Question

A compound formed by elements X,Y,Z has a cubic structure in which X atoms are at the corner of the cube and also at alternate face centre Y atoms are present at the body centre and Z atoms are present at the alternate edge centre then what will be the molecular formula of the compound

Answer 1

Answer:

$X_2YZ$

Explanation:

In the crystal, X are present in corners

An atom in corner contributes 1/8 to the unit cell,

so number of X present in unit cell are 1/8*8=1

i.e. number of X=1 present at corner

Also X is present in alternate face centres. So, X is present in two faces.

Atom on face centres contributes 1/2

So X present in alternate face centre will contribute 1/2*2=1

So total number of X in unit cell are 2

Y is present in the body centre and an atom in the body centre contributes 1 whole atom to the the unit cell so number of Y in the unit cell is 1

Z is present in edge centre, there are 4 alternate edge centres.

Atom present in edge centre contributes 1/4 to the system

So number of Z present in unit cell is 1/4*4=1

So finally number of X=2 Y=1 Z=1

so formula is $X_2YZ$