Question

In $NaCl$ crystal what is the $\dfrac{{{r^ + }}}{{{r^ - }}}$ ratio?
A.0.4
B.0.98
C.0.64
D.0.50

Answer 1

Radius Ratio Rule; It is the ratio of radius of cation to the radius of anion.
Radius Ratio Rule $R\, = \,\dfrac{{{r^ + }}}{{{r^ - }}}$
The radius ratio is calculated only in ionic compounds. And if the radius of the cation is more than the radius ratio is more and vice versa. If the radius ratio of any compound is high then its stability is high.
If the radius of cation is high then the coordination number of the ionic compound is high.

Complete step by step answer:
Atomic radius of Sodium cations in sodium chloride crystal is one hundred two pm
and the atomic radius of the anions that are the $C{l^ - }$ ions is one hundred eighty one pm
Hence, the Radius Ratio of $NaCl$ crystal in this case is:
$R\, = \,\dfrac{{{r^ + }}}{{{r^ - }}}$ : Here in this formula the positive r in the numerator denotes the radius of cation and the negative r in the denominator denotes the radius of the anion
R\, =\dfrac{{{r^ + }}}{{{r^ - }}}\, = \,\dfrac{{102}}{{181}}\, \\\ = \,0.5...pm \\\
Hence, the radius ratio of the $NaCl$ crystal lattice given is 0.5..pm approximately.

So, the correct answer is Option D.

Note: The $NaCl$ crystal lattice has a coordination number of 6 and the ionic compounds falling in in the range of coordination number 6 have a radius ratio between 0.414 – 0.732 pm. In order to solve these questions simply and in less time one should mug up the coordination numbers of various crystal lattices and then simply determine their CN from the category they are falling into.