A) \[1.215\,\times {{10}^{-7}}\,m\]
B) \[1.215\,\times {{10}^{-5}}\,m\]
C) \[1.215\,\times {{10}^{-4}}m\]
D) \[1.215\,\times {{10}^{-3}}m\]
Correct Answer: A
Solution :
Here: initial orbit\[{{n}_{1}}=1\] Final orbit \[{{n}_{2}}=2\] The relation for the wavelength is \[\frac{1}{\lambda }=R\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)=R\left[ \frac{1}{{{(1)}^{2}}}-\frac{1}{{{(2)}^{2}}} \right]=\frac{3R}{4}\] \[\lambda =\frac{4}{3R}=\frac{4}{3(1.097\times {{10}^{7}})}\] \[=1.215\times {{10}^{-7}}\,m\](where Rydberg constant \[R=1.097\times {{10}^{7}}{{m}^{-1}}\])
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