A. For what kinetic energy of neutron will the associated de Broglie wavelength be `1.40xx10^(-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`. Given the mass of neutron`=1:66xx10^(-27)kg` and `k=1.38xx10^(-23)Jkg^(-1)`.`

Explanation

Given, T = 300 k and `K = 1.38xx10^(-23)J//K`
`KE=(3)/(2) KT - (3)/(2)xx1.38xx10^(-21)xx300=6.21xx10^(-21)J`
`lambda = (h)/(sqrt(2m(KE)))=(6.63xx10^(-34))/(sqrt(2xx1.675xx10^(-27)xx6.21xx10^(-21))) therefore lambda = 1.45xx10^(-10)m = 1.45 Å`.