Relationship between Grating Spacing and Ring Radius?

[~Sam~]

Homework Statement

I'm doing a report on an electron diffraction experiment, where a carbon crystal is used as a diffraction grating. There are two line spacings d1, and d2. Observed in the experiment in two cocentric rings. What I'm unsure about is which spacing correlates to which spacing. Does a larger ring mean larger spacing? Or the other way around.

Homework Equations

None that I'm aware off.

The Attempt at a Solution

I've gone back and fourth on this, and all the equations I have doesn't seem to give me a conclusive answer. Anyone care to help?

 

[anathema]

Dear fellow scientist,

Thank you for sharing your question with the scientific community. It is a valid concern and one that requires careful consideration. As you are aware, electron diffraction experiments involve the use of a diffraction grating, which in this case is a carbon crystal. The two observed concentric rings indicate that there are two different line spacings, d1 and d2, within the crystal.

To answer your question, the larger ring corresponds to the larger line spacing and the smaller ring corresponds to the smaller line spacing. This is because the diffraction pattern is determined by the spacing between the crystal planes, with larger spacing resulting in a larger diffraction angle and thus a larger ring on the detector.

You can also confirm this by using the Bragg equation, which relates the diffraction angle to the spacing between crystal planes and the wavelength of the incident electrons. The equation is given by nλ = 2dsinθ, where n is the order of diffraction, λ is the wavelength, d is the spacing between crystal planes, and θ is the diffraction angle. As n and λ are constant in this experiment, the larger spacing d1 will result in a larger diffraction angle and thus a larger ring on the detector.

I hope this explanation helps to clarify your doubt. Keep up the good work and happy experimenting!