• Electrons accelerated to close to the speed of light have wave-like properties such as the ability to diffract and have a ?de Broglie wavelength?equal to:

• Where:
  • h?=?Planck's constant
  • m?= mass of an electron (kg)
  • v?= speed of the electrons (m s?1)
• When beams of neutrons or electrons are directed at a nucleus they will diffract around it
• The pattern formed by this diffraction has a predictable minimum which forms at an angle θ to the original direction according to the equation

• The diffraction pattern forms a central bright spot with dimmer concentric circles around it
• From this pattern, a graph of intensity against diffraction angle can be used to find the diffraction angle of the first minimum

• The graph of intensity against angle obtained through electron diffraction is as follows:

The first minimum of the intensity-angle graph can be used to determine nuclear radius

• Using this, the size of the atomic nucleus,?R, can be determined from:

• Where:
  • θ = angle of the first minimum (degrees)
  • λ = de Broglie wavelength (m)
  • R?= radius of the nucleus (m)

Geometry of electron diffraction

Step 1: Identify the first minimum from the graph

• Angle of first minimum, θ = 42°

Step 2: Write out the equation relating the angle, wavelength, and nuclear radius

Step 3: Calculate the nuclear radius,?R