Einstein's Photoelectric Equation PYQs: JEE Mains Physics

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1. 1. A light wave described by \(E =60 \sin \left(3 \times 10^{15}\right) t + \sin \left(12 \times 10^{15}\right)\) t] (in SI units) falls on a metal surface of work function 2.8 eV . The maximum kinetic energy of ejected photoelectron is (approximately) _________ eV . 2026 Medium
2. 2. For a certain metal, when monochromatic light of wavelength \(\lambda\) is incident, the stopping potential for photoelectrons is \(3V_0\). When the same metal is illuminated by light of wavelength \(2\lambda\), then the stopping potential becomes \(V_0\). The threshold wavelength for photoelectric emission for the given metal is \(\alpha\lambda\). The value of \(\alpha\) is _______. 2026 Medium
3. 3. \(K_1\) and \(K_2\) be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength \(\lambda_1\) and \(\lambda_2\), respectively. If \(\lambda_1=2\lambda_2\) then the work function of material is given by: 2026 Medium
4. 4. Light is incident on a metallic plate having work function \( 110\times10^{-20} \) J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is __________ rad/s. (\( h=6.63\times10^{-34} \) J.s) 2026 Medium
5. 5. Light source having wavelength \(331\) nm is used to generate photo-electrons whose stopping potential is \(0.2\) V. The work function of the used metal in the experiment is \(\alpha \times 10^{-19}\) J. The value of \(\alpha\) is _____.
   (\(h = 6.62 \times 10^{-34}\) J s, \(e = 1.6 \times 10^{-19}\) C and \(c = 3 \times 10^8\) m/s) 2026 Medium
6. 6. The graph shows variation of stopping potential \(V_o\) with the frequency \(\nu\) of the incident radiation for three photosensitive metals \(X_1\), \(X_2\) and \(X_3\). Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?
   2026 Medium
7. 7. A light source of wavelength \(\lambda\) illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength \(\frac{\lambda}{2}\), then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV ) 2025 Easy
8. 8. A monochromatic light is incident on a metallic plate having work function \(\phi\). An electron, emitted normally to the plate from a point \(A\) with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point \(B\). The distance between A and B is :
   (Given : The magnitude of charge of an electron is e and mass is \(\mathrm{m}, \mathrm{h}\) is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron) 2025 Medium
9. 9. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
   Assertion (A) : Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance.
   Reason (R) : A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation.
   In the light of the above statements, choose the most appropriate answer from the options given below : 2025 Medium
10. 10. In an experiment with photoelectric effect, the stopping potential, 2025 Medium
11. 11. In photoelectric effect, the stopping potential \(\left(\mathrm{V}_0\right) \mathrm{v} / \mathrm{s}\) frequency \((\nu)\) curve is plotted.
    ( h is the Planck's constant and \(\phi_0\) is work function of metal )
    (A) \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) is linear.
    (B) The slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) curve \(=\frac{\phi_0}{\mathrm{~h}}\)
    (C) h constant is related to the slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) line.
    (D) The value of electric charge of electron is not required to determine \(h\) using the \(V_0 \mathrm{v} / \mathrm{s} \nu\) curve.
    (E) The work function can be estimated without knowing the value of \(h\).
    Choose the correct answer from the options given below : 2025 Easy
12. 12. The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is _______. 2025 Easy
13. 13. For the photoelectric effect, the maximum kinetic energy \(\left(E_{\mathrm{k}}\right)\) of the photoelectrons is plotted against the frequency \((v)\) of the incident photons as shown in figure. The slope of the graph gives _______.
