A neutron beam used for diffraction has de Broglie wavelength (with ).

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Nuclear Physics · Origins of quantum theory

The Nucleus Resolved, Ch Neutrons: the reagent with no barrier

Problem

A neutron beam used for diffraction has de Broglie wavelength

\lambda = 1.80\,\text{\AA}

(with

1\,\text{\AA}=10^{-10}\,\mathrm{m}

). ((a)) Using the non-relativistic relation between momentum and kinetic energy, with

pc = 2\pi\hbar c/\lambda

\hbar c = 197.327\,\mathrm{MeV\,fm}

and neutron rest energy

m_nc^2 = 939.57\,\mathrm{MeV}

, find the neutron's kinetic energy in eV. ((b)) State which of the three neutron energy regions (thermal, resonance or fast) this energy falls in, and give the temperature

T=E/k_B

of a moderator that would be in equilibrium with a neutron of this energy. ((c)) A second beam has neutrons of speed

4400\,\mathrm{m\,s^{-1}}

, exactly twice the

2200\,\mathrm{m\,s^{-1}}

reference speed. Find its kinetic energy and equivalent temperature, and discuss whether it is reasonable to call this beam thermal, given that the thermal region extends up to the cadmium cut-off of about

0.5\,\mathrm{eV}

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