Thermal neutrons emitted from a nuclear reactor can be used in experiments, espe

Question

Thermal neutrons emitted from a nuclear reactor can be used in experiments, especially if a broad range of neutron energies can be filtered to create a monoenergetic beam. Unfortunately, due to their lack of electric charge, neutrons essentially ignore the electric and magnetic fields that we typically use to manipulate electron and proton beams. Instead, we can intercept the neutrons with a graphite crystal. If the layers of the graphite crystal are 3.35 A apart and we isolate the portion of the beam diffracting through an angle of 59 , what will be the energy of the neutrons in this beam? (Such a device is called a crystal monochromator and it enables us to examine an unknown crystal using diffraction from the monoenergetic beam of neutrons.)

Explanation / Answer

from the Brag's law

2 d sintheta = m L

L = 2 d sintheta /m = 2 ( 3.35 * 10 ^ -10 ) sin 59 = 5.74 * 10 ^-10 m

energy is

E = hc/L = ( 6.63 * 10 ^-34 ) ( 3 * 10 ^8 )/ 5.74 * 10 ^-10 m

=3.46 * 10 ^-16 J

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