A reflaction from (111) planes of a cubic crystal was observed ad at a glancing angle of ` 11.2^(@)` when X -rays of wavelength 154 pm were used. What is the length of the side of the unit cell ? `( sin 11.2^(@) = 0.1944)`

Explanation

Here, `lambda`=154 pm, n=1 , `theta=11.2^@`
Applying Bragg's equation `2 d sin theta= n lambda`
i.e., `d_111=(nlambda)/(2 sin theta)=(1xx154)/(2xx0.1944) ` pm =396 pm
Further , the separation between the planes of a cubic crystal is given by
`d_"hkl"=a/(sqrt(h^2+k^2+l^2))`
`therefore d_11=a/(sqrt(1^2+1^2+1^2))`=396 pm (calculated above )
or `a=396xxsqrt3`=686 pm