For a primitive cubic crystal with `a = 3 xx 10^(3)m`, what is the smallest diffraction angle `theta,` for (1 1 0) plane for `lambda = 1.50 xx 10^(-10)` m?

Explanation

We have,
`nlambda = 2dsin theta`
and `d = a/sqrt(h^(2) + k^(2) + l^(2))`
`therefore n lambda = (2a)/sqrt(h^(2) +k^(2) + l^(2)) sin theta`
For first-degree reflection, n=1
`1 xx 1.50 xx 10^(-10) = (2 xx 3 xx 10^(10))/sqrt(1^(2) + 1^(2) +0^(2)) sin theta`
`sin theta = (sqrt(2) xx 1.50 xx 10^(-10))/(6 xx 10^(10))`
`therefore theta = 20.70^(@)`.