# The Solid State

Question 153

## A metallic element exists as a cubic lattice. Each edge of the unit cell is 2.88 A°. The density of the metal is 7.20 g cm–3. How many unit cells will be there in 100 g of the metal?

Solution

solution:
we have given a= 2.88A0
Density = 7.20g cm-3
mass = 100g

Volume of the unit cell =

Volume of 100g of the metal

No. of unit cell in

Question 154

## The unit cell of an element of atomic mass 96, and density 10.3 g cm–3 is a cube with edge length of 314 pm. Find the structure of crystal lattice (simple cubic, F.C.C. or B.C.C.) Avogadro’s constant. NA = 6.023 x 1023 mol–1?

Solution

solution:
we have given

Density of element,
Cell edge  a= 314pm or 3.14 x 10-10 cm

Atomic mass

The structure of the crystal lattice is B.C.C.

Question 155

## An element a crystallises in fcc structure. 200 g of this element has 4.12 x 1024atoms. The density of A is 7.2 g cm-3. Calculate the edge length of the unit cell?

Solution
solution:
we have given that
mass = 200g
density = 7.2 g cm-3
NA = 4.12 x 1024
Z = 4
by using the following equation,

$⇒$

hence the edge length is 299.7pm
Question 156

## An element crystallises in BCC structure. The edge length of its unit cell is 288 pm. If the density of crystal is 7.2 g cm–3, what is the atomic mass of the element?

Solution

Solution:
we have given that
density, d= 7.2g cm-3
edge = 288 x 10-10 cm
NA = 6.02 x 1023
for Bcc structure Z= 2

Atomic mass = ?

Thus, atomic mass of element is =51.77 g/mol