1.We have , AB has rock salt structure (A:B::1:1)(A:B::1:1)
2. That is , F.C.C structure (n=4) and formula weight of AB is 6.023yg closest distance A−B=yA−B=y nm
Therefore, edge length of unit cell, a=2(A++B−)=210−9m
Therefore , density of AB =5.0kgm−3

Theoretical Density of Compound AB

The theoretical density of a compound is a measure of how closely packed its atoms or ions are within a given volume. In order to calculate the theoretical density of AB, we need to consider its crystal structure, the formula mass, and the shortest distance between the A and B atoms.

Crystal Structure of AB

AB crystallizes in a rock salt structure, which is a type of cubic close-packed (ccp) arrangement. In this structure, A and B atoms alternate in the crystal lattice, with A atoms occupying the corners of the unit cell and B atoms occupying the face-centered positions. The coordination number of both A and B atoms is 6.

Shortest Distance between A and B

The shortest distance between A and B atoms in the rock salt structure is given as Y⅓ nm. This distance corresponds to the diagonal of a face-centered cubic unit cell, which can be calculated using the Pythagorean theorem.

Diagonal of a Face-Centered Cubic Unit Cell

In a face-centered cubic unit cell, the diagonal can be calculated by considering the edge length of the unit cell. The edge length (l) of a cubic unit cell can be determined using the shortest distance between A and B atoms.

l = 2(Y⅓ nm) (1)

The diagonal is given by the formula:

d = √(l^2 + l^2 + l^2) = √3l (2)

Substituting equation (1) into equation (2), we get:

d = √3(2(Y⅓ nm)) = √3(2Y⅓ nm)

Formula Mass of AB

The formula mass of AB is given as 6.023 Y amu. Since the ratio of A to B in AB is 1:1, the formula mass can be split equally between the two atoms.

Mass of A = Mass of B = (6.023 Y amu) / 2 = 3.012 Y amu

Theoretical Density Calculation

The theoretical density (ρ) of a compound can be calculated using the formula:

ρ = (formula mass of AB) / (volume of unit cell)

The volume of a face-centered cubic unit cell can be determined by considering the edge length (l) calculated earlier:

Volume of unit cell (V) = l^3

Substituting the value of l from equation (1), we get:

V = (2(Y⅓ nm))^3 = 8(Y nm)^3

Now, substituting the values of the formula mass and volume into the formula for theoretical density, we have:

ρ = (6.023 Y amu) / 8(Y nm)^3

Simplifying the expression, we get:

ρ = 0.753 Y amu / (Y nm)^3

Thus, the theoretical density of the compound AB is 0.753 Y amu / (Y nm)^3.