Question
The radius of $$L{a^{3 + }}$$ (Atomic number of $$La = 57$$ ) is $$1.06\mathop {\text{A}}\limits^o .$$ Which one of the following given values will be closest to the radius of $$L{u^{3 + }}$$ (Atomic number of $$Lu = 71$$ )?
A.
$$1.04\,\mathop {\text{A}}\limits^o $$
B.
$$1.06\,\mathop {\text{A}}\limits^o $$
C.
$$0.85\,\mathop {\text{A}}\limits^o $$
D.
$$1.60\,\mathop {\text{A}}\limits^o $$
Answer :
$$0.85\,\mathop {\text{A}}\limits^o $$
Solution :
$$\eqalign{
& {\text{Ionic}}\,{\text{radii}}\, \propto \frac{1}{z} \cr
& {\text{Thus}},\,\frac{{{z_2}}}{{{z_1}}}\, \Rightarrow \frac{{1.06}}{{\left( {{\text{Ionic}}\,{\text{radii}}\,{\text{of}}\,L{u^{3 + }}} \right)}} = \frac{{71}}{{57}} \cr
& \Rightarrow \,{\text{Ionic}}\,{\text{radii}}\,{\text{of}}\,L{u^{3 + }} = 0.85\,\mathop {\text{A}}\limits^o \cr} $$