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Question 14

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.

Answer

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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