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An alloy of g...

Question

An alloy of gold and copper crystallizes in a cubic lattice in which Au atoms occupy the lattice points at the corner of the cube and Cu atoms occupy the center of each of the cube faces. The formula of the compound is_________.

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Solution

$A u a t o m s o c c u p y t h e c o r n e r s n o . o f c o r n e r s = 8 c o n t r i b u t i o n o f 1 c o r n e r = \frac{1}{8} a t o m N o . o f a t o m s o f A u = \frac{1}{8} \times 8 = 1 a t o m s C u a t o m s o c c u p y t h e c e n t e r o f f a c e s n o . o f f a c e s = f c o n t r i b u t i o n o f 1 f a c e = \frac{1}{2} a t o m s n o . o f a t o m s o f C u = \frac{1}{2} \times 6 = 3 H e n c e t h e f o r m u l a w i l l b e A u C u_{3} S o i t i s T R U E .$

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