A reflection from (111) planes of a cubic crystal was observed 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)

A reflection from (111) planes of a cubic crystal was observed at a gl

1.	A reflection from (111) planes of a cubic crystal was observed 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)
Answer» Solution :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