- 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:
- 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:
- θ = angle of the first minimum (degrees)
- λ = de Broglie wavelength (m)
- R = radius of the nucleus (m)
Geometry of electron diffraction
The graph shows how the relative intensity of the scattered electrons varies with angle due to diffraction by the oxygen-16 nuclei. The angle is measured from the original direction of the beam.
The de Broglie wavelength λ of each electron in the beam is 3.35 × 10−15 m.
Calculate the radius of an oxygen-16 nucleus using information from the graph.
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