5.6.4 Wave-particle duality and the de Broglie wavelength Quiz: Pearson Edexcel Physics, Unit 5

The 20 questions

1. What is the de Broglie equation?

   • lambda = h/(m v^2)
   • lambda = h p
   • lambda = h/p, where p is the momentum of the particle
   • lambda = p/h

2. How is the momentum p of a particle of mass m and speed v defined?

   • p = m/v
   • p = m v
   • p = m^2 v
   • p = (1/2) m v^2

3. Which observation provides evidence that electrons have wave properties?

   • Electrons being ejected from a metal surface by light
   • Diffraction patterns produced when electrons pass through a thin crystal or metal foil
   • Electrons being repelled by like charges
   • Electrons having a measurable charge of -1.6 x 10^-19 C

4. What is meant by wave-particle duality?

   • The idea that both matter and electromagnetic radiation show wave and particle behaviour, depending on the experiment
   • The idea that light is always a particle
   • The idea that only photons have wave properties
   • The idea that electrons are always waves

5. What is the momentum of a photon of wavelength lambda?

   • p = h/lambda squared
   • p = lambda/h
   • p = h lambda
   • p = h/lambda

6. As the speed of an electron increases, what happens to its de Broglie wavelength?

   • It stays the same
   • It increases
   • It increases in proportion to the square of the speed
   • It decreases

7. Why are electrons used in electron microscopes rather than visible light?

   • Electrons are not affected by magnetic fields
   • Electrons have a much shorter de Broglie wavelength than visible light, giving higher resolution
   • Electrons travel faster than light
   • Electrons have a longer wavelength than visible light

8. An electron of mass 9.1 x 10^-31 kg moves at 2.0 x 10^6 m/s. What is its de Broglie wavelength? Take h = 6.63 x 10^-34 J s.

   • 3.6 x 10^-7 m
   • 2.2 x 10^9 m
   • 1.2 x 10^-15 m
   • 3.6 x 10^-10 m

9. A proton of mass 1.67 x 10^-27 kg moves at 1.0 x 10^4 m/s. What is its de Broglie wavelength? Take h = 6.63 x 10^-34 J s.

   • 4.0 x 10^-14 m
   • 2.5 x 10^-10 m
   • 4.0 x 10^-8 m
   • 4.0 x 10^-11 m

10. A ball of mass 0.15 kg moves at 30 m/s. What is its de Broglie wavelength? Take h = 6.63 x 10^-34 J s.

    • 1.5 x 10^-30 m
    • 1.5 x 10^-34 m
    • 2.2 x 10^-33 m
    • 1.5 x 10^-37 m

11. What is the momentum of a photon of wavelength 500 nm? Take h = 6.63 x 10^-34 J s.

    • 1.3 x 10^-21 kg m s^-1
    • 1.3 x 10^-27 kg m s^-1
    • 2.5 x 10^-7 kg m s^-1
    • 6.6 x 10^-40 kg m s^-1

12. An electron is accelerated from rest through a potential difference of 100 V. What is its de Broglie wavelength? Take m = 9.1 x 10^-31 kg, e = 1.6 x 10^-19 C and h = 6.63 x 10^-34 J s.

    • 1.2 x 10^-8 m
    • 3.6 x 10^-10 m
    • 1.2 x 10^-10 m
    • 1.2 x 10^-13 m

13. An electron has de Broglie wavelength 0.20 nm. What is its speed? Take m = 9.1 x 10^-31 kg and h = 6.63 x 10^-34 J s.

    • 3.6 x 10^3 m/s
    • 7.3 x 10^6 m/s
    • 1.8 x 10^6 m/s
    • 3.6 x 10^6 m/s

14. A photon and an electron have the same de Broglie wavelength. What is the ratio of the photon's momentum to the electron's momentum?

    • 2
    • 1836
    • 0.5
    • 1, because they have equal momenta

15. A student says that electrons are particles, so they cannot show diffraction. Which evaluation is correct?

    • Incorrect, because electrons have a de Broglie wavelength and so show diffraction and other wave behaviour
    • Correct, because diffraction needs a photon to be involved
    • Incorrect, because electrons are always waves and never particles
    • Correct, because only waves can diffract

16. An electron is accelerated from rest through 150 V. Using lambda = 1.23 nm/sqrt(V), with V in volts, what is its de Broglie wavelength?

    • About 1.2 x 10^-11 m
    • About 1.0 x 10^-10 m
    • About 1.5 x 10^-10 m
    • About 3.0 x 10^-10 m

17. An electron has de Broglie wavelength 0.10 nm. Roughly what is its kinetic energy? Take m = 9.1 x 10^-31 kg, h = 6.63 x 10^-34 J s, and 1 eV = 1.6 x 10^-19 J.

    • About 150 eV
    • About 1500 eV
    • About 0.15 eV
    • About 15 eV

18. By what factor does the de Broglie wavelength of an electron change when its accelerating potential is doubled?

    • It is halved
    • It is multiplied by 4
    • It is doubled
    • It is multiplied by about 0.71, which is 1/sqrt(2)

19. Why does electron diffraction provide support for the de Broglie hypothesis?

    • It shows electrons carry charge but have no wavelength
    • The pattern spacing matches the wavelength predicted by h/p for the electrons used
    • It shows electrons have zero mass
    • It shows electrons are photons carrying energy hf

20. A student states that a beam of electrons and a beam of photons with the same momentum have the same de Broglie wavelength. Which evaluation is correct?

    • Incorrect, because electrons have a fixed wavelength regardless of momentum
    • Incorrect, because wavelength depends only on charge
    • Incorrect, because photons have no momentum
    • Correct, because lambda = h/p applies to both, so equal momenta give equal wavelengths

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