    2024 Hard
14. 14. In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at \(10.2 \mathrm{~V}\). The wavelength of light emitted by hydrogen atom when excited to the first excitation level is _______ \(\mathrm{nm}\). \(\left(\right.\) Given \(\mathrm{hc}=1245 \mathrm{eV} \mathrm{nm}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\) ). 2024 Hard
15. 15. In photoelectric experiment energy of \(2.48 \mathrm{eV}\) irradiates a photo sensitive material. The stopping potential was measured to be \(0.5 \mathrm{~V}\). Work function of the photo sensitive material is _______. 2024 Hard
16. 16. The de Broglie wavelengths of a proton and an \(\alpha\) particle are \(\lambda\) and \(2 \lambda\) respectively. The ratio of the velocities of proton and \(\alpha\) particle will be _______. 2024 Hard
17. 17. The threshold frequency of a metal with work function \(6.63\  \mathrm{eV}\) is: 2024 Hard
18. 18. \(UV\) light of \(4.13 \mathrm{eV}\) is incident on a photosensitive metal surface having work function \(3.13 \mathrm{eV}\). The maximum kinetic energy of ejected photoelectrons will be _______. 2024 Hard
19. 19. When a metal surface is illuminated by light of wavelength \(\lambda\), the stopping potential is \(8 \mathrm{~V}\). When the same surface is illuminated by light of wavelength \(3 \lambda\), stopping potential is \(2 \mathrm{~V}\). The threshold wavelength for this surface is _______. 2024 Hard
20. 20. When UV light of wavelength \(300 \mathrm{~nm}\) is incident on the metal surface having work function \(2.13 \mathrm{eV}\), electron emission takes place. The stopping potential is _______. (Given hc \(=1240 \mathrm{eV} \mathrm{nm}\) ) 2024 Hard
21. 21. A metallic surface is illuminated with radiation of wavelength \(\lambda\), the stopping potential is \(V_0\). If the same surface is illuminated with radiation of wavelength \(2 \lambda\), the stopping potential becomes \(\frac{V_0}{4}\). The threshold wavelength for this metallic surface will be - 2023 Medium
22. 22. Given below are two statements: Statement \(I:\) Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement \(II:\) Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light. In the light of above statements, choose the correct answer from the options given below: 2023 Medium
23. 23. Given below are two statements : Statement \(I :\) Stopping potential in photoelectric effect does not depend on the power of the light source. Statement \(II :\) For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light. In the light of above statements, choose the most appropriate answer from the options given below. Options : 2023 Medium
24. 24. Match List \(I\) with List \(II\)

    LIST \(I\)	LIST \(II\)
    \(A\) Planck's constant \(( h )\)	\(I\) \(\left[ M ^1 L ^2 T ^{-2}\right]\)
    \(B\) Stopping potential \(( Vs )\)	\(II\) \(\left[ M ^1 L ^1 T ^{-1}\right]\)
    \(C\) Work function \((\phi)\)	\(III\) \(\left[ M ^1 L ^2 T ^{-1}\right]\)
    \(D\) Momentum \(( p )\)	\(IV\) \(\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]\)

    2023 Medium
25. 25. The difference between threshold wavelengths for two metal surfaces \(A\) and \(B\) having work function \(\phi_A=9\,eV\) and \(\phi_{ B }=4.5\,eV\) in \(nm\) is:(Given, \(hc =1242\,eV\,nm\)) 2023 Easy
26. 26. The threshold frequency of metal is \(f_0\). When the light of frequency \(2 f_0\) is incident on the metal plate, the maximum velocity of photoelectron is \(v_1\). When the frequency of incident radiation is increased to \(5 f _0\). the maximum velocity of photoelectrons emitted is \(v_2\). The ratio of \(v_1\) to \(v_2\) is: 2023 Medium
27. 27. The work functions of Aluminium and Gold are \(4.1\,eV\) and \(5.1\,eV\) respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is \(.......\) 2023 Medium
28. 28. A metal exposed to light of wavelength \(800\,nm\) and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength \(500\, nm\) is used. The work function of the metal is \(...eV\) (Take \(hc =1230 \,eV - nm\) ). 2022 Medium
29. 29. A metal surface is illuminated by a radiation of wavelength \(4500 \; \mathring A\). The ejected photo-electron enters a constant magnetic field of \(2 \; mT\) making an angle of \(90^{\circ}\) with the magnetic field. If it starts revolving in a circular path of radius \(2 \; mm\), the work function of the metal is approximately ............. \(eV\) 2022 Hard
30. 30. An electron with speed \(v\) and a photon with speed \(c\) have the same \(de-Broglie\) wavelength. If the kinetic energy and momentum of electron are \(E_{ e }\) and \(pe _{ e }\) and that of photon are \(E _{ ph }\) and \(p _{ ph }\) respectively. Which of the following is correct? 2022 Medium
31. 31. Let \(K_{1}\) and \(K_{2}\) be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength \(\lambda_{1}\) and \(\lambda_{2}\), respectively are incident on a metallic surface. If \(\lambda_{1}=3 \lambda_{2}\) then 2022 Medium
32. 32. The electric field at the point associated with a light wave is given by \(E=200\left[\sin \left(6 \times 10^{15}\right) t+\sin \left(9 \times 10^{15}\right) t\right] \,Vm ^{-1}\) Given : \(h=4.14 \times 10^{-15} \,eVs\) If this light falls on a metal surface having a work function of \(2.50 \,eV\), the maximum kinetic energy of the photoelectrons will be ........... \(eV\) 2022 Hard
