12.2.9 Relativistic Kinetic Energy

Do Electrons Diffract?

• To investigate whether electrons did exhibit wave-like properties, an electron diffraction tube was produced
• The electrons were accelerated in an electron gun with a high potential difference, such as 5000 V, and were then directed through a thin film of graphite
  • The gaps between the carbon atoms were sufficiently small to cause diffraction, using the predicted DeBroglie wavelength of electrons 
  • Diffraction is a property of waves when passing through a small gap - if the electrons were seen to diffract then this was proof of their wave-like properties
• The electrons were indeed seen to diffract from the gaps between carbon atoms and produce a circular pattern on a fluorescent screen made from phosphor

Diagram of the electron diffraction experiment

A low voltage causes thermionic emission of electrons at the cathode, then these are accelerated towards anode directed through the graphite. The electrons diffract through the gaps between atoms in the graphite, forming a circular diffraction pattern made visible by the phosphor screen.

The Effect of Potential Difference on the Diffraction Pattern

• Recall that DeBroglie's hypothesis predicted that, if more work was done on the electrons, their wavelength would be shorter
  • Recall from the diffraction grating subtopic of the Waves topic, that a shorter wavelength leads to a smaller diffraction angle θ  for a given gap width
• Therefore, if DeBroglie was right, increasing the potential difference would cause the diffraction rings to move closer to the centre of the phosphor screen

Diagram showing the effect of increasing potential difference on diffraction

The left of this diagram shows the equipment from another angle. The right of this diagram shows that increasing the voltage caused the diffraction rings to move closer to the centre of the screen, following DeBroglie's equation.

• This was the first experimental proof of electrons exhibiting wave-like properties
  • The wavelength of electrons was significantly smaller than high energy forms of electromagnetic radiation, such as X-rays

• Changing the voltage across the anode (it is the voltage that causes the electrons to accelerate), scientists can manipulate the wavelength of the electron
• A microscope's resolving power (its ability to differentiate between two nearby points on an object) depends on the wavelength of the radiation being used
  • A shorter wavelength means the microscope can be used to see finer details in an object
  • Electrons had wavelengths much shorter than X-rays
• The size of an atom is roughly 10⁻¹⁰ m
  • By using DeBroglie's equation for an accelerated electron, researchers could find the accelerating voltage needed to make the electron's wavelength the same size as an atom