Question

caluclate the density of a cubic close packing solid having molar mass 63.3g/mol and edge legnth of 288pm (NA= 6.023×10²³)​

Answer 1

Answer:

The number of atoms in a face-centred cubic structure is calculated as:

Number of corners in each cube = g

But each corner atom is shared with 8 other cubes, so its contribution to one cube is (18)th

.

Number of faces in a cube = 6

Each atom on a face-centre is shared by two cubes, therefore, the contribution of each face centred atom is 12

.

Hence, total number of atoms in a cube

= Contribution of corner atoms + Contribution of face - centred atoms

=8×18+6×12=4atoms

Use the formula, =z.MNA.a3

; where d is the density, z is the number of atoms per unit cell, M is the molecular or atomic mass in g/mol, NA

is the Avogadro’s number and ‘a’ is the edge length.

d=4×60×gmol6.022×1023×1mol×(400pm)3×1cm3(1010pm)3

=>d=4×606.022×1023×4003×10−30.gcm3

=>d=6.22gcm−3∼6gcm−3

Therefore the density of the unit cell is 6 gcm−3.