Electron Diffraction | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Electron diffraction is the evidence for matter waves

An electron diffraction tube with an electron gun on the left, a thin graphite target in the tube and green concentric rings on the screen at the right. — A real electron-diffraction tube, redrawn as a clean apparatus illustration. The numbered anchors are explained below the image so labels never cover the apparatus.

1 · Electron gunA potential difference accelerates electrons into a narrow beam.
2 · Thin graphiteRegular atomic spacing diffracts the electron waves.
3 · Phosphor screenIndividual impacts build a pattern of concentric rings.

Electrons are accelerated through a potential difference and pass through thin polycrystalline graphite. The regular atomic spacing acts like a diffraction grating. Concentric rings form on the phosphor screen.

Each electron reaches one point on the screen, showing particle detection. Many electron impacts build a diffraction pattern, showing wave behaviour (9702/41/M/J/23 Q7(b)).

Key idea

One spot is not evidence of a wave. The regular pattern formed by many spots is the wave evidence.

Two identical hand-drawn phosphor screens compare widely spaced and closely spaced electron diffraction rings. — Raise the accelerating p.d.: momentum increases, de Broglie wavelength decreases, diffraction angle decreases, and the rings move closer together.

A larger accelerating potential difference gives the electrons more kinetic energy.
The electron momentum increases.
The de Broglie wavelength decreases.
The diffraction angle decreases, so the rings move closer together.

The graphite spacing has not changed. The pattern changes because the electron momentum and wavelength change.

Connect accelerating p.d. directly to momentum

For an electron accelerated from rest, the electrical energy transferred becomes kinetic energy. The relation below assumes that the electron remains non-relativistic.

eV=\dfrac{p^2}{2m}

Symbols

$e$ = magnitude of the electron charge (C)
$V$ = accelerating potential difference (V)
$p$ = electron momentum (N s)
$m$ = electron mass (kg)

p=\sqrt{2meV}

Momentum is proportional to the square root of the accelerating potential difference, so the de Broglie wavelength is inversely proportional to that square root.

Common mistake

Higher accelerating p.d. does not produce wider rings. It produces larger momentum, shorter wavelength and rings that are closer together.

Your turn9702/41/M/J/23 Q7(c)

Explain why increasing the accelerating potential difference makes the electron-diffraction rings move closer together.

Show worked answer

The electrons gain more kinetic energy, so their momentum increases and their de Broglie wavelength decreases. For the same graphite spacing, the diffraction angle is smaller, so the rings are closer.

Electron diffraction is the required evidence: individual electron impacts form a wave-like diffraction pattern.