Why Does Bragg's Law Require Integers?

In summary, integers are used in Bragg's law because they represent the number of wavelengths of X-rays that are diffracted by a crystal. These integers also correspond to the order of diffraction peaks in the diffraction pattern and cannot be non-integer values. Using whole numbers in Bragg's law is important for accurately representing the diffraction pattern and determining the structure of a crystal. The intensity of the diffraction peaks is directly related to the integer values, with higher order peaks having lower diffraction efficiency.
  • #1
aoner
11
0
Hi there,

So in bragg's law [itex]2d\sin \theta =n\lambda[/itex], n needs to be an integer. Can anyone explain why? I mean, what if the extra path 2d that the 'second beam' has is not dividable by a wavelength?
Not sure if this is asked before but could not find it!

Cheers,
Adnan
 
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  • #2
Welcome to Physics Forums.

If the extra path 2dsinθ is not an integer multiple of the wavelength, then you don't get constructive interference, hence no wave for that angle θ.

img_full_47305.gif
 
  • #3
Ah, yes! Sorry just also came up with that haha. Thanks!
 

1. Why do we use integers in Bragg's law?

Integers are used in Bragg's law because they represent the number of wavelengths of X-rays that are diffracted by a crystal. This is based on the relationship between the angle of incidence, the spacing between crystal lattice planes, and the wavelength of the X-rays.

2. How do integers relate to the diffraction pattern in Bragg's law?

The integers in Bragg's law correspond to the order of diffraction peaks in the diffraction pattern. For example, the first integer (n=1) represents the first diffraction peak, the second integer (n=2) represents the second diffraction peak, and so on.

3. Can non-integer values be used in Bragg's law?

No, non-integer values cannot be used in Bragg's law because the law is based on the assumption that the X-rays are diffracted by the crystal lattice planes at specific angles. Non-integer values would not accurately represent the diffraction pattern.

4. Why is it important to use whole numbers in Bragg's law?

Using whole numbers in Bragg's law ensures that the diffraction pattern is accurately represented and that the angles of diffraction are precise. This is crucial for determining the structure of a crystal and interpreting the data obtained from X-ray diffraction experiments.

5. How do the integer values in Bragg's law affect the intensity of the diffraction peaks?

The intensity of the diffraction peaks in Bragg's law is directly related to the integer values. As the integer value increases, the intensity of the diffraction peak decreases. This is because the higher order peaks are further away from the central peak and therefore have a lower diffraction efficiency.

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