Wave nature of electrons and de Broglie wavelengthEdexcel International A Level Physics: Subtopic test

1. 1
   A physics technician is demonstrating an electron diffraction tube. Electrons from a heated filament are accelerated and directed at a very thin polycrystalline graphite film inside an evacuated glass tube. A fluorescent screen beyond the film shows a pattern of concentric bright rings.

   (a)

   What does the pattern of concentric rings on the screen show about electrons?

   [1 mark]

   • AElectrons are always deflected through a fixed angle by the graphite
   • BElectrons can show wave-like behaviour because they are diffracted
   • CElectrons are heavier than the carbon atoms in the graphite
   • DElectrons lose all their energy when they pass through graphite

   (b)

   The tube is evacuated. What is the reason for this?

   [1 mark]

   • ATo stop the graphite film from melting
   • BTo make the electrons travel more slowly
   • CTo stop electrons being scattered by air molecules
   • DTo increase the wavelength of the electrons

   (c)

   Explain why the ring pattern is evidence for the wave nature of electrons.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A teacher compares the behaviour of electrons with that of larger moving objects such as a tennis ball. She uses the de Broglie equation, with Planck constant h = 6.63 × 10⁻³⁴ J s and electron mass 9.11 × 10⁻³¹ kg, and considers an electron moving at 4.0 × 10⁶ m s⁻¹ in a vacuum.

   (a)

   Which expression gives the de Broglie wavelength λ of a particle of mass m moving at speed v, where h is the Planck constant?

   [1 mark]

   • Aλ = h / (mv)
   • Bλ = hmv
   • Cλ = mv / h
   • Dλ = hv / m

   (b)

   The electron's speed is now doubled, with all else unchanged. What happens to its de Broglie wavelength?

   [1 mark]

   • AIt doubles
   • BIt stays the same
   • CIt becomes one quarter of its original value
   • DIt halves

   (c)

   Calculate the de Broglie wavelength of the electron moving at 4.0 × 10⁶ m s⁻¹.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Electrons in a beam have a kinetic energy of 4.0 × 10⁻¹⁷ J. The beam is directed at a crystal in which the spacing between neighbouring layers of atoms is 0.21 nm. A student wants to know whether the electrons will be noticeably diffracted by the crystal.

   (a)

   Calculate the speed of an electron with kinetic energy 4.0 × 10⁻¹⁷ J.

   [3 marks]

   (b)

   Calculate the de Broglie wavelength of these electrons and deduce whether they will be noticeably diffracted by the crystal.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Electron diffraction experiments, first carried out in the 1920s, showed that particles such as electrons have wave properties. Electron beams are now used in electron microscopes, where the wavelength of the electrons determines how much fine detail can be seen.

   (a)

   Describe how an electron diffraction experiment provides evidence for the wave nature of electrons, and explain how the pattern changes if the electrons are made to travel faster.

   [6 marks]

   (b)

   An electron microscope uses electrons travelling at 2.0 × 10⁷ m s⁻¹. Calculate their de Broglie wavelength and deduce why the microscope can resolve finer detail than a light microscope using green light of wavelength 5.5 × 10⁻⁷ m.

   [6 marks]

   Total for question 4: 12 marks

End of questions