How Does Copper's X-ray Wavelength Relate to Aluminum's Bragg Angle Calculation?

In summary, the problem discusses the use of x-rays to determine the interplanar distance from (111) planes in an aluminum sample with an fcc structure. The question mentions a previous statement about a copper target emitting an x-ray line of wavelength 1.54 Angstroms and then asks for the interplanar distance using Bragg's Law, which takes into account both the wavelength and atomic spacing. This is due to the fact that constructive interference of diffracted x-rays, like other types of waves, depends on both the wavelength and the lattice spacing.
  • #1
PsychonautQQ
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Homework Statement


I'm a bit confused by this question. It starts off by saying a Cu target emits an x-ray line of wavelength λ=1.54 Angstroms. It then goes and says part A of the problem..
A) Given that the Bragg angle for reflection from the (111) planes in Al is 19.2 degrees, computer the interplanar distance from these planes. Recall that aluminum has an fcc structure.

I don't understand why they start off by telling me about copper and then go onto aluminum in the actual question part... is there a connection that I am missing here?


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The Attempt at a Solution

 
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  • #2
For Bragg's Law you have nλ = 2dsinθ. This corresponds to when constructive interference of the diffracted x-rays occurs. You can also see from this equation that constructive interference depends on both the x-ray wavelength (λ) and the atomic spacing (d). It's the same for light diffraction or water wave diffraction - constructive interference always depends on the wavelength and the lattice spacing.

Note: The whole idea behind using x-rays to image crystals is that the wavelength of x-rays is on the same order as atomic spacings.
 

1. What are X-rays and how are they produced?

X-rays are a type of electromagnetic radiation with a shorter wavelength and higher energy than visible light. They are produced when high-speed electrons collide with a metal target, such as copper, in a process called bremsstrahlung.

2. What is the Bragg equation and how is it used in X-ray crystallography?

The Bragg equation, named after physicist William Henry Bragg, is used to determine the spacing between crystal planes in a crystal lattice. In X-ray crystallography, X-rays are directed at a crystal and the resulting diffraction pattern is used to calculate the angles and spacing of the crystal lattice.

3. Why is copper commonly used as a target material in X-ray tubes?

Copper is commonly used as a target material in X-ray tubes because it has a high atomic number, which means it can produce a higher intensity of X-rays compared to other metals. It also has a high melting point and good thermal conductivity, making it more durable and able to handle the heat generated during X-ray production.

4. How does the atomic structure of copper make it suitable for use in X-ray tubes?

Copper has an atomic structure that allows for efficient energy conversion from electrons to X-rays. It also has a high K-shell binding energy, which means it can produce a high-energy X-ray beam. Additionally, copper has a large number of electrons in its outer shell, making it more likely to interact with incoming electrons and produce X-rays.

5. How do X-ray/Bragg/Cu target systems work in medical imaging?

In medical imaging, X-ray/Bragg/Cu target systems work by using X-rays to penetrate the human body and create an image. The X-rays are produced by bombarding a copper target with high-speed electrons, which creates a beam of X-rays that pass through the body and are captured by a detector. The resulting image provides valuable information about the internal structures of the body.

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