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QUESTION: 1

For which type of cubic lattice, a = 2r?

Solution:

In simple cubic lattice the side of the solid structure is equal to twice the radius of atom. Hence the correct answer is simple cubic.

QUESTION: 2

Packing efficiency of body centred cubic unit cell is:

Solution:

The packing efficiency of both types of close packed structure is 74%, i.e. 74% of the space in hcp and ccp is filled. The hcp and ccp structure are equally efficient; in terms of packing. The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

QUESTION: 3

Packing efficiency in a unit cell is never 100% because constituent particles are assumed to be:

Solution:

The constituent particles i.e. atoms, molecules and ions are assumed to be spheres.

QUESTION: 4

If r is radius of void and R is radius of the sphere, then for an atom to ocuppy an octahedral void which relation holds true?

Solution:

Let the radius of the octahedral void be r and radius of the atoms in close-packing be R and the edge length be a.

In the right angle triangle ABC,

AB = BC = a

For the diagonal AC,

Using Pythagoras Theorem we get;

Also,

And, AB = 2R

AC = R + 2r + R = 2R + 2r

∴

r = 0.414R

Hence, the relation is r = 0.414R.

QUESTION: 5

Which type of void is represented by the following diagram?

Solution:

A tetrahedral void is formed when one sphere or particle is placed in the depression formed by three particles.

**Definition of Tetrahedral Void: **The vacant space or void among the four constituent particles having tetrahedral arrangement in the crystal lattice is called tetrahedral void.

QUESTION: 6

HCP structure is present in:

Solution:

- Magnesium has hexagonal close-packed (HCP) crystal structure.
- Bonding is non-directional metallic bonding.
- Magnesium is metallic solid. The units occupying lattice sites are Mg ions and these ions are surrounded by mobile or delocalised electrons.
- The arrangement of ions in one plane the arrangement of ions is a hexagonal array or closed packed layer. Thus each metal ion is touching six adjacent ions in one plane.

QUESTION: 7

If r is the radius of the void and R is the radius of the sphere, what is AC in the following diagram?

Solution:

AC = Diameter of void + (2× Radius of sphere) 》AC = 2r + 2R = 2(R+r)

QUESTION: 8

Which of the following shows maximum packing efficiency?

Solution:

HCP = 74% packing efficiency

BCC = 68% packing efficiency

Simple cubic = 52.4% packing efficiency

QUESTION: 9

The number of atoms in each unit cell in ccp structure is:

Solution:

In ccp structure: number of atoms per unit cell is

**► **8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom

**► **6 face-centred atoms × 1/2 atom per unit cell = 3 atoms

Therefore, the total number of atoms in a unit cell = 4 atoms.

QUESTION: 10

The number of atoms per unit cell in a body centred cubic arrangement is:

Solution:

For a bcc unit cell, number of atoms per unit cell = (8 *1/8) + 1 = 2

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