Question

A metal crystallizes in a body centred cubic structure. If 'a' is the edge length of its unit cell, 'r' is the
radius of the sphere. What is the relationship between 'r' and 'a'? derive​

Answer 1

Answer:

Usually, the length of the cell edge is represented by a.  

The direction from a corner of a cube to the farthest corner is called body diagonal (say bd).

Face diagonal = fd

bd  

2

=fd  

2

+a  

2

 

     =a  

2

+a  

2

+a  

2

 

     =3a  

2

 

Atoms along the body diagonal (say bd) touch each other. Thus, the body diagonal has a length that is four times the radius of the atom, R.

bd=4R

The relationship between a and R can be worked out by the Pythagorean theorem:

(4R)  

2

=3a  

2

 

Thus,

4R=  

3

​  

a

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