Solution
Detailed explanation
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 \(\tan \theta=\frac{h c}{e}\)
\(\phi_1: \phi_2: \phi_3 =\frac{h c}{\lambda_{01}}: \frac{h c}{\lambda_{02}}: \frac{h c}{\lambda_{03}}=\frac{1}{\lambda_{01}}: \frac{1}{\lambda_{02}}:\) \(\frac{1}{\lambda_{03}}=1: 2: 4 \)
\( \frac{1}{\lambda_{01}} =0.001 \mathrm{~nm}^{-1} \text { or } \lambda_{01}=10000 Å \)
\( \frac{1}{\lambda_{02}} =0.002 \mathrm{~nm}^{-1} \text { or } \lambda_{02}=5000 Å \)
\( \frac{1}{\lambda_{03}} =0.004 \mathrm{~nm}^{-1} \text { or } \lambda_{03}=25000 Å\)
Violet colour has wavelength \(4000 Å\).
So, violet colour can eject photoelectrons from metal-1 and metal-2.
Slope is \(\tan \theta=\frac{h c}{e}\)
\(\phi_1: \phi_2: \phi_3 =\frac{h c}{\lambda_{01}}: \frac{h c}{\lambda_{02}}: \frac{h c}{\lambda_{03}}=\frac{1}{\lambda_{01}}: \frac{1}{\lambda_{02}}:\) \(\frac{1}{\lambda_{03}}=1: 2: 4 \)
\( \frac{1}{\lambda_{01}} =0.001 \mathrm{~nm}^{-1} \text { or } \lambda_{01}=10000 Å \)
\( \frac{1}{\lambda_{02}} =0.002 \mathrm{~nm}^{-1} \text { or } \lambda_{02}=5000 Å \)
\( \frac{1}{\lambda_{03}} =0.004 \mathrm{~nm}^{-1} \text { or } \lambda_{03}=25000 Å\)
Violet colour has wavelength \(4000 Å\).
So, violet colour can eject photoelectrons from metal-1 and metal-2.
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