Answer to Question #212970 in General Chemistry for Ncabzitho

Question #212970

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


1
Expert's answer
2021-07-05T03:22:27-0400

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"

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