Answer to Question #212970 in General Chemistry for Ncabzitho

Question

Define the relation of the unit cell parameter and the atomic rafius

Answer 1

Let the edge length of the unit cell be a and the radius of the atom be r

FOR BCC LATTICE:

In bcc lattice the atoms on the body diagonal are in contact with each other

So length of diagonal = r + 2r + r = 4r

Also, body diagonal = $\sqrt{3}$ a

So, $\sqrt{3}$ a = 4 r

r = $\dfrac{\sqrt{3}a}{4}$

FOR FCC LATTICE:

In FCC lattice there are atoms at the corners and at the face centers . The nearest atoms touch each other.

So, distance between a corner and a face center particle = $\dfrac{\sqrt{2}}{2}a$

Also the distance between the corner and face center particle = 2r

So, 2r = $\dfrac{\sqrt{2}}{2}a$

r = $\dfrac{\sqrt{2}}{4}a$