Question

If the radius of the octahedral void is r and the radius of the atoms in the close packing is R, derive relationship between r and R.

Answer 1

 Let take r and R are the radii of the octahedral site and atoms respectively,

 then use 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          

Answer 2

Answer:

0.414 is the answer you needed