Electron Diffraction and Interference

Quantum Physics

Define electron diffraction.

The spreading of electrons when they pass through a gap or interact with a crystal lattice, producing a diffraction pattern.

Why does electron diffraction provide evidence that electrons behave as waves?

Diffraction is a wave phenomenon, so electrons producing a diffraction pattern demonstrates their wave nature.

What experiment first demonstrated electron diffraction?

The Davisson–Germer experiment.

What did Davisson and Germer do?

They fired a beam of electrons at a nickel crystal and measured the intensity of reflected electrons at different angles.

What did the nickel crystal act as in the Davisson–Germer experiment?

A diffraction grating for the electrons.

What did Davisson and Germer observe?

The intensity of reflected electrons varied with angle and produced a diffraction pattern.

Why was the Davisson–Germer experiment important?

It provided experimental evidence that electrons can behave as waves.

What can electron diffraction be used to determine?

The spacing between atoms in a crystal.

Who proposed that particles such as electrons could have a wavelength?

Louis de Broglie.

What is the de Broglie equation?

λ = h/p.

What does λ represent in the de Broglie equation?

The de Broglie wavelength of the particle in metres (m).

What does h represent in the de Broglie equation?

Planck's constant, 6.63 × 10⁻³⁴ J s.

What does p represent in the de Broglie equation?

The momentum of the particle in kg m s⁻¹.

How is the de Broglie wavelength related to momentum?

It is inversely proportional to momentum.

What happens to de Broglie wavelength when momentum increases?

The wavelength decreases.

What happens to de Broglie wavelength when momentum decreases?

The wavelength increases.

What is the equation for momentum at non-relativistic speeds?

p = mv.

How can the de Broglie equation be written using mass and velocity?

λ = h/mv.

What happens to an electron's de Broglie wavelength if its speed increases?

It decreases because its momentum increases.

What happens to an electron's de Broglie wavelength if its speed decreases?

It increases because its momentum decreases.

Why do everyday objects not show noticeable wave behaviour?

Their large momentum gives them an extremely small de Broglie wavelength.

Why can electrons show observable wave behaviour?

Their very small mass gives them a de Broglie wavelength large enough for diffraction and interference to be observed.

How are electrons accelerated in an electron diffraction tube?

A high potential difference accelerates the electrons.

What happens to electron speed when the accelerating potential difference increases?

The electron speed increases.

What happens to electron momentum when accelerating potential difference increases?

The momentum increases.

What happens to electron wavelength when accelerating potential difference increases?

The wavelength decreases.

What material can be used to diffract electrons in an electron diffraction tube?

Graphite.

Why does graphite produce electron diffraction?

Its regularly spaced carbon atoms act like a diffraction grating.

What pattern is produced by electron diffraction through graphite?

A circular diffraction pattern of rings.

What does observing diffraction rings from electrons demonstrate?

That electrons have wave properties.

What is electron interference?

The superposition of electron waves to produce regions of constructive and destructive interference.

Why does electron interference provide evidence for the wave nature of electrons?

Interference is a characteristic wave phenomenon.

What happens when electrons pass through a double slit?

They form an interference pattern.

What happens when electrons are sent through a double slit one at a time?

Individual electrons arrive as separate particles, but over time they build up an interference pattern.

Why is the single-electron double-slit experiment important?

It shows that individual electrons exhibit both particle and wave behaviour.

How do individual electrons appear when detected on a screen?

As individual localised spots.

What happens after many individual electrons have reached the screen?

The individual spots build up into an interference pattern.

What does the detection of individual electron spots demonstrate?

The particle nature of electrons.

What does the overall interference pattern demonstrate?

The wave nature of electrons.

What principle is demonstrated by electrons behaving as particles when detected but producing interference patterns?

Wave–particle duality.

Define wave–particle duality.

The principle that quantum objects such as electrons can display both wave-like and particle-like behaviour.

What are two examples of electrons behaving as waves?

Electron diffraction and electron interference.

What is an important application of the wave nature of electrons?

Electron microscopy.

Why can electron microscopes produce higher-resolution images than optical microscopes?

Electrons can have much shorter wavelengths than visible light.

How does wavelength affect the smallest object that can be resolved?

A shorter wavelength allows smaller objects to be resolved.

Why is the wavelength of an electron beam useful for microscopy?

It can be similar to or smaller than the dimensions of atoms.

Approximately what wavelength can electrons in an electron microscope have?

About 10⁻¹⁰ m.

How does the wavelength of electrons compare with visible light in electron microscopy?

Electron wavelengths can be around 1000 times shorter than visible-light wavelengths.

What effect does a shorter electron wavelength have on resolution?

It increases resolution, allowing much smaller structures to be distinguished.

How can the wavelength of electrons in an electron microscope be controlled?

By changing the accelerating voltage.

Why would a higher accelerating voltage be used to view a smaller object?

It increases electron momentum, decreasing the de Broglie wavelength and improving resolution.

What is the chain of effects when accelerating voltage is increased?

Higher voltage → greater electron speed → greater momentum → shorter de Broglie wavelength → better resolution.

What can electron microscopes be used to observe?

Extremely small structures such as bacteria, atoms and molecules.

Why can electron microscopes image objects much smaller than visible-light microscopes?

The wavelength of the electrons is much shorter than the wavelength of visible light.

What is the kinetic energy gained by an electron accelerated through a potential difference V?

KE = eV.

For a non-relativistic electron, how is kinetic energy related to momentum?

KE = p²/2m.

How can electron momentum be found after acceleration through a potential difference V?

p = √(2meV).

What is the de Broglie wavelength of an electron accelerated through a potential difference V?

λ = h/√(2meV).

What happens to electron wavelength if accelerating voltage is increased?

It decreases according to λ ∝ 1/√V.

What evidence shows that electrons have particle properties?

Electrons have a fixed charge and can be detected as individual localised particles.

What evidence shows that electrons have wave properties?

They produce diffraction and interference patterns.

Why is diffraction particularly strong when wavelength and atomic spacing are similar?

Significant diffraction occurs when the wavelength is comparable to the size of the gap or spacing.

Why are crystals suitable for electron diffraction experiments?

The regular spacing of atoms is comparable to the de Broglie wavelength of electrons.

State the main conclusion from electron diffraction experiments.

Electrons, although particles, possess a wavelength and can behave as waves.