What is the de Broglie wavelength of a particle of momentum p?

h ÷ p. More momentum, shorter wavelength.

What is the evidence that electrons have wave properties?

electron diffraction. Diffraction is something only waves do.

A proton and an electron move at the same speed. Which has the longer de Broglie wavelength?

the electron. The electron has far less momentum.

Which pair of observations shows that light has both wave and particle properties?

diffraction and the photoelectric effect. Diffraction needs waves; the photoelectric effect needs photons.

Electron diffraction and matter waves · Cambridge A Level Physics

In plain words

If light, a wave, can behave like particles, can particles behave like waves? They can. Fire a beam of electrons through a thin layer of graphite and they make rings on a screen: a diffraction pattern, the signature of a wave.

Three things to know

Wave–particle duality: light shows wave behaviour (interference, diffraction) and particle behaviour (the photoelectric effect). So do electrons and other particles.
Every moving particle has a de Broglie wavelength λ = h ÷ p, where p = mv is its momentum.
Electron diffraction is the evidence. Speeding the electrons up gives them more momentum and a shorter wavelength, so the rings get smaller.

Worked example

Find the de Broglie wavelength of an electron moving at 2.0 × 10⁶ m/s. (Mass of an electron = 9.11 × 10⁻³¹ kg.)

Momentum p = mv = 9.11 × 10⁻³¹ × 2.0 × 10⁶ = 1.82 × 10⁻²⁴ kg m/s.
λ = h ÷ p = 6.63 × 10⁻³⁴ ÷ 1.82 × 10⁻²⁴.
= 3.6 × 10⁻¹⁰ m, about the spacing of the atoms in a crystal.

Tips and tricks

A faster or heavier particle has a shorter wavelength: λ is inversely proportional to momentum.
Diffraction only shows up when the wavelength is about the size of the gap. That is why electrons diffract through crystals and footballs don't diffract through doorways.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Electron diffraction and matter waves: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is the de Broglie wavelength of a particle of momentum p?
- hp
- h ÷ p (the answer)
- p ÷ h
- h ÷ p²
More momentum, shorter wavelength.
What is the evidence that electrons have wave properties?
- the photoelectric effect
- electron diffraction (the answer)
- line spectra
- radioactive decay
Diffraction is something only waves do.
A proton and an electron move at the same speed. Which has the longer de Broglie wavelength?
- the proton
- the electron (the answer)
- they are equal
- neither has one
The electron has far less momentum.
The speed of an electron is doubled. What happens to its de Broglie wavelength?
- It halves. (the answer)
- It doubles.
- It stays the same.
- It falls to a quarter.
λ = h ÷ mv.
Which pair of observations shows that light has both wave and particle properties?
- diffraction and the photoelectric effect (the answer)
- diffraction and interference
- reflection and refraction
- polarisation and interference
Diffraction needs waves; the photoelectric effect needs photons.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

Electron diffraction and matter waves

Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org

Name ______________________________ Date ______________

State what electron diffraction shows about electrons.[2]
Show answerHide answer
That they have wave properties: they behave as waves as well as particles.
I got this one
Find the de Broglie wavelength of a 0.060 kg tennis ball moving at 50 m/s.[2]
Show answerHide answer
2.2 × 10⁻³⁴ m. 6.63 × 10⁻³⁴ ÷ 3.0. It is far too small ever to notice.
I got this one
The accelerating p.d. in an electron diffraction tube is increased. State and explain what happens to the rings.[3]
Show answerHide answer
They get smaller. The electrons are faster, so they have more momentum and a shorter de Broglie wavelength, and a shorter wavelength is diffracted through smaller angles.
I got this one

Answers: Electron diffraction and matter waves

1. That they have wave properties: they behave as waves as well as particles.
2. 2.2 × 10⁻³⁴ m. 6.63 × 10⁻³⁴ ÷ 3.0. It is far too small ever to notice.
3. They get smaller. The electrons are faster, so they have more momentum and a shorter de Broglie wavelength, and a shorter wavelength is diffracted through smaller angles.