Calcite X-Ray Diffraction: Find Smallest Angle

[johnherald]

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!

 

[jvicens]

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.