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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.

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.

Grade:8

1 Answers

Gaurav
askIITians Faculty 164 Points
8 years ago
Using Pythagoras theorem we get
(2R)2= (R+r)2+(R+r)2
4R2= 2(R+r)2
Divide by 2 we get
2R2= (R+r)2
Take root both side we get
R√2 =R+r
R√2 – R = r
r= R(√2–1)
value of √2= 1.414
r= R(1.414–1)
r = 0.414 R

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