If the radius of the octachedral void is r and radius of the atoms in close packing is R, derive relation between r and R.
Radius of octahedral void = r (given)
Radius of atom = R (given)
Now by Pythagoras theorem,we have
2R2 = (R+ r)2 + (R+ r)2
Or
4R2 = 2(R +r)2
Or
2R2 = (R+ r)2
TAKING ROOT BOTH SIDES ,WE GET
R√2 = R +r
Or
R√2 – R = r
Or
r = R√2 – R
Putting the value of √2, we get .
r = R(1.414-1)
r = 0.414R
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