Solving Bragg's Law: X-Ray & Electron Measurement

In summary, for part (a), the only angle at which there will be constructive interference is 30 degrees. For part (b), the classical model of an elastic collision can be used to calculate the energy of the electrons, which is necessary for them to be detected at the same angle as the X-rays.
  • #1
steve233
20
0
I'm preparing for a midterm exam and this is one of the practise questions I'm having a bit of trouble with.

Homework Statement



We have access to X-ray and electrons for the incident beam.
[itex] \theta [/itex] is the inner angle between the sample and the incident beam.

Spacing in sample = d =10^-10 m
[itex] \lambda [/itex] = 10^-10 m

a) What values of [itex] \theta [/itex] will we measure X-rays at a detector, that is, when will there be constructive interference (assume elastic collision)?

b) If we use electrons instead of X-rays, at which energy should they be to detect the electrons at the same angle as the X-rays (assume elastic collision)?

Homework Equations



Bragg's Law:
[itex]2 d sin(\theta) = m \lambda[/itex]
E = hf
p = h / [itex] \lambda [/itex]
Compton effect

The Attempt at a Solution


For part (a) what I did was basically use:

[itex]sin(\theta) = (1 \lambda) / (2d)[/itex]
[itex]sin(\theta) = (2 \lambda) / (2d)[/itex]

Since [itex]sin(\theta) = (2 \lambda) / (2d)[/itex] gives 90 degrees, my answer is that the only angle is 30 degrees, that is, m = 1.

For part (b) I'm not really sure how to approach this question. Is this just the classical model of an elastic collision?

Thanks.
 
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  • #2


Dear student,

For part (a), your approach is correct. The only angle at which there will be constructive interference is 30 degrees, as this satisfies the Bragg's Law equation. However, it is important to note that this is the ideal case and in reality, there may be some deviation from this angle due to imperfections in the sample or experimental setup.

For part (b), you are correct in thinking that this involves the classical model of an elastic collision. In this case, the energy of the electrons can be calculated using the equation E = p^2 / (2m), where p is the momentum of the electron and m is its mass. Since we know the wavelength of the electrons (10^-10 m) and the angle at which they should be detected (30 degrees), we can calculate the momentum using the equation p = h / \lambda * sin(\theta). Once we have the momentum, we can use it to calculate the energy of the electrons.

I hope this helps. Good luck on your exam!
 

FAQ: Solving Bragg's Law: X-Ray & Electron Measurement

1. What is Bragg's Law?

Bragg's Law is a mathematical equation that describes the relationship between the wavelength of X-rays or electrons and the angle at which they are diffracted by a crystal lattice. It is a fundamental principle in X-ray and electron diffraction techniques used in materials science and structural biology.

2. How is Bragg's Law used in X-ray and electron measurement?

Bragg's Law is used to determine the spacing between atoms or molecules in a crystal lattice. By measuring the diffraction angles and using Bragg's Law, researchers can calculate the distance between the planes of atoms in a material, revealing important structural information about the material.

3. Can Bragg's Law be applied to other types of waves?

Yes, Bragg's Law can be applied to any type of wave that exhibits diffraction, including sound waves and water waves. However, it is most commonly used in X-ray and electron diffraction techniques due to their ability to interact with the atomic structure of materials.

4. What is the significance of Bragg's Law in materials science?

Bragg's Law is crucial in materials science as it allows researchers to determine the atomic and molecular structure of materials, which is essential for understanding their physical and chemical properties. This information is used in the development of new materials and in improving existing ones.

5. How has Bragg's Law contributed to scientific research and discoveries?

Bragg's Law has played a significant role in many scientific discoveries and breakthroughs in various fields. It has been used to determine the structure of DNA, proteins, and other important biological molecules. It has also been used in the development of new materials, such as semiconductors, and in the study of crystal structures in minerals. Overall, Bragg's Law has greatly contributed to our understanding of the atomic world and has paved the way for countless scientific advancements.

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