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Worksheet: Particle Diffraction

Q1:

A diffraction pattern formed by X-rays of wavelength 0.170 nm determines that the spacing between crystalline planes in an NaCl crystal is 0.281 nm. A neutron beam produces diffraction intensity peaks at the same locations that such peaks occur in the X-ray diffraction pattern. What is the energy of neutrons in the beam?

Q2:

For an electron to be maximally diffracted by a crystal, its wavelength must be equal to the spacing of the crystal’s planes. For a separation between planes of 0.250 nm, find the potential difference through which an electron must be accelerated from rest if it is to be maximally diffracted by these planes.

Q3:

Experiments are performed with ultracold neutrons having velocities as small as 1.00 m/s.

Find the wavelength of such a neutron.

Find the kinetic energy of such a neutron.