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Nuclear Scattering (DP IB Physics: HL)

Revision Note

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Katie M

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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 

sin theta equals lambda over b

 

  • 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:

Electron Diffraction Graph, downloadable AS & A Level Physics revision notes

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:

sin space theta space equals space fraction numerator lambda over denominator 2 R end fraction

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

Electron Diffraction Method, downloadable AS & A Level Physics revision notes

Geometry of electron diffraction 

Worked example

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.Worked Example - Electron Diffraction Intensity GraphWorked Example - Electron Diffraction Intensity Graph, downloadable AS & A Level Physics revision notes

The de Broglie wavelength λ of each electron in the beam is 4.22 × 10−15 m.

Calculate the radius of an oxygen-16 nucleus using information from the graph.

   Step 1: Identify the first minimum from the graphWE - Electron Diffraction Intensity Graph Answer, downloadable AS & A Level Physics revision notes

    • Angle of first minimum, θ = 42°

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

sin space theta space equals space fraction numerator lambda over denominator 2 R end fraction

   Step 3: Calculate the nuclear radius, R

R space equals space fraction numerator lambda over denominator 2 sin space theta end fraction space equals space fraction numerator 4.22 space cross times space 10 to the power of negative 15 end exponent over denominator 2 cross times sin space open parentheses 42 close parentheses end fraction = 3.15 × 10−15 m

Examiner Tip

In the data booklet, you may notice the relation between angle and diameter appears a couple of times - in the Resolution topic, you are given the full equation for calculating the Rayleigh criterion

theta equals 1.22 lambda over b

However, in this topic, you are given the approximated version

sin space theta almost equal to lambda over D

This means you only need to use that version in exam questions about nuclear scattering, omitting the factor of 1.22 is acceptable and likely expected unless asked!

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.