Wave-particle duality and de Broglie wavelengthEdexcel A-Level Physics: Subtopic test

1. 1
   Electrons travelling at a speed of 4.0 × 10⁶ m s⁻¹ are directed at a thin crystal in an evacuated tube. The spacing between neighbouring atoms in the crystal is about 2 × 10⁻¹⁰ m. The Planck constant is 6.63 × 10⁻³⁴ J s and the mass of an electron is 9.11 × 10⁻³¹ kg.

   (a)

   What is the momentum of one of the electrons?

   [1 mark]

   • A1.8 × 10⁻²⁴ kg m s⁻¹
   • B3.6 × 10⁻²⁴ kg m s⁻¹
   • C2.3 × 10⁻³⁷ kg m s⁻¹
   • D3.6 × 10⁻²¹ kg m s⁻¹

   (b)

   What is the de Broglie wavelength of the electrons?

   [1 mark]

   • A9.1 × 10⁻¹¹ m
   • B3.6 × 10⁻¹⁰ m
   • C5.5 × 10⁹ m
   • D1.8 × 10⁻¹⁰ m

   (c)

   Explain why a beam of these electrons would be expected to show noticeable diffraction at the crystal.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In an electron diffraction tube, electrons are accelerated through a potential difference in a vacuum and directed at a thin film of graphite. They then strike a fluorescent screen, where a pattern of concentric bright rings is seen.

   (a)

   Which type of pattern on the screen provides evidence for the wave nature of electrons?

   [1 mark]

   • AA single bright spot on the axis
   • BA uniform glow across the screen
   • CA random scatter of spots
   • DAlternating bright and dark regions

   (b)

   The accelerating potential difference is increased. What happens to the radii of the rings?

   [1 mark]

   • AThey decrease, because the de Broglie wavelength decreases
   • BThey increase, because the kinetic energy increases
   • CThey stay the same, because the film is unchanged
   • DThe rings disappear, because the electrons behave only as particles

   (c)

   Explain how the ring pattern shows that electrons have wave properties.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Electrons are released from rest and accelerated through a potential difference of 250 V in a vacuum, then directed at a thin crystal. The electron charge is 1.60 × 10⁻¹⁹ C, the electron mass is 9.11 × 10⁻³¹ kg and the Planck constant is 6.63 × 10⁻³⁴ J s.

   (a)

   Calculate the speed of the electrons after acceleration.

   [3 marks]

   (b)

   Calculate the de Broglie wavelength of the electrons. Protons are accelerated through the same potential difference. Explain how their de Broglie wavelength compares with that of the electrons.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student compares the wave behaviour of electrons with that of an everyday object. A beam of electrons of speed 2.0 × 10⁷ m s⁻¹ is directed at a thin graphite film, in which the spacing between atoms is about 2 × 10⁻¹⁰ m. She also considers a cricket ball of mass 0.16 kg thrown at 25 m s⁻¹ through a doorway 0.90 m wide. Use h = 6.63 × 10⁻³⁴ J s and electron mass 9.11 × 10⁻³¹ kg.

   (a)

   Describe how the electron beam would be used in an electron diffraction experiment with the graphite film and how the observations provide evidence for the wave nature of electrons. Explain what would be seen if the electrons were accelerated to a higher speed.

   [6 marks]

   (b)

   Calculate the de Broglie wavelength of the electrons and of the cricket ball. Evaluate the student's suggestion that the cricket ball should be diffracted as it passes through the doorway, and explain why electrons passing through the graphite behave differently.

   [6 marks]

   Total for question 4: 12 marks

End of questions