Question

Atom of element y form fcc lattice and those of element x occupy 1/3rd of tetrahedral void. What is the formula of compound formed by x & y
1) X4Y3
2)X3Y4
3)X3Y2
4)X2Y3​

Answer 1

The Formula of the compound is X₂Y₃.

GIVEN

Element Y forms FCC lattice.

Element X occupies 1/3rd of tetrahedral voids.

TO FIND

The formula of the compound

SOLUTION

We can simply solve the above problem as follows-

To find out the formula of the compound we need to calculate the ratio of the number of atoms of X and Y.

Number of atoms of Y.

It is given that the Elements Y forms FCC lattice.

We know that,

The number of atoms per unit cell of a face-centered cubic lattice = 4

So, The Number of Y atoms = 4.

Number of atoms of X

It is given that,

Atoms of elements X occupies 1/3rd of the tetrahedral void.

We know that,

In a face-centered cubic lattice, there are 8 tetrahedral voids.

So, the number of atoms of X =

$8 \times \frac{1}{3} = \frac{8}{3}$

This means 8/3 atoms of X have occupied the total tetrahedral voids.

The ratio of element X to element Y =

$\frac{8}{3} :4$

On simplifying, we get -

$X : Y = 2: 3$

So, The Formula Of The Compound Is X₂Y₃.

And The correct option is (4) X₂Y₃.

#spj2

Answer 2

Concept:

Imagine a cube with one atom on each corner and an atom on each face as the Face-Centered Cubic (FCC) unit cell. It is one of the most common metal structures. FCC contains 4 atoms per unit cell, a lattice constant of 2R√2, a coordination number of 12, and an atomic packing factor of 74%. The FCC is a compact structure with ABC-ABC stacking.

Given

Y-element forms the FCC lattice.

Tetrahedral voids are occupied by elements X to 1/3.

Find

What is the formula for the compound formed by X & Y?

Solution

The above problem can easily be resolved by doing the following:

The fact that the Elements Y form an FCC lattice is a given.

Having said that,

4 atoms make up each unit cell of a face-centered cubic lattice.

Therefore, there are four Y atoms.

Atoms of element X occupy 1/3 of the tetrahedral void, which is a given.

Having said that,

The number of tetrahedral voids in a face-centered cubic lattice is eight.

The total number of X atoms, therefore, equals 8. This indicates that X atoms have filled 8/3 of the tetrahedral voids.

Element X to element Y ratio = 8/3 : 4

After simplification, we get X:Y = 2:3. Therefore, the compound's formula is X₂Y₃.

Hence, the correct option is  (4) X₂Y₃.

#SPJ2