Question

An element X crystallizes in bcc. Find the volume of the unit cell in ${({\text{{A}}})^3}$ , if the atomic radius is $\sqrt 3 {\text{{A^0}}}$.

Answer 1

Hint: To answer this question, you should recall the concept of the unit cell. The unit cells are systematically arranged in such a way that fills the space without overlapping. A bcc unit cell has 2 atoms present in it.
The formula used:
$4r = \sqrt 3 a$ where $r$ is radius and $a$ = length of the side of the unit cell.

Complete step by step answer:
These crystal lattices can be broadly classified into primitive cubic, body-centred cubic (BCC) or face-centred cubic (FCC).
In the case of a BCC unit cell, there are atoms at each corner of the cube and an atom at the centre of the structure. For bcc, the relation between the radius of constituent atoms and the edge of the unit cell is $4r = \sqrt 3 a$.
In the question, we are given that
$r$ = radius = and $a$ = length of the side of the unit cell
Substituting the value we can calculate the value:
$a = \dfrac{{4 \times \sqrt 3 }}{{\sqrt 3 }} = 4$
Therefore, the volume of the unit cell is \[{4^3} = 64{{\text{{A}}}}\]

Hence, the volume is \[64{{\text{{A}}}}\].

Note:

Crystalline solids	Amorphous solids
Crystals have definite and regular geometry and have a long-range as well as short-range order of constituent particles.	The particles in the constituent are arranged irregularly. They do not have any definite geometry and have a short-range order.
Crystals possess high melting points.	They are devoid of sharp melting points.
The crystals' external forms have regularity when these are formed.	No external regularity in their form when these amorphous solids are formed.
They give a clean surface after cleavage with a knife.	Usually, the amorphous solids exhibit irregular cuts.
They have definite heat of fusion.	Amorphous solids do not possess any particular heat of fusion.
Crystalline solids are very rigid and their molecules cannot be deformed by mild distorting force.	Amorphous solids do not exhibit rigidity. The deformation could be done by bending or compressing them.
Crystalline solids are considered as true solid.	Amorphous solids are considered as supercooled liquids or also pseudo solids.
Crystalline solids display anisotropism.	Amorphous solids display isotropism.