Question

A cubic unit cell of a compound has x atoms at the corners ofthe cube and the body centre and y atoms at the face centre .The formula ofthe compound wouldbe

Answer 1

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No. of X-atoms per unit cell = 88

=1

No. of Y-atoms per unit cell = 62

=3

Thus the formula is XY3

Hence answer is (c)

Answer 2

The formula of compound is x₂y₃.

A cubic unit cell of a compound has x atoms at the corners of the cube and the body centre and y atoms at the face centres.

We have to find the formula of compound.

Concept :

• A cubic unit cell has 8 corners and each corner is shared by 8 similar unit cells. so the number of atoms present in corners of unit cell is 8/8 = 1
• Body centre means, complete inside of a cubical unit cell. A cubic unit cell has only one body centre atom and it has been shared by only one unit cell. so the number of atoms present in body centre of unit cell is 1/1 = 1
• There are six faces in a cubic unit cell and each face is shared by two unit cells. so the number of atoms present in face centre of unit cell is 6/2 = 3

Here, x atoms present at the corners and body centre.

so number of x atoms = 1 + 1 = 2

y atoms present at the face centres

so number of y atoms = 3

Now, the ratio of x and y = x : y = 2 : 3

Therefore the formula of compound is x₂y₃.

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