A beam of thermal neutrons emerging from a research reactor has an average kinetic…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

A beam of thermal neutrons emerging from a research reactor has an average kinetic energy of

0.025\,\text{eV}

. The neutrons are directed toward a narrow crystalline channel whose diameter is

0.50\,\text{nm}

. Assume the neutron mass is

1.67\times10^{-27}\,\text{kg}

. Useful constants:

h = 6.63\times10^{-34}\,\text{J\,s}

and

1\,\text{eV}=1.60\times10^{-19}\,\text{J}

. (a) Calculate the momentum of a neutron with this kinetic energy. (b) Determine the neutron’s wavelength and state whether diffraction by the

0.50\,\text{nm}

channel is expected. Justify your answer quantitatively. (c) The neutrons are subsequently cooled until their wavelength doubles. Compute the new kinetic energy corresponding to the doubled wavelength.

Related theory

Matter Waves
Dual Nature of Radiation and Matter
De Broglie explanation of Bohr quantisation
Atoms

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