student activity
12.3 Synchrotron light: X-ray diffraction reading comprehension
The $206 million Australian Synchrotron that has recently been built in Melbourne will be used by
over 1200 scientists per year.
What is a synchrotron?
It is a very bright source of infrared light, visible light, ultraviolet light, and X-rays.
A useful technique that utilises the X-rays from a synchrotron is X-ray diffraction. It allows scientists
to determine the arrangement of atoms and molecules in a substance.
How does it do this?
Consider the diagram of a lattice of atoms shown below. Two X-ray paths are incident on the lattice.
X-ray
X-ray

d

dsin
dsin
Diagram of crystal lattice
Image courtesy: DUIT Multimedia
The spacing between the planes of the atoms is labelled d and X-rays strike the planes at an angle . By
considering the two right angle triangles shown, the bottom X-ray has to travel further by a distance Y.
Equation 1 – the Bragg equation
Y  d sin   d sin   2d sin 

If the distance Y is a whole multiple of wavelengths then constructive interference will occur between
the two X-rays and a bright spot will appear in the diffraction pattern.
Equation 2
2d sin   n for constructive interference, where n = 1, 2, 3….
(eq. 1)

Section 12.3
Page 263
A photograph of the first X-ray diffraction patterns taken by Max von Laue (Nobel Prize in Physics
1914).
Image courtesy: Nobel Foundation, Sweden
The structure of an X-ray diffraction pattern can be used to determine the spacings of atoms in a
crystal.
If the angle  in the Bragg equation at which constructive interference occurs is known, and if the
wavelength of the X-rays (  ) is known, then the crystal lattice spacing (d) between the atoms can be
calculated.

William
Bragg and his son Lawrence were awarded the 1915 Nobel Prize in Physics for their work on
X-ray diffraction 
and their ability to determine the structure of crystals.
The famous double helix structure of DNA was determined with X-ray diffraction techniques. Crick,
Watson and Wilson were awarded the 1964 Nobel Prize in Medicine for their discovery of the
structure of DNA.
The Australian Synchrotron will provide scientists with the opportunity to perform very accurate X-ray
diffraction studies as the synchrotron produces an abundance of X-rays that are highly tuneable to a
precise wavelength. It is therefore possible to determine the structure of many molecules and solids of
interest in medicine, biology and materials science.
Section 12.3
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Questions
1.
X-rays of energy 1.32 kiloelectron volts are directed at an unknown crystal. What is the
wavelength of the X-rays? [2 marks]
2.
These X-rays diffract from the unknown crystal and the second order, that is when n equals 2
( n  2 ), and a diffraction bright spot is recorded at an angle   23.4. What is the spacing
between the crystal planes? [3 marks]


3.
Why are the X-rays produced in the Australian Synchrotron useful for X-ray diffraction
experiments? [1 mark]
4.
How would the Bragg equation be written for the condition of destructive interference of Xrays? [2 marks]
Section 12.3
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5.
a) If we assume that n is of the order of 1, and sin is very close to 1, what can you suggest
about the size of the spacing between atoms in a crystal? [1 mark]
b) Therefore, can you suggest why UV light, visible light, and infrared light are not as useful
for diffraction experiments? [1 mark]
6.
If the lattice spacing of a crystal is known, X-ray diffraction can also be used to calculate the
wavelength of unknown X-rays. If the first order ( n  1 ) constructive interference location for
X-rays is 20°, and the crystal spacing is 0.22 nm, what is the wavelength of the X-rays? [3 marks]

7.
The crystals used in X-ray diffraction often become very hot. Why would this occur? [2 marks]
Section 12.3
Page 266