A) \[\text{1}\text{.16 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[\text{3}\text{.18 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[\text{2}\text{.12 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[\text{1}\text{.59 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: C
Solution :
Bohrs radius for \[{{n}^{th}}\] orbit is given by \[{{r}_{n}}=\frac{{{n}^{2}}{{h}^{2}}}{4{{\pi }^{2}}m{{e}^{2}}k\cdot z}\] \[i.e.,\] \[{{r}_{n}}\propto {{n}^{2}}\] Hence, \[\frac{{{r}_{3}}}{{{r}_{2}}}={{\left( \frac{3}{2} \right)}^{2}}=\frac{9}{4}\] \[\therefore \] \[{{r}_{2}}=\frac{4}{9}\times {{r}_{3}}=\frac{4}{9}\times 4.77=2.12\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
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