Neutron Detection with Cold Atoms · AI Generator #GEN-AFD46677

Physics · modern-physics

Problem

A novel neutron detector uses ultracold cesium atoms trapped in an optical lattice. When thermal neutrons (with kinetic energy corresponding to room temperature T=300  KT = 300\;\text{K}) collide with the cesium atoms, they can be detected through the recoil motion of the atoms. For detection to occur, the de Broglie wavelength of the recoiling cesium atom must be smaller than the lattice spacing d=500  nmd = 500\;\text{nm} so that the atom can be localized to a specific lattice site. Assume that in a head-on elastic collision, a thermal neutron transfers half of its kinetic energy to a initially stationary cesium-133 atom. The mass of a neutron is mn=1.67×10−27  kgm_n = 1.67 \times 10^{-27}\;\text{kg} and the mass of a cesium-133 atom is mCs=2.21×10−25  kgm_{Cs} = 2.21 \times 10^{-25}\;\text{kg}. Find the de Broglie wavelength of the recoiling cesium atom after the collision.

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