# Wave-particle duality for OCR A-level Physics

1. Diffraction
2. The photoelectric effect
3. De Broglie's wavelength

Diffraction is the process of waves spreading out as a result of passing through a narrow gap or by a barrier. This process is exhibited by waves, but not by particles, as shown in the diagram. Diffraction can occur in all types of wave and there are a few key examples to know, for example x-rays through metal foil and using a crystal to diffract light. Different experiments and types of waves create different diffraction patterns.

The photoelectric effect is an example of evidence that shows that electromagnetic waves have particle like behaviour. In the photoelectric effect, electromagnetic radiation is fired at a metal foil surface, and as a result electrons are emitted from the foil’s surface. There are no electrons emitted if the energy of the radiation is below the threshold frequency of the metal and above that frequency, the energy of the electrons can range to a maximum kinetic energy. The relationship between the energy of the photon and its frequency is given by the formula in the diagram.

The de Broglie equation links the momentum of the particle to its wavelength. This is related to the theory of wave particle duality, saying that all moving particles act like waves.

# 1

Photons with 4 × 10⁻¹⁹ J of energy hit a gold foil that has a work function of 1.78 × 10⁻¹⁹ J. What is the maximum kinetic energy of an electron emitted from its surface? Give your answer with 3 significant figures.

hf = φ + EkMax
EkMax = hf − φ =
= 4 × 10⁻¹⁹ − 1.78 × 10⁻¹⁹ =
= 2.22 × 10⁻¹⁹ J

2.22 × 10⁻¹⁹ J

# 2

Define the meaning of the de Broglie wavelength.

The de Broglie wavelength of a particle is the wavelength that is manifested in it for it to exhibit wave like properties.

# 3

What is meant by the term ‘work function’?

Work function is the minimum amount of energy required to remove an electron from the surface of a metal. This is dependent on the properties of the metal used in the experiment.

# 4

How is the pattern of wavefront altered as they emerge from a gap as its distance is significantly decreased?

As the gap decreases the amount of diffraction increases, the wavefronts become more curved at the edges. (You can also draw a diagram showing this).

# 5

The mass of an electron is 9.11 × 10⁻³¹ kg. What is the de Broglie wavelength of an electron which is travelling at 3.8 × 10³ ms⁻¹?

λ = h ÷ mv = 6.63 × 10⁻³⁴ ÷ (9.11 × 10⁻³¹ × 3.8 × 10³) = 1.92 × 10⁻⁷ m

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