Calcite X-Ray Diffraction: Find Smallest Angle

In summary, the smallest angle at which diffracted x-rays can be detected is 30°, which can be calculated using the Bragg's law equation. The distance between the atomic planes in calcite is 0.30 nm and the incident x-rays have a wavelength of 30 pm.
  • #1
johnherald
3
0
Hello, I have a question about this optics related problem.

The distance between atomic planes in calcite is 0.30 nm. what is the smallest angle between these planes and an incident beam of 30pm x-rays at which diffracted x-rays can be detected?

Thank you so much for the help guys!
 
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  • #2


Hello, thank you for your question. The smallest angle at which diffracted x-rays can be detected can be calculated using the Bragg's law equation:

nλ = 2dsinθ

Where:
n = order of diffraction (usually 1)
λ = wavelength of the incident x-rays (30 pm = 3x10^-11 m)
d = distance between atomic planes (0.30 nm = 3x10^-10 m)
θ = angle of diffraction

Plugging in the values, we get:

1(3x10^-11 m) = 2(3x10^-10 m)sinθ
sinθ = 1/2
θ = sin^-1(1/2)
θ = 30°

Therefore, the smallest angle between the atomic planes and the incident beam of 30 pm x-rays at which diffracted x-rays can be detected is 30°.

I hope this helps! Let me know if you have any further questions.
 

1. What is calcite X-ray diffraction and how does it work?

Calcite X-ray diffraction is a technique used in the field of mineralogy to determine the crystal structure of a mineral. It works by shining a beam of X-rays onto a sample of the mineral and measuring the angles at which the X-rays are diffracted. These angles can then be used to determine the arrangement of atoms within the mineral's crystal lattice.

2. Why is finding the smallest angle important in calcite X-ray diffraction?

Finding the smallest angle in calcite X-ray diffraction is important because it allows for more accurate determination of the mineral's crystal structure. The smallest angle corresponds to the distance between the atoms in the crystal lattice, which is a crucial piece of information for identifying the mineral.

3. How is the smallest angle determined in calcite X-ray diffraction?

The smallest angle is determined by analyzing the diffraction pattern produced when X-rays are shined onto the mineral sample. This pattern consists of peaks and valleys, and the smallest angle can be found by measuring the distance between the first two peaks.

4. What factors can affect the accuracy of the smallest angle in calcite X-ray diffraction?

Several factors can affect the accuracy of the smallest angle in calcite X-ray diffraction, including the quality of the mineral sample, the intensity and wavelength of the X-ray beam, and the precision of the measuring equipment. It is important to carefully control these factors to obtain reliable results.

5. How is calcite X-ray diffraction used in practical applications?

Calcite X-ray diffraction is used in a variety of practical applications, including identifying minerals in geological samples, analyzing the composition of rocks and minerals, and determining the crystal structure of new materials in materials science. It is also used in the pharmaceutical industry to analyze the crystal structure of drugs, which can affect their properties and effectiveness.

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