In a cubic structure, atoms of 'X' occupy the corners, atoms of 'Y' occupy the centre of the body and atoms of 'Z' occupy the centres of all six faces. Write the composition of the unit cell.

Explanation

Position of .X. is corners of cube.
Number of corners = 8 
Contribution of atom as .X. to unit cell = 1/8 
Number of atoms of .X.` = 8 xx 1//8 = 1` 
Position of .Y. is centre of the body. 
Number of body centres = 1 
Contribution of atom of .Y. to unit cell = 1 
Number of atoms of `.Y.= 1xx1= 1` 
  Position of .Z. is centre of the face. 
Number of face centres = 6 
Contribution of atom of .Z. to unit cell = 1/2 
Number of atoms of `Z. = 6 xx1//2 = 3` 
The composition of unit cell containing atoms of X, Y and `Z=XYZ_(3)`