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Wave/Particle Duality

de Broglie - Multiple Choice Questions

Q1. Electrons and protons in two beams are travelling at the same speed.

The beams are diffracted by objects of the same size.

Which correctly compares the de Broglie wavelength λe of the electrons with the de Broglie wavelength λp of the protons and the width of the diffraction patterns that are produced by these beams?
Comparison of de Broglie wavelength
Diffraction Pattern
A
λe>λp
 electron beam width > proton beam width
B
λe<λp
 electron beam width > proton beam width
C
λe>λp
 electron beam width < proton beam width
D
λe<λp
 electron beam width < proton beam width

 

The velocity of the protons and electrons is the same - so the momentum of the protons will be greater - this means the de Broglie wavelength for electrons will be greater than for protons.

The greater the wavelength, the greater the diffraction suffered by the wave. Therefore the electrons will be diffracted the most and have the bigger beam width.

The answer is therefore choice A

 

Q2. A proton moving with a speed 𝑣 has a de Broglie wavelength λ.

What is the de Broglie wavelength of an alpha particle moving at the same speed 𝑣?

A
¼ λ
B
λ
C
2λ
D
4λ

The alpha particle has four times the mass - and therefore four times the momentum of the proton.

The wavelength is invesely proportional to the momentum of the particle therefore:

The answer is choice A.

 

Q3. Electrons moving in a beam have the same de Broglie wavelength as protons in a separate beam moving at a speed of 2.8 × 104 m s–1 .

What is the speed of the electrons?

The proton has a much bigger mass than the electron.

As the wavelength is related to the momentum of the particle - the momentum of the electron must be the same as the momentum of the proton.

meve = mpvp

ve = mpvp/me

ve = 1.67 x 10-27 x 2.8 × 104/(9.11 x 10-31)

ve = 5.13 x 107 m s−1

Choice D

 

A
1.5 × 101 m s−1
B
2.8 × 104 m s−1
C
1.2 × 106 m s−1
D
5.1 × 107 m s−1

 

Q4. Which of the following statements suggests that electrons have wave properties?

A
 Electrons are emitted in photoelectric effect experiments.
B
 Electrons are released when atoms are ionised.
C
 Electrons produce dark rings in diffraction experiments.
D
 Electron transitions in atoms produce line spectra.