Worksheet: Particle Diffraction

In this worksheet, we will practice calculating the de Broglie wavelength of particles and the kinetic energy of such matter waves.


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?


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.


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.

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