Question

AB crystallises in FCC. A at 5 corners B at 2 faces. Predict the formula.

Answer 1

Answer:

• The formula of the compound is A₅ B₈

Given:

1. A is present at 5 corners.
2. B is present at 2 faces.

Explanation:

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Its given that AB crystallizes in FCC lattice.so, each corner will contribute 1/8 atom.

Therefore,

⇒ 1 Corner = 1/8 atoms

⇒ 5 corner = 5 × 1/8

                   = 5/8 atoms

⇒ No. of atoms of A = 5/8 atoms.

∴ No. of atoms of A is 5/8.

(Note this the no. of atoms present in one unit cell)

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Now we know each face center contributes 1/2 atom.

So,

⇒ 1 face center = 1/2 atom.

⇒ 2 face center = 2 × 1/2

                           = 1 atom

⇒ No. of atoms of B = 1 atom.

∴ No. of atom of B is 1.

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⇒ Formula of compound = A : B

⇒ A : B = 5/8 : 1

Multiplying by 8

⇒ A : B = (5/8 × 8) : (1 × 8)

⇒ A : B = 5 : 8

⇒ A : B = 5 : 8

∴ The formula of the compound is A₅ B₈.

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