Question
The radius of hydrogen atom in ground state is $$0.53\,\,\mathop {\text{A}}\limits^{\text{o}} .$$ What will be the radius of $$_3L{i^{2 + }}$$ in the ground state ?
A.
$$1.06\,\mathop {\text{A}}\limits^{\text{o}} $$
B.
$$0.265\mathop {\text{A}}\limits^{\text{o}} $$
C.
$$0.176\mathop {\text{A}}\limits^{\text{o}} $$
D.
$$0.53\mathop {\text{A}}\limits^{\text{o}} $$
Answer :
$$0.176\mathop {\text{A}}\limits^{\text{o}} $$
Solution :
Radius of $${n^{th}}$$ orbit is given by $${r_n} = \frac{{{r_0} \times {n^2}}}{Z}$$
For $$_3L{i^{2 + }},r = \frac{{{r_0}}}{3} = \frac{{0.53}}{3} = 0.176\mathop {\text{A}}\limits^{\text{o}} $$