A) \[9{{a}_{0}}\]
B) \[16{{a}_{0}}\]
C) \[4{{a}_{0}}\]
D) \[25{{a}_{0}}\]
Correct Answer: B
Solution :
The energy absorbed by the atom is\[\frac{hc}{\lambda }\] So,\[\frac{hc}{\lambda }=-13.6\left( \frac{1}{n_{2}^{2}}-\frac{1}{n_{1}^{2}} \right)\] \[\Rightarrow \]\[\frac{12500}{980\times 13.6}=\frac{1}{{{(1)}^{2}}}-\frac{1}{n_{2}^{2}}\Rightarrow {{n}_{2}}\simeq 4\] The radius of \[{{n}^{th}}\] orbit is \[{{a}_{0}}{{n}^{2}}.\] So, the radius of atom in excited state is \[{{4}^{2}}{{a}_{0}}=16{{a}_{0}}\]
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