# Solid State

## NCERT Exercise Solution (part 2)

Question – 1.7 - How will you distinguish between the following pairs of terms:

(i) Hexagonal close-packing and cubic close-packing?

**Answer:**

Hexagonal Close Packing | Cubic Close Packing |
---|---|

The spheres of molecules of a particular row in a particular dimension are in a position that they fit into depressions between adjacent spheres of the previous row. | The spheres of molecules are adjacent to each other that each row of spheres in a particular dimension is a repetition of the previous row. |

This type of packed lattice is found in many metals, e.g. Mg, Zn, etc. | This type is found in metals like Cu, Ag, etc. |

Volume of unit cell is `24sqrt2\r^3` | Volume of unit cell `=16sqrt2\r^3` |

(ii) Crystal lattice and unit cell?

**Answer:** Orderly three dimensional arrangements of atoms is called crystal lattice. It is diagrammatic representation of constituent particles. The smallest unit of a crystal lattice is called unit cell. Repeated unit cells form crystal lattice.

(iii) Tetrahedral void and octahedral void?

**Answer:** Void surrounded by four spheres in a lattice is called tetrahedral void, while void surrounded by six spheres in a lattice is called octahedral void.

Question – 1. 8 - How many lattice points are there in one unit cell of each of the following lattice?

(i) Face-centred cubic

**Answer:** One unit cell of a face-centered cubic has 8 lattice points are corners and 6 lattice points at faces, total 14 lattice points.

(ii) Face-centred tetragonal

**Answer:** One unit cell of face-centered tetragonal has 8 lattice points are corners and 6 lattice points at faces, total 14 lattice points.

(iii) Body-centred

**Answer:** One unit cell of body centered has 8 lattice points are corners and 1 lattice points at faces, total 9 lattice points.

Question – 1.9 - Explain

(i) The basis of similarities and differences between metallic and ionic crystals.

**Answer:** Similarities: Constituent particles are held together with electrostatic force of attraction. Both have high melting points.

Difference: Electrons are free to move in metallic crystals, but ions are not free to move in ionic crystals. Metallic crystals are good conductor of electricity, while ionic crystals are not good conductors.

(ii) Ionic solids are hard and brittle.

**Answer:** In ionic solids, constituent particles are held together with strong electrostatic force of attraction along with their fixed position. The fixed position of ions and strong electrostatic force of attraction make ionic solids hard and brittle.

Question – 1.10 - Calculate the efficiency of packing in case of a metal crystal for

(i) simple cubic

**Answer:** Let the side of a simple cubic lattice is ‘a’ and radius of atom present in it is ‘r’.

Since, edges of atoms touch each other, therefore, a = 2r (for simple cubic lattice)

Volume of cube =Side^{3} `=a^3=(2r)^3`

Volume of one atom `=4/3πr^3`

Packing efficiency `=text(Volume of 1 sphere in unit cell)/text(Total volume of unit cell)xx100`

`=(4/3πr^3)/((2r)^3)xx100`

`=(4πr^3)/(3xx8xx\r^3)xx100`

`=(4xx3.14xx100)/(24)=52.4%`

(ii) body-centred cubic

**Answer:** Volume of cube `=((4r)/(sqrt3))^3`

Volume of 2 atoms present in bcc structure `=2xx4/3πr^3`

Packing efficiency `=text(Volume of 2 sphere in unit cell)/text(Total volume of unit cell)xx100`

`=(2xx4/3πr^3)/(((4r)/(sqrt3))^3)xx100`

`=((8πr^3)/(2))/((64r^3)/(3sqrt3))xx100`

`=(8πr^3xx3xx1.732)/(2xx64r^3)xx100`

`=(8xx314xx3xx1.732)/(2xx64)xx100=68%`

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

**Answer:** For body centred cubic, side `a=2sqrt2r`

Volume of unit cell `=(2sqrtr)^3`

Volume of 4 spheres `=4xx4/3πr^3`

Packing efficiency `=text(Volume of 4 sphere in unit cell)/text(Total volume of unit cell)xx100`

`=(4xx4/3πr^3)/((2sqrt2r)^3)xx100`

`=(314)/(4.242)=74%`