STD 12 - Dual nature of radiation and matter 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. A monochromatic source of light operating at \(15\) kW emits \(2.5\times 10^{22}\) photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ________. (Take \(h=6.6\times 10^{-34}\) J·s and \(c=3\times 10^8\) m/s). 2026 Medium
3. 3. A particle having electric charge \(3 \times 10^{-19} C\) and mass \(6 \times 10^{-27} kg\) is accelerated by applying an electric potential of 1.21 V . Wavelength of the matter wave associated with the particle is \(\alpha \times 10^{-12} m\). The value of \(\alpha\) is _________ .
   (Take Planck's constant \(\left.=6.6 \times 10^{-34} J . s \right)\) 2026 Medium
4. 4. An electron is travelling with a velocity \(v\) in free space and when it enters a medium, its velocity is reduced by \(20\%\). The de Broglie wavelength of electron in the medium is \(\alpha\lambda_0\), where \(\lambda_0\) is its de Broglie wavelength in free space. The value of \(\alpha\) is _______. 2026 Medium
5. 5. An electron of mass \(m\) is moving in an electric field \(\vec{E} = -2E_0\hat{i}\) (\(E_0 =\) constant \(> 0\)), with an initial velocity \(\vec{V} = v_0\hat{i}\) (\(v_0 =\) constant \(> 0\)). If \(\lambda_0 = \dfrac{h}{4mv_0}\), its de Broglie wavelength at time \(t\) is __________.
   (\(e =\) charge of electron) 2026 Hard
6. 6. 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
7. 7. \(K_1\) 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
8. 8. 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
9. 9. 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
10. 10. Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ___________.
    (Given: \(h=6.63\times10^{-34}\) J.s and \(c=3\times10^{8}m/s\)) 2026 Hard
11. 11. The de Broglie wavelength associated with an electron accelerated through a potential difference V is \(\lambda_e\) and the de Broglie wavelength associated with a proton accelerated through the same potential difference is \(\lambda_p\). If their corresponding masses are \(m_e\) and \(m_p\), respectively, then the ratio of their de Broglie wavelengths \(\left(\dfrac{\lambda_e}{\lambda_p}\right)\) is ______. 2026 Medium
12. 12. The de Broglie wavelength for an electron accelerated through the potential difference of \(V_1\) volt is \(\lambda_1\). When the potential difference is changed to \(V_2\) volt, the associated de Broglie wavelength is increased by \(50\%\). If \((V_1/V_2) = (9/\alpha)\), then the value of \(\alpha\) is __________. 2026 Medium
13. 13. The de Broglie wavelength of an oxygen molecule at \(27^{\circ} C\) is \(x \times 10^{-12} m\). The value of \(x\) is (take Planck's constant \(=6.63 \times 10^{-34} J . s\), Boltzmann constant \(=1.38 \times 10^{-23} J / K\), mass of oxygen. Molecule \(\left.=5.31 \times 10^{-26} kg\right)\). 2026 Hard
14. 14. 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
15. 15. The ratio of de Broglie wavelength of a deutron with kinetic energy \(E\) to that of an alpha particle with kinetic energy \(2 E\), is \(n: 1\). The value of \(n\) is ___________.
    (Assume mass of proton = mass of neutron) : 2026 Hard
16. 16. When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V . If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V . The wavelength of first light is _________ m .
    \(\left( h =6.63 \times 10^{-34} J . s , e =1.6 \times 10^{-19} C , c =3 \times 10^8 m / s \right)\) 2026 Medium
17. 17. 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
18. 18. 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
19. 19. A photo-emissive substance is illuminated with a radiation of wavelength \(\lambda_i\) so that it releases electrons with de-Broglie wavelength \(\lambda_e\). The longest wavelength of radiation that can emit photoelectron is \(\lambda_0\). Expression for de-Broglie wavelength is given by :
    ( \(\mathrm{m}:\) mass of the electron, \(\mathrm{h}:\) Planck's constant and \(c\) : speed of light) 2025 Medium
20. 20. A proton of mass ' \(m_{\mathrm{p}}\) ' has same energy as that of a photon of wavelength ' \(\lambda\) '. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is _______. 2025 Medium
21. 21. A small mirror of mass \(m\) is suspended by a massless thread of length \(l\). Then the small angle through which the thread will be deflected when a short pulse of laser of energy \(E\) falls normal on the mirror ( \(\mathrm{c}=\) speed of light in vacuum and \(\mathrm{g}=\) acceleration due to gravity) 2025 Hard
22. 22. A sub-atomic particle of mass \(10^{-30} \mathrm{~kg}\) is moving with a velocity \(2.21 \times 10^6 \mathrm{~m} / \mathrm{s}\). Under the matter wave consideration, the particle will behave closely like _______. \(\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)\) 2025 Easy
23. 23. An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' \(-\sigma\) '. The rate of change of de-Broglie wave length associated with the electron varies inversely as \(\mathrm{n}^{\text {th }}\) power of time. The numerical value of \(n\) is ________. 2025 Hard
24. 24. An electron of mass ' m ' with an initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0\gt0\right)\) enters an electric field \(\overrightarrow{\mathrm{E}}=-\mathrm{E}_{\mathrm{o}} \hat{\mathrm{k}}\). If the initial de Broglie wavelength is \(\lambda_0\), the value after time t would be _______. 2025 Hard
25. 25. An electron with mass ' \(m\) ' with an initial velocity \((\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}} \quad\left(\mathrm{v}_0 \gt 0\right)\) enters a magnetic field \(\vec{B}=B_0 \hat{j}\). If the initial de-Broglie wavelength at \(\mathrm{t}=0\) is \(\lambda_0\) then its value after time ' t ' would be : 2025 Medium
26. 26. 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
27. 27. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : Electromagnetic waves carry energy but not momentum.
