Q. A solid compound contains$\ X$, Y and Z atoms in a cubic lattice with X atom occupying the corners. Y atoms in the body centred positions and Z atoms at the centres of faces of the unit cell. What is the empirical formula of the compound?
A) $XY_{2}Z_{3}$
B) $XYZ_{3}$
C) $X_{2}Y_{2}Z_{3}$
D) $X_{8}YZ_{6}$
Explanation
(b)
Since atom $X$ is present at corner and one corner is shared by eight unit cells,
Number of X atoms per unit cell $= \frac{1}{8} \times 8 = 1$
Atom $Y$ is present at body centred position and used by only one unit cell. So, number of Y atoms per unit cell = 1
Atom Z is present at the center of each face, so shared by two unit cells,
Thus, number of Z atoms per unit cell $= \frac{1}{2} \times 6 = 3$
Hence, the formula of compound $= XYZ_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.