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30/12/2021 6:24 pm
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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.
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30/12/2021 6:31 pm
A sphere with centre O, is fitted into the octahedral void as shown in the above figure. It can be observed from the figure that ΔPOQ is right-angled
∠POQ = 90°
Now, applying Pythagoras theorem, we can write,
PQ2 = PO2 + OQ2
⇒ (2R)2 = (R + r)2 + (R + r)2
⇒ (2R)2 = 2(R + r)2
⇒ 2R2 = (R + r)2
⇒ √2R = R + r
⇒ r = √2R - R
⇒ r = (√2 - 1)R
⇒ r = 0.414R