    Reason (\(\mathbf{R}\)): Mass of a photon is zero.
    In the light of the above statements, choose the most appropriate answer from the options given below : 2025 Easy
28. 28. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason \(\mathrm{R}\)
    Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases.
    Reason R : Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency.
    In the light of the above statements, choose the correct answer from the options given below 2025 Medium
29. 29. In an experiment with photoelectric effect, the stopping potential, 2025 Medium
30. 30. In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V , what is the wavelength of the em-wave ?
    (Given hc \(=1242 \mathrm{eVnm}\) where h is the Planck's constant and c is the speed of light in vaccum.) 2025 Easy
31. 31. 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
32. 32. The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is : 2025 Medium
33. 33. The ratio of the power of a light source \(S_1\) to that the light source \(S_2\) is \(2 . S_1\) is emitting \(2 \times 10^{15}\) photons per second at 600 nm . If the wavelength of the source \(S_2\) is 300 nm , then the number of photons per second emitted by \(S_2\) is _______ \(\times 10^{14}\). 2025 Medium
34. 34. 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
35. 35. The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of 2025 Medium
36. 36. Which of the following phenomena can not be explained by wave theory of light ? 2025 Medium
37. 37. A convex lens of focal length \(40 \mathrm{~cm}\) forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length \(20 \mathrm{~cm}\). The photoelectric current now is: 2024 Hard
38. 38. A point source is emitting sound waves of intensity \(16 \times 10^{-8} \mathrm{Wm}^{-2}\) at the origin. The difference in intensity (magnitude only) at two points located at a distances of \(2 \mathrm{~m}\) and \(4 \mathrm{~m}\) from the origin respectively will be _______ \(\times 10^{-8} \mathrm{Wm}^{-2}\) 2024 Hard
39. 39. A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as _______. 2024 Hard
40. 40. A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is _______. (Assume \(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{~m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}\) and \(\mathrm{m}_{\mathrm{p}}=1836\) times \(\mathrm{m}_{\mathrm{e}}\) ) 2024 Hard
41. 41. A proton and an electron have the same de Broglie wavelength. If \(K_p\) and \(K_e\) be the kinetic energies of proton and electron respectively. Then choose the correct relation : 2024 Hard
42. 42. Average force exerted on a non-reflecting surface at normal incidence is \(2.4 \times 10^{-4} \mathrm{~N}\). If \(360 \mathrm{~W} / \mathrm{cm}^2\) is the light energy flux during span of \(1\) hour \(30\) minutes. Then the area of the surface is _______. 2024 Hard
43. 43. 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
44. 44. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). \(Assertion\) \(A\) : Number of photons increases with increase in frequency of light. \(Reason\) \(R\) : Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation. In the light of the above statements, choose the most appropriate answer from the options given below : 2024 Hard
45. 45. Given below are two statements: Statement-\(I\): Figure shows the variation of stopping potential with frequency \((v)\) for the two photosensitive materials \(M_1\) and \(M_2\). The slope gives value of \(\frac{h}{e}\), where \(h\) is Planck's constant, \(e\) is the charge of electron. Statement-\(II\): \(M_2\) will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency. In the light of the above statements, choose the most appropriate answer from the options given below.
    2024 Hard
46. 46. If the total energy transferred to a surface in time \(t\) is \(6.48 \times 10^5 \mathrm{~J}\), then the magnitude of the total momentum delivered to this surface for complete absorption will be _______. 2024 Hard
47. 47. In a photoelectric effect experiment a light of frequency \(1.5\) times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be _______. 2024 Hard
48. 48. 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
49. 49. 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
50. 50. Monochromatic light of frequency \(6 \times 10^{14} \mathrm{~Hz}\) is produced by a laser. The power emitted is \(2 \times 10^{-3} \mathrm{~W}\). How many photons per second on an average, are emitted by the source? (Given \(\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\) ) 2024 Hard

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