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Q.
If the radius of an octahedral void and that of atom in close packing is $r\&R$ respectively then relation between $r\&R$ is :-
NTA AbhyasNTA Abhyas 2022
Solution:
Octahedral void is formed when four atoms are in same plane and one atom is upper and lower plane.
Follow the diagram which is shown below:
From triangle $ABC:$
$\left(AB\right)^{2}=\left(AC\right)^{2}+\left(BC\right)^{2}\left(AB\right)^{2}=\left(2 R\right)^{2}+\left(2 R\right)^{2}\left(AB\right)^{2}=8R^{2}AB=2\sqrt{2}RAB=2r+2R=2\sqrt{2}R\frac{r}{R}=0.414r=0.414R$
