A solid A+B- has NaCl type close packing structure. If the anion has radius 241.5, what should be the ideal radius of the cation? Can a cation C+ having a radius of 50pm be fitted into the tetrahedral hole of the crystal A+B-
Answers
Answer:
In Na
+
CI
−
crystal each Na
+
ion is surrounded by 6 CI
+
ions and vice versa. Thus Na
+
ion is placed in
octahedral hole.
The limiting radius ratio for octahedral site = 0.414
or
B
−
A
+
=
R
r
=0.414
Given that radius of anion (B
−
)R=250 pm
i.e. radius of cation (A
+
)r=0.414R=0.414×250 pm
or r=103.5 pm
Thus ideal radius for cation (A
+
) is r=103.5 pm.
We know that (r/R) for tetrahedral hole is 0.225.
∴
R
r
=0.225
or r=0.225 R=0.225×250=56.25pm
Thus ideal radius for cation is 56.25 pm for tetrahedral hole. But the radius of C
+
is 180 pm. It is much larger
then ideal radius i.e. 56.25 pm. Therefore we can not slipped cation C
+
into the tetrahedral site.
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