Question

In a cubic unit cell, a atoms are present on alternate faces and c atoms are present on alternate edges and body centre of the cube. The simplest formula of compound is:

Answer 1

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Answer 2

Answer:

The formula of compound is $ac_2$.

Explanation:

We are given that a cubic unit cell . Atoms a are present at alternate faces.

Atoms c are present on alternate edges and body centre of the cube.

We know that contribution of atom to a unit cell  at face=$\frac{1}{2}$

Contribution of atoms to a unit cell  at edge=$\frac{1}{4}$

Contribution of atom to a unit cell=1

If atoms a present at alternate faces of a cube  then there are 2 alternate faces on which atoms are present

Therefore, the number of atoms of a=$\frac{1}{2}\times2=1$

If atoms c are present on alternate edges of a cube then we have 4 edges on which atoms c are present and at centre.

Therefore, the number of atoms of c=$\frac{1}{4}\times4 +1$

The number of atoms of c in a cubic unit cell=1+1=2

Hence, the formula of compound $ac_2$.