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

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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.

Q 10 I Image of Simple Cubic

Q 10 I Image of Simple Cubic

Q 10 I Image of Simple Cubic

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

So, we can write:

Now, volume of the cubic unit cell

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

Therefore, volume of the occupied unit cell

Hence, packing efficiency

(ii) Body-Centred Cubic

Q 10 II Image of Body-Centred Cubic

Q 10 II Image of Body-Centred Cubic

Q 10 II Image of 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 , we have:

Again, from , we have:

Let the radius of the atom be r.

Length of the body diagonal,

Volume of the cube,

A body – centred cubic lattice contains 2 atoms.

So, volume of the occupied cubic lattice

(III) Face-centred cubic

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

Q 10 III Image of Face-Centred Cubic

Q 10 III Image of Face-Centred Cubic

Q 10 III Image of Face-Centred Cubic