In a face centred cubic arrangement of A and B atoms whose A atoms are at the corner of the unit cell and B atoms at the face centered. One of the A atom is missing from one corner in unit cell. The simplest formula of compound is

Question

$(a)\;A_7B_3\qquad(b)\;AB_3\qquad(c)\;A_7B_{24}\qquad(d)\;A_4B_3$

Answer 1

No. of atoms of A from corners of unit cell = $\large\frac{7}{8}$

No. of atoms of B from faces of unit cell = 3

Thus A:B = $\large\frac{7}{8} :3$

$\;\;\;\;\;\;\;\;Or = 7:24$

Thus the formula is $A_7B_{24}$

Hence answer is (c)