If the radius of an octahedral void and that of atom in close packing is r &R respectively then relation between r &R is :-

Question

If the radius of an octahedral void and that of atom in close packing is r &R respectively then relation between r &R is :- (A) r=0.155R (B) r=0.255R (C) r=0.414R (D) r=0.732R

Tardigrade Admin · Accepted Answer

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:
Solution

From triangle

A BC :

(A B)^{2} = (A C)^{2} + (BC)^{2} (A B)^{2} = (2 R)^{2} + (2 R)^{2} (A B)^{2} = 8 R^{2} A B = 22 R A B = 2 r + 2 R = 22 R \frac{r}{R} = 0.414 r = 0.414 R

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 :-

$r = 0.155 R$

$r = 0.255 R$

$r = 0.414 R$

$r = 0.732 R$

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 :-

r=0.155R

r=0.255R

r=0.414R

r=0.732R

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: (AB)2=(AC)2+(BC)2(AB)2=(2R)2+(2R)2(AB)2=8R2AB=22​RAB=2r+2R=22​RRr​=0.414r=0.414R

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 :-

$r = 0.155 R$

$r = 0.255 R$

$r = 0.414 R$

$r = 0.732 R$