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Waves and Particle Nature of Light

de Broglie calculations and wave-particle duality

  • 2 things to know
  • Papers 2 and 3

Overview

Recall questions on finding a de Broglie wavelength from speed or accelerating voltage, why a cricket ball shows no diffraction, and why an electron is not simply a wave.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Process

Why is it wrong to call an electron simply a wave, and how would you shorten the electrons' wavelength in a microscope?

Numbers

Which observations show the wave nature of electrons and which the particle nature, and how does de Broglie wavelength change with speed?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    An electron is accelerated from rest through 100 V. What is its de Broglie wavelength?

    Model answer

    Its kinetic energy is 1.60 × 10⁻¹⁷ J, giving p = √(2 × 9.11 × 10⁻³¹ × 1.60 × 10⁻¹⁷) = 5.40 × 10⁻²⁴ kg m s⁻¹, so λ = 1.23 × 10⁻¹⁰ m.

  2. 2

    What happens to the diffraction rings when the accelerating potential difference is increased?

    Model answer

    The electrons gain more momentum, so their de Broglie wavelength is shorter and they diffract less, and the rings shrink towards the centre.

  3. 3

    How would the pattern change if protons replaced electrons travelling at the same speed?

    Model answer

    A proton is far more massive, so its momentum is much greater and its wavelength much shorter, and the diffraction would be very much weaker.

  4. 4

    What is the de Broglie wavelength of a 0.16 kg cricket ball moving at 30 m s⁻¹, and why is it never seen to diffract?

    Model answer

    Its wavelength is 6.63 × 10⁻³⁴ ÷ 4.8 = 1.4 × 10⁻³⁴ m, which is unimaginably smaller than any available gap, so no diffraction can be detected.

  5. 5

    Does the de Broglie wavelength of an object increase or decrease as it speeds up?

    Model answer

    It decreases, because the wavelength is inversely proportional to the momentum.

  6. 6

    What is meant by wave-particle duality?

    Model answer

    It is the idea that matter and radiation both show wave-like behaviour in some experiments and particle-like behaviour in others, so neither model alone is sufficient.

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