12.2.2 Nuclear Scattering

• 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 using:

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

Geometry of electron diffraction 

Worked Example

   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

= 3.15 × 10⁻¹⁵ m

Exam Tip