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An alloy of gold (Au) and cadmium (Cd) c...

An alloy of gold (Au) and cadmium (Cd) crystallises with a cubic structure in which gold atoms occupy the corners and cadmium atoms fit into the face centers. What is the formula of this alloy?

Text Solution

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Gold atoms occupy all the corners of a unit cell, So, the number of gold atoms per unit cell ` = 8 xx (1)/(8)=1` atom
And cadmium atoms fit into the face centres, therefore, the number of cadmium atoms per unit cell `=6 xx (1)/(2) =3` atoms
`:.` Ratio of gold (Au) and cadmium (Cd) = 1:3
Hence, formula for the given alloy is `AuCd_(3)`.
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