A) \[1.215\times {{10}^{-7}}m\]
B) \[1.215\times {{10}^{-3}}m\]
C) \[1.215\times {{10}^{-5}}m\]
D) none of these
Correct Answer: A
Solution :
Initial orbit \[{{n}_{1}}=1,\] final orbit Tie \[{{n}_{2}}=2\] The relation for wavelength is given by \[\frac{1}{\lambda }=R\left[ \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right]=R\left[ \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right]=\frac{3R}{4}\] \[\Rightarrow \] \[\lambda =\frac{4}{3R}=\frac{4}{3\times 1.098\times {{10}^{7}}}=1.215\times {{10}^{-7}}\] (Where Rydberg constant \[R=1.098\times {{10}^{7}}/m\]).
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