Electron Acceleration and Diffraction

00:00 8 marks

An electron is accelerated from rest through a potential difference of 5.0 kV.

Part a

3 minutes 2 marks

Question

Calculate the speed of the electron after acceleration, ignoring relativistic effects. [2]

Hint Hint

Hint

Equate the kinetic energy gained (\(\frac{1}{2}mv^2\)) to the potential energy lost (\(eV\)). Solve for \(v\).

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The speed of the electron is \(v \approx 4.2 \times 10^7 \text{ m s}^{-1}\).

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Part b

3 minutes 2 marks

Question

Calculate the de Broglie wavelength of the electron. [2]

Hint Hint

Hint

Use \(\lambda = h/p\), where \(p = m_e v\) is the momentum from part (a).

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The de Broglie wavelength is \(\lambda \approx 1.7 \times 10^{-11} \text{ m}\).

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Part c

2 minutes 2 marks

Question

This electron is incident on a thin graphite crystal. Describe the pattern that would be observed on a screen placed behind the crystal. [2]

Hint Hint

Hint

Consider diffraction of waves by a crystal lattice, e.g., Davisson-Germer experiment.

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A diffraction pattern consisting of concentric rings (or spots) showing maxima and minima of electron intensity.

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Part d

2 minutes 2 marks

Question

Explain how this observation provides evidence for the wave nature of particles. [2]

Hint Hint

Hint

What is diffraction and what does it imply?

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Diffraction is characteristic of waves. Observing diffraction with electrons shows they exhibit wave-like behavior, supporting wave-particle duality.

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