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A compound made up of elements A and B c...

A compound made up of elements `A` and `B` crystallizes in the cubic structures. Atoms `A` are present on the corners as well as face centres whereas atoms `B` are present on the edge centres centres as well as body centre. What is the formula of the compound? Draw the structure of its unit cell.

Text Solution

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The correct Answer is:
AB
Contribution made by the atoms (A)
Contribution on the corners `=8xx1//8=1`
Contribution on the faces `=6xx1//2=3`
`therefore` No. of atoms of A present = 1 + 3 = 4
Contribution made by the atoms (B)
Contribution on one edge = 1/4
Contribution on all the twelve edges `=12xx1//4=3`
Contribution on the body centre = 1
`therefore` No. of atoms of B present = 3 + 1 = 4
The formula of the compound : `A_(4)B_(4)` or AB.
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