(a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 x 10-10 m? (b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) kT at 300 K.
(a) The wavelength associated with neutron, λ=1.4×10−10m Mass of neutron, m=1.66×10−27 kg The kinetic energy is given byK=21mv2 For de broglie wavelength and velocity, λ=mvh So, K=2λ2mh2=6.75×1021J=4.219×102eV (b) The temperature of surrounding T=300K, m is the mass of neutron. Boltzmann constant, K=1.38×10−23kgm2s−2K−1 Average K.E. of neutron is, K′=23KT K′=23KT⇒23(1.38×10−23×300)=6.21×10−21J From de broglie equation, λ′=2K′mh⇒2×6.21×10−21×1.66×10−276.6×10−34=0.146
