The neutron has a mass of 1.67 10-27 kg. Neutrons emitted in nuclear reactions c

Question

The neutron has a mass of 1.67 10-27 kg. Neutrons emitted in nuclear reactions can be slowed down by collisions with matter. They are referred to as thermal neutrons after they come into thermal equilibrium with the environment. The average kinetic energy ( 3/2 kBT) of a thermal neutron is approximately 0.04 eV. (a) Calculate the de Broglie wavelength of a neutron with a kinetic energy of 0.04 eV (b) How does your answer compare with the characteristic atomic spacing in a crystal? (c) Explain whether you expect thermal neutrons to exhibit diffraction effects when scattered by a crystal.

Explanation / Answer

Diffraction is the bending of waves around obstacles, or the spreading of waves by passing them through anaperture, or opening. Any type of energy that travels in a wave is capable of diffraction, and the diffraction of sound and light waves produces a number of effects. (Because sound waves are much larger than light waves, however, diffraction of sound is a part of daily life that most people take for granted.) Diffraction of light waves, on the other hand, is much more complicated, and has a number of applications in science and technology, including the use of diffraction gratings in the production of holograms.

How It Works

Comparing Sound and Light Diffraction

Imagine going to a concert hall to hear a band, and to yourchagrin, you discover that your seat is directly behind a wide post. You cannot see the band, of course, because the light waves from the stage are blocked. But you have little trouble hearing the music, since sound waves simplydiffractaround the pillar. Light waves diffract slightly in such a situation, but not enough to make a difference with regard to yourenjoymentof the concert: if you looked closely while sitting behind the post, you would be able to observe the diffraction of the light waves glowing slightly, as they widened around the post.

Suppose, now, that you had failed to obtain a ticket, but a friend who worked at the concert venue arranged to let you stand outside an open door and hear the band. The sound quality would be far from perfect, of course, but you would still be able to hear the music well enough. And if you stood right in front of thedoorway, you would be able to see light from inside the concert hall. But, if you moved away from the door and stood with your back to the building, you would see little light, whereas the sound would still be easilyaudible.

Wavelength and Diffraction

The reason for the difference

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