Question
The radius of which of the following orbit is same as that of the first Bohr’s orbit of hydrogen atom?
A.
$$H{e^ + }\left( {n = 2} \right)$$
B.
$$L{i^{2 + }}\left( {n = 2} \right)$$
C.
$$L{i^{2 + }}\left( {n = 3} \right)$$
D.
$$B{e^{3 + }}\left( {n = 2} \right)$$
Answer :
$$B{e^{3 + }}\left( {n = 2} \right)$$
Solution :
TIPS/Formulae :
$$\eqalign{
& {r_n} = 0.529\frac{{{n^2}}}{Z}\,\mathop {\text{A}}\limits^{\text{o}} \cr
& {\text{For hydrogen,}}\,\,n = 1\,\,and\,Z = 1; \cr
& \therefore \,\,\,{r_H} = 0.529 \cr
& {\text{For}}\,B{e^{3 + }},n = 2\,\,{\text{and}}\,\,Z = 4\,; \cr
& \therefore \,\,{r_{B{e^{3 + }}}} = \frac{{0.529 \times {2^2}}}{4} = 0.529 \cr} $$