1. The problem statement, all variables and given/known data A beam of thermal neutrons emerges from a nuclear reactor and is incident on a crystal as shown in the figure below. The beam is Bragg scattered, as in the figure, from a crystal whose scattering planes are separated by 0.253 nm. From the continuous energy spectrum of the beam we wish to select neutrons of energy 0.0109 eV. Find the Bragg-scattering angle that results in a scattered beam of this energy. 2. Relevant equations Bragg Scattering 2dsin(θ)=nλ λ=[itex]hc/E[/itex]= [itex]hc/sqrt(2mc^2 * k)[/itex] hc= 1240 eV.nm 2mc2=511 keV 3. The attempt at a solution This is from a textbook chapter mostly on Heisenberg Uncertainty Relationships, so I feel like that must factor in, but I'm unsure as to how. Initially I just tried to solve for λ so I could plug that into the Bragg equation. I assumed the energy given for the neutrons is kinetic energy, so I attempted to solve for λ this way: λ=[itex]hc/E[/itex]=[itex](1240eV.nm)/sqrt(2 * 511E3 eV * 0.0109 eV)[/itex]=11.75nm. However, when you plug this value for λ into 2dsin(θ)=nλ (assuming n is 1), and take the inverse sin of 11.75nm/(2 * .253nm) you get an error. I also tried solving λ=[itex]hc/E[/itex], assuming that .0109 eV is just the E, but that also resulted in an answer for which you cannot take the inverse sin. I realize I'm probably missing something simple, but I've been stuck on this problem for a while. I don't understand what I'm doing wrong or how Heisenberg Uncertainty principles factor into this problem, if at all. Any help would be greatly appreciated.