33. 33. The kinetic energy of emitted electron is \(E\) when the light incident on the metal has wavelength \(\lambda\). To double the kinetic energy, the incident light must have wavelength. 2022 Medium
34. 34. The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength \(6630 \; \mathring A\) is \(0.42 \; V\). If the threshold frequency is \(x \times\) \(10^{13}  / s\), where \(x\) is\(\dots\) (nearest integer). (Given, speed light \(=3 \times 10^{8} \; m / s\), Planck's constant \(=6.63 \times 10^{-34} \; Js\) ) 2022 Medium
35. 35. When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted election is \(v _{1}\). When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes \(v _{2}\). If \(v _{2}= x\) \(v _{1}\), the value of \(x\) will be........... 2022 Medium
36. 36. With reference to the observations in photo-electric effect, identify the correct statements from below: \(A.\) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. \(B.\) The value of saturation current increases on moving the source of light away from the metal surface. \(C.\) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light. \(D.\) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves. \(E.\) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves. Choose the correct answer from the options given below: 2022 Hard
37. 37. A light beam of wavelength \(500\, {nm}\) is incident on a metal having work function of \(1.25\, {eV}\), placed in a magnetic field of intensity \(B\). The electrons emitted perpendicular to the magnetic field \(B\), with maximum kinetic energy are bent into circular arc of radius \(30\, {cm}\). The value of \(B\) is \(....\,\times 10^{-7} \,{T}\). Given \({hc}=20 \times 10^{-26}\, {J}-{m}\), mass of electron \(=9 \times 10^{-31} \,{kg}\) 2021 Hard
38. 38. A monochromatic neon lamp with wavelength of \(670.5\, {nm}\) illuminates a photo-sensitive material which has a stopping voltage of \(0.48\, {V}\). What will be the stopping voltage if the source light is changed with another source of wavelength of \(474.6 \,{nm} ?\) (In \({V}\)) 2021 Hard
39. 39. In a photoelectric experiment ultraviolet light of wavelength \(280\, {nm}\) is used with lithium cathode having work function \(\phi=2.5\, {eV}\). If the wavelength of incident light is switched to \(400\, {nm}\), find out the change in the stopping potential (in \({V}\)). \(\left({h}=6.63 \times 10^{-34}\, {J} \cdots\right.\), \(\left.{c}=3 \times 10^{8} \,{ms}^{-1}\right)\)  2021 Hard
40. 40. The radiation corresponding to \(3 \rightarrow 2\) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \(5 \times 10^{-4} \,{T}\). Assume that the radius of the largest circular path followed by these electrons is \(7\, {mm}\), the work function of the metal is \(.....\,{eV}\) (Mass of electron \(=9.1 \times 10^{-31} \,{kg}\) ) 2021 Hard
41. 41. The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength \(491\, nm\) is \(0.710\, V\). When the incident wavelength is changed to a new value, the stopping potential is \(1.43\, V\). The new wavelength is ....... \(nm.\) 2021 Medium
42. 42. The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation 2021 Easy
43. 43. Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is \(x: y .\) The value of \(x\) is ...... . 2021 Hard
44. 44. When radiation of wavelength \(\lambda \) is incident on a metallic surface, the stopping potential is \(4.8\) volts. If the same surface is illuminated with radiation of double the wavelength, then the stopping potential becomes \(1.6\) volts. Then the threshold wavelength for the surface is 2021 Hard
45. 45. Given figure shows few data points in a photo electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surfface is\(.......eV\) (Plancks constant \(\left. h =6.62 \times 10^{-34}\, J . s \right)\)
    2020 Medium
46. 46. Radiation \(p\) with wavelength \(6561\;\mathring A\) falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of \(3 \times 10^{-4}\; T\). If the radius of the largest circular path followed by the electrons is \(10 \;\mathrm{mm},\) the work function of the metal is close to ............... \(eV\) 2020 Hard
47. 47. The surface of a metal is illuminated altemately with photons of energies \(E _{1}=4\, eV\) and \(E _{2}=2.5\, eV\) respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is \(2 .\) The work function of the metal in \(( eV )\) is\(......ev\) 2020 Medium
48. 48. Two sources of light emit X-rays of wavelength \(1\, nm\) and visible light of wavelength \(500\, nm ,\) respectively. Both the sources emit light of the same power \(200\, W\). The ratio of the number density of photons of X-rays to the number densitty of photons of the visible light of the given wavelengths is 2020 Medium
49. 49. When radiation of wavelength \(\lambda\) is used to illuminate a metallic surface, the stopping potential is \(V.\) When the same surface is illuminated with radiation of wavelength \(3 \lambda,\) the stopping potential is \(\frac{ V }{4} .\) If the threshold wavelength for the metallic surface is \(n \lambda\) then value of \(n\) will be...... 2020 Medium
50. 50. When the wavelength of radiation falling on a metal is changed from \(500 \,nm\) to \(200\, nm ,\) the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to\(.....eV\) 2020 Medium

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