A) \[6563\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[4102\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[4861\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[1215\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: D
Solution :
From Bohrs theory, wavelength of radiations emitted in H-atom \[\frac{1}{\lambda }=R\left( \frac{1}{n_{2}^{2}}-\frac{1}{n_{1}^{2}} \right)\] Here \[{{n}_{1}}=2,1,R=1.097\times {{10}^{7}}{{m}^{-1}}\] \[\therefore \] \[\frac{1}{\lambda }=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)=\frac{3}{4}R\] \[\Rightarrow \] \[\frac{1}{\lambda }=\frac{4}{3R}=\frac{4}{3\times 1.097\times {{10}^{7}}}\] \[\begin{align} & =1.215\times {{10}^{-7}}m \\ & =1215\,\overset{\text{0}}{\mathop{\text{A}}}\, \\ \end{align}\]
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