Q. 173.8( 25 Votes )

# Which of the following lattices has the highest packing efficiency

(i) simple cubic

(ii) body-centred cubic and

(iii) Hexagonal close-packed lattice?

Answer :

(i)

In a simple cubic lattice the atoms are located only at the corners of the cube.

Let us assume the edge length or the side of the cube = a

And the radius of each particle = r

The relation between radius and edge a

Can be given as a = 2r

The volume of the cubic unit cell = side^{3} = a^{3}

= (2r^{3})

= 8r^{3}

Number of atoms in unit cell

The volume of the occupied space

And we know that, the packing efficiency

= 52.36%

(ii)

Let us assume the edge length or the side of the cube = a

And the radius of each particle = r

The diagonal of a cube is always a

The relation between radius and the edge will be = 4r

Divide by root 3 we get A

Total number of atoms in body centred cubic

Number of atoms at the corner

Number of atoms at the centre = 1

Total number of atoms = 2

The volume of the cubic unit cell = side^{3}

= a^{3}

= (4r/a√3)^{3}

The volume of the occupied space

Packing efficiency

= 68%

(iii) Let the base of the hexagon is a and the height is c

Each angle in hexagonal will be 60 degree at the base

Packing efficiency of

Hexagonal close- packed lattice

a = 2r c = 1.633a

= 74%

Thus, hexagonal close- packed lattice has the highest packing efficiency of 74%.

Rate this question :

An element ‘*X*’ (At. mass = 40 g mol^{–1}) having f.c.c. structure, has unit cell edge length of 400 pm. Calculate the density of ‘*X*’ and the number of unit cells in 4 g of ‘*X*’. (*N _{A}* = 6.022 × 10

^{23}mol

^{–1})

Note : In the following questions a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices.

Chemistry - ExemplarThe correct order of the packing efficiency in different types of unit cells is ________.

Chemistry - ExemplarThe edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell are respectively________.

Chemistry - ExemplarA cubic solid is made of two elements P and Q. Atoms of Q are at the corners of the cube and P at the body-centre. What is the formula of the compound? What are the coordination numbers of P and Q?

NCERT - Chemistry Part-I