Matter Waves and de Broglie Wavelength PYQs: JEE Mains Physics

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1. 1. 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
2. 2. 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
3. 3. 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
4. 4. 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
5. 5. 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
6. 6. 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
7. 7. 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
8. 8. 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
9. 9. 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
10. 10. 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
11. 11. 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
12. 12. 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
13. 13. 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
14. 14. A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as _______. 2024 Hard
15. 15. 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
16. 16. 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
17. 17. The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is \(25 \%\) of the velocity of light, then the ratio of \(K.E.\) of electron and \(K.E.\) of photon will be: 2024 Hard
18. 18. A proton and an \(\alpha\)-particle are accelerated from rest by \(2\,V\) and \(4\,V\) potentials, respectively. The ratio of their de-Broglie wavelength is: 2023 Medium
19. 19. A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of \(\lambda\). An alpha particle having certain kinetic energy has the same de-Brogle wavelength \(\lambda\). The ratio of kinetic energy of proton and that of alpha particle is: 2023 Medium
20. 20. An electron accelerated through a potential difference \(V_1\) has a de-Broglie wavelength of \(\lambda\). When the potential is changed to \(V _2\), its de-Broglie wavelength increases by \(50 \%\). The value of \(\left(\frac{ V _1}{ V _2}\right)\) is equal to : 2023 Medium
21. 21. An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength: 2023 Medium
22. 22. Electron beam used in an electron microscope, when accelerated by a voltage of \(20\,kV\). has a de-Broglie wavelength of \(\lambda_0\). If the voltage is increased to \(40\,kV\). then the de-Broglie wavelength associated with the electron beam would be: 2023 Medium
23. 23. Proton \((P)\) and electron \((e)\) will have same deBroglie wavelength when the ratio of their momentum is (assume, \(m _{ p }=1849\,m _{ e }\)) 2023 Easy
24. 24. The de Broglie wavelength of a molecule in a gas at room temperature \((300\,K )\) is \(\lambda_1\). If the temperature of the gas is increased to \(600\,K\), then the de Broglie wavelength of the same gas molecule becomes \(..............\). 2023 Medium
25. 25. The de Broglie wavelength of an electron having kinetic energy \(E\) is \(\lambda\). If the kinetic energy of electron becomes \(\frac{E}{4}\), then its de-Broglie wavelength will be : 2023 Easy
26. 26. The kinetic energy of an electron, \(\alpha\)-particle and a proton are given as \(4K,2K\) and \(K\) respectively. The de-Broglie wavelength associated with electron ( \(\lambda e), \alpha\)-particle \((\lambda \alpha)\) and the proton \((\lambda p)\) are as follows: 2023 Medium
27. 27. The ratio of de-Broglie wavelength of an \(\alpha\)-particle and a proton accelerated from rest by the same potential is \(\frac{1}{\sqrt{ m }}\), the value of \(m\) is \(........\) 2023 Easy
28. 28. The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy: (Assume \(m_p=m_e \times 1849\) ) 2023 Medium
29. 29. A nucleus of mass \(M\) at rest splits into two parts having masses \(\frac{M^{\prime}}{3}\) and \(\frac{2 M^{\prime}}{3}\left(M^{\prime} < M\right)\). The ratio of de Broglie wavelength of two parts will be. 2022 Easy
30. 30. A proton, a neutron, an electron and an \(\alpha\,-\)particle have same energy. If \(\lambda_{ p }, \lambda_{ n }, \lambda_{ e }\) and \(\lambda_{\alpha}\) are the de Broglie's wavelengths of proton, neutron, electron and \(\alpha\) particle respectively, then choose the correct relation from the following 2022 Medium
