IB DP Physics: HL复习笔记12.2.2 Nuclear Scattering

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:

Nuclear-Radius-4

  • 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:

8.3.4-Electron-Diffraction-Graph

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:

Nuclear-Radius-5

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

8.3.4-Electron-Diffraction-Method

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.

Q5d

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

8.3.4-WE-Electron-Diffraction-Intensity-Graph-Answer

  • Angle of first minimum, θ = 42°

Step 2: Write out the equation relating the angle, wavelength, and nuclear radius
Electron-Diffraction-WE-1

Step 3: Calculate the nuclear radius, R
Electron-Diffraction-WE-2

 

 

 

 

 

 

转载自savemyexams

更多IB课程
翰林国际教育资讯二维码