Question #212970

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

Expert's answer

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"** **

Learn more about our help with Assignments: Chemistry

## Comments

## Leave a comment