Chemistry Class 12 NCERT Solutions: Chapter 1 The Solid State Part 6

Q: 10. Calculate the efficiency of packing in case of a metal crystal for

(i) Simple cubic

(ii) Body-centred cubic

(iii) Face-centred cubic (with the assumptions that atoms are touching each other)

Ans:

(i) Simple cubic in a simple cubic lattice, the particles are located only at the corners of the cube and touch each other along the edge.

Let the edge length of the cube be ‘a’ and the radius of each particle be r.

So, we can write:

Equation

Now, volume of the cubic unit cell Equation

Equation

Equation

We know that the number of particles per unit cell is 1.

Therefore, volume of the occupied unit cell Equation

Hence, packing efficiency Equation

Equation

Equation

Equation

Equation

(ii) Body-Centred Cubic

It can be observed from the above figure that the atom at the centre is in contact with the other two atoms diagonally arranged.

From Equation , we have:

Equation

Equation

Equation

Again, from Equation , we have:

Equation

Equation

Equation

Equation

Let the radius of the atom be r.

Length of the body diagonal, Equation

Equation

Equation

Equation

Volume of the cube, Equation

A body – centred cubic lattice contains 2 atoms.

So, volume of the occupied cubic lattice Equation

Equation

Equation

Equation

Equation

Equation

(III) Face-centred cubic

Let the edge length of the unit cell be 'a' and the length of the face diagonal Equation be Equation .

Equation

Equation

Equation

Equation

Equation

Equation

Equation

Equation

Equation

Equation

Equation

Equation

Equation

Equation

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