# If the radius of the octahedral void is r and radius of the atoms in close packing is R, derive relation between r and R. In the given figure, let the sphere have the centre, O and is fitted in the octahedral void.

As given, radius of the sphere fitted in the octahedral void = r

And the radius of the atoms in close packing = R

Here, angle AOD = 900

In triangle AOD,

DA2 = OA2 + OD2

(R+R)2 = ( R + r )2+ (R+r)2

4R2 = 2(R+r)2

2R2 = (R+r)2

√2 R = (R+r)

R + r = R

r = R – R

r = R (1.414 - 1)

r = 0.414 R

This is the required relation between r and R.

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