Question
A solid $$AB$$ has a rock salt structure. If radius of cation $${A^ + }$$ is $$120\,pm,$$ what is the minimum value of radius of $${B^ - }\,anion?$$
A.
120$$\,pm$$
B.
240$$\,pm$$
C.
290$$\,pm$$
D.
360$$\,pm$$
Answer :
290$$\,pm$$
Solution :
$$\eqalign{
& {\text{Limiting ratio}}, \cr
& \frac{{{r_{{A^ + }}}}}{{{r_{{B^ - }}}}} = 0.414 \cr
& {r_{{B^ - }}} = \frac{{{r_{{A^ + }}}}}{{0.414}} \cr
& \,\,\,\,\,\,\,\,\,\, = \frac{{120}}{{0.414}} \cr
& \,\,\,\,\,\,\,\,\,\, = 290\,pm \cr} $$