A neutron beam of energy E scatters from atoms on a surface with a spacing d=0.1nm. The first maximum of intensity in the reflected beam occures at `theta=30^(@)`. What is the kinetic energy of E of the beam in eV?

Explanation

Here, `d=0.1nm, theta=30^(@), n=1`. According to Bragg's law
`2d sin theta=n lambda or 2xx0.1xxsin 30^(@)=1xxlambda or lambda=0.1nm=10^(-10)m`
`p=h/lambda=(6.62xx10^(-34))/(10^(-10))=6.62xx10^(-24)kgms^(-1)`
`KE=1/2 (p^(2))/m=1/2xx((6.62xx10^(-24))^(2))/(1.67xx10^(-27))J=1/2((6.62xx10^(-24))^(2))/((1.67xx10^(-27))xx(1.6xx10^(-19)))eV=0.082 eV`