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22.3. Wave-particle duality
A subsection of Physics, 9702, through 22. Quantum physics
Listing 10 of 14 questions
State one piece of experimental evidence for: the particulate nature of electromagnetic radiation the wave nature of matter. Calculate the de Broglie wavelength λ of an alpha-particle moving at a speed of 6.2 × 107 m s–1. λ = m The speed v of the alpha-particle in is gradually reduced to zero. On , sketch the variation with v of λ. λ 6.2 v / 107 m s–1 Suggest an explanation for why people are not observed to diffract when they walk through a doorway.
9702_s22_qp_42
THEORY
2022
Paper 4, Variant 2
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State an effect, one in each case, that provides evidence for the wave nature of a particle, the particulate nature of electromagnetic radiation. Four electron energy levels in an isolated atom are shown in . energy –0.54 eV –0.85 eV –1.51 eV –3.40 eV For the emission spectrum associated with these energy levels, on , mark with an arrow the transition that gives rise to the shortest wavelength, show that the wavelength of the transition in is 4.35 × 10–7 m. State what is meant by the de Broglie wavelength. Calculate the speed of an electron having a de Broglie wavelength equal to the wavelength in . speed = m s–1
9702_w16_qp_42
THEORY
2016
Paper 4, Variant 2
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State an experimental phenomenon that provides evidence for: the particulate nature of electromagnetic radiation the wave nature of matter. A particle of matter moves with momentum p. State the equation that gives the effective wavelength λ of the particle. State the name of any other symbols used. State the name given to the wavelength of the moving particle. Electrons are accelerated from rest through a potential difference (p.d.) of 4.8 kV. Show that the final speed of the electrons is 4.1 × 107 m s–1. Calculate the effective wavelength of a beam of electrons moving at the speed in . wavelength = m
9702_w21_qp_41
THEORY
2021
Paper 4, Variant 1
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State an experimental phenomenon that provides evidence for: the particulate nature of electromagnetic radiation the wave nature of matter. A particle of matter moves with momentum p. State the equation that gives the effective wavelength λ of the particle. State the name of any other symbols used. State the name given to the wavelength of the moving particle. Electrons are accelerated from rest through a potential difference (p.d.) of 4.8 kV. Show that the final speed of the electrons is 4.1 × 107 m s–1. Calculate the effective wavelength of a beam of electrons moving at the speed in . wavelength = m
9702_w21_qp_43
THEORY
2021
Paper 4, Variant 3
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State the formula for the de Broglie wavelength λ of a moving particle. State the meaning of any other symbol used. Electrons accelerate through a potential difference, pass through a thin crystal and are then incident on a fluorescent screen. The pattern in is observed on the fluorescent screen. edge of screen not to scale State the name of the phenomenon shown by the electrons at the crystal. State what this phenomenon shows about the nature of electrons. Suggest why the thin crystal causes the phenomenon in . The electron is accelerated through a different potential difference. The new pattern observed on the screen is shown in . edge of screen not to scale State and explain the change that has been made to the potential difference to create the pattern shown in .
9702_m22_qp_42
THEORY
2022
Paper 4, Variant 2
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An electron has charge –q and mass m. It is accelerated from rest in a vacuum through a potential difference V. Show that the momentum p of the accelerated electron is given by p = ( ) mqV . The potential difference V through which the electron is accelerated is 120 V. State what is meant by the de Broglie wavelength. Calculate the de Broglie wavelength of the electron. wavelength = m The separation of copper atoms in a copper crystal is approximately 2 × 10–10 m. By reference to your answer in , suggest whether electron diffraction could be observed using a beam of electrons that have been accelerated through a potential difference of 120 V and are then incident on a thin copper crystal.
9702_s17_qp_42
THEORY
2017
Paper 4, Variant 2
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State what is meant by the de Broglie wavelength. shows a glass tube in which electrons are accelerated through a high p.d. to form a beam that is incident on a thin graphite crystal. filament cathode anode vacuum fluorescent screen glass tube high p.d. collimator electron beam graphite crystal – + (not to scale) After passing through the graphite crystal, the electrons reach the fluorescent screen. The screen glows where the electrons strike it. shows the fluorescent screen viewed end-on, from the right-hand side of . State the name of the phenomenon demonstrated by the pattern shown in . Explain what can be concluded from the pattern in about the nature of electrons. The electrons in are now accelerated through a greater potential difference between the cathode and the anode. On , sketch the pattern that is now seen on the fluorescent screen in . Explain, with reference to de Broglie wavelength, the change in the pattern on the fluorescent screen.
9702_s23_qp_41
THEORY
2023
Paper 4, Variant 1
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State what is meant by the de Broglie wavelength. shows a glass tube in which electrons are accelerated through a high p.d. to form a beam that is incident on a thin graphite crystal. filament cathode anode vacuum fluorescent screen glass tube high p.d. collimator electron beam graphite crystal – + (not to scale) After passing through the graphite crystal, the electrons reach the fluorescent screen. The screen glows where the electrons strike it. shows the fluorescent screen viewed end-on, from the right-hand side of . State the name of the phenomenon demonstrated by the pattern shown in . Explain what can be concluded from the pattern in about the nature of electrons. The electrons in are now accelerated through a greater potential difference between the cathode and the anode. On , sketch the pattern that is now seen on the fluorescent screen in . Explain, with reference to de Broglie wavelength, the change in the pattern on the fluorescent screen.
9702_s23_qp_43
THEORY
2023
Paper 4, Variant 3
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Questions Discovered
14