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 occurs at `theta=30^(@)`. What is the kinetic energy of E of the beam in eV?

Explanation

Given,d = 0.1 nm,
`" "theta=30^(@)impliesn=1`
Now, according to Bragg's law
`" "2d sin theta=nlamdaimplies2xx0.1xxsin 30=1lamda`
`implies" "lamda =0.1nm implies=10^(-10)m`
Now, `" "lamda=h/(mv)=h/p`
`implies" "p=h/lamda=(6.62xx10^(-34))/(10^(-10))`
`implies" "=6.62xx10^(-24)kg-m//s`
Now, `" "KE=1/2mv^(2)=1/2(m^(2)v^(2))/(m)=1/2(p^(2))/(m)`
`" "=1/2xx((6.62xx10^(-24))^(2))/(1.67xx10^(-27))J=0.21eV`