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


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 ∆POQ 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=0.414 R