31. 31. An electron of mass m with an initial velocity \(\overrightarrow{ V }= V_0 \hat i \,(V_0 > 0)\) enters an electric field \(\vec E = -\vec E_0 \hat i \,(E_0 =\) constant \(> 0)\) at \(t = 0.\) If \(\lambda_0\) is its de-Broglie wavelength initially,then its de-Broglie wavelenght at time \(t\) is 2022 Hard
32. 32. An \(\alpha\) particle and a carbon \(12\) atom has same kinetic energy \(K\). The ratio of their de-Broglie wavelength \(\left(\lambda_{a}: \lambda_{C 12}\right)\) is 2022 Medium
33. 33. The equation \(\lambda=\frac{1.227}{ x } nm\) can be used to find the de-Brogli wavelength of an electron. In this equation \(x\) stands for : Where,\(m =\) mass of electron \(P =\) momentum of electron \(K =\) Kinetic energy of electron \(V =\) Accelerating potential in volts for electron 2022 Easy
34. 34. The ratio of wavelengths of proton and deuteron accelerated by potential \(V_{p}\) and \(V_{d}\) is 1: \(\sqrt{2}\). Then, the ratio of \(V_{p}\) to \(V_{d}\) will be 2022 Medium
35. 35. A moving proton and electron have the same deBroglie wavelength. If \({K}\) and \({P}\) denote the \({KE}\). and momentum respectively. Then choose the correct option : 2021 Medium
36. 36. A particle is travelling \(4\) times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is \(2: 1,\) the mass of the particle is 2021 Medium
37. 37. A particle of mass \(4\, {M}\) at rest disintegrates into two particles of mass \({M}\) and \(3 \,{M}\) respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass \(M\) to that of mass \(3\, {M}\) will be : 2021 Medium
38. 38. A particle of mass \(9.1 \times 10^{-31}\, {kg}\) travels in a medium with a speed of \(10^{6}\, {m} / {s}\) and a photon of a radiation of linear momentum \(10^{-27} \,{kg}\, {m} / {s}\) travels in vacuum. The wavelength of photon is \(....\) times the wavelength of the particle. 2021 Medium
39. 39. An electron moving with speed \(v\) and a photon moving with speed \(c,\) have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is - 2021 Medium
40. 40. An electron of mass \(m\) and a photon have same energy \(E.\) The ratio of de-Broglie wavelengths associated with them is 2021 Medium
41. 41. An electron of mass \(m _{ e }\) and a proton of mass \(m _{ p }=1836 m _{ e }\) are moving with the same speed. The ratio of their de Broglie wavelength \(\frac{\lambda_{\text {electron }}}{\lambda_{\text {proton }}}\) will be ....... . 2021 Medium
42. 42. An electron of mass \(m_{e}\) and a proton of mass \(m_{p}\) are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is 2021 Medium
43. 43. An \(\alpha\) particle and a proton are accelerated from rest by a potential difference of \(200\, V\). After this, their de Broglie wavelengths are \(\lambda_{\alpha}\) and \(\lambda_{p}\) respectively. The ratio \(\frac{\lambda_{p}}{\lambda_{a}}\) is 2021 Medium
44. 44. Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :- 2021 Hard
45. 45. The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of \(100\, V\). What should nearly be the ratio of their wavelengths ? \(\left( m _{ P }=1.00727\, u , m _{ e }=0.00055 \,u \right)\) 2021 Medium
46. 46. The de-Broglie wavelength of a particle having kinetic energy \(E\) is \(\lambda\). How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to \(75 \,\%\) of the initial value ? 2021 Hard
47. 47. The de Broglie wavelength of a proton and \(\alpha\) -particle are equal. The ratio of their velocities is ...... . 2021 Medium
48. 48. The temperature of an ideal gas in \(3-\)dimensions is \(300\, {K}\). The corresponding de-Broglie wavelength of the electron approximately at \(300\,{K}\), is \(....\,nm\) \(\left\lfloor{m}_{e}=\text { mass of electron }=9 \times 10^{-31} \,{kg}\right.\) \({h}=\text { Planck constant }=6.6 \times 10^{-34} {Js}\) \(\left.{k}_{{B}}=\text { Boltzmann constant }=1.38 \times 10^{-23}\, {JK}^{-1}\right]\) 2021 Medium
49. 49. What should be the order of arrangement of de-Broglie wavelength of elelctron \(\left(\lambda_{{e}}\right)\), an \(\alpha-\) particle \(\left(\lambda_{\alpha}\right)\) and proton \(\left(\lambda_{p}\right)\) given that all have the same kinetic energy ? 2021 Medium
50. 50. A particle is moving \(5\) times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is \(1.878 \times 10^{-4}\). The mass of the particle is close to 2020 Medium

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