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Diffraction of neutrons

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3 part problem pertaining to neutrons being diffracted.

A ray of neutrons, with mass = 1.67x10^-27 kg, energy (E), is incident on a linear chain of nuclei, each of size (beta) arranged in a straight line with regular spacing.

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The expert examines diffractions of neutrons.

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(i)

You can blame Niels Bohr and De-Broglie.
What we see here is the classic example of the particle-wave duality of matter. If we look at the neutrons as hard spheres that interact via collisions with the nuclei, we should see a smooth distribution of angles in which the neutrons hit the screen. Obviously, no columbic interactions take place, since neutrons have no charge.

However, if the neutrons behave like waves, then we have a diffraction ...

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