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

(a) `lambda=h/(sqrt(2Km)) of K=(h^(2))/(2lambda^(2)m)=((6.63xx10^(-34))^(2))/(2xx(1.4xx10^(-10))^(2)xx1.675xx10^(-27))=6.634xx10^(-21)J`
(b) `K=3/2kT=3/2xx(1.38xx10^(-23))xx300=6.21xx10^(-21)J`
`lambda=h/(sqrt(2Km))=(6.63xx10^(-34))/(sqrt(2xx6.21xx10^(-21)xx1.675xx10^(-27)))=1.45xx10^(-10)m`