Neutron Crystal Spectrometer · AI Generator #GEN-FE382E14

Physics · modern-physics

Problem

A thermal neutron spectrometer uses a single crystal of lithium fluoride (LiF) to analyze the energy distribution of neutrons from a nuclear reactor. The crystal has a lattice spacing of d=2.01×10−10  md = 2.01 \times 10^{-10}\;\text{m}. When neutrons undergo first-order Bragg diffraction at a glancing angle of θ=15.0°\theta = 15.0° from the crystal planes, they are detected by a counter. The neutrons have been thermalized at temperature T=300  KT = 300\;\text{K} and can be assumed to have a Maxwell-Boltzmann energy distribution. For neutrons at this temperature, the most probable kinetic energy is Emp=12kBTE_{mp} = \frac{1}{2}k_B T where kB=1.38×10−23  J/Kk_B = 1.38 \times 10^{-23}\;\text{J/K}. Find the de Broglie wavelength of the neutrons that satisfy the Bragg condition for first-order diffraction. Given: neutron mass mn=1.67×10−27  kgm_n = 1.67 \times 10^{-27}\;\text{kg}, Planck's constant h=6.63×10−34  J⋅sh = 6.63 \times 10^{-34}\;\text{J⋅s}.

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