A) 13122 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) 3280 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) 4860 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) 2187 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: C
Solution :
The wavelength of spectral line in Balmer series is given by, \[\frac{1}{\lambda }=R\left[ \frac{1}{{{2}^{2}}}-\frac{1}{{{n}^{2}}} \right]\] For first line of Balmer series, n = 3 \[\Rightarrow \] \[\frac{1}{{{\lambda }_{1}}}=R\left[ \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right]\] \[=\frac{5R}{36}\] For second line, n = 4 \[\frac{1}{{{\lambda }_{2}}}=R\left[ \frac{1}{{{2}^{2}}}-\frac{1}{{{4}^{2}}} \right]=\frac{3R}{16}\] \[\therefore \] \[\frac{{{\lambda }_{2}}}{{{\lambda }_{1}}}=\frac{20}{27}\] \[\Rightarrow \] \[{{\lambda }_{2}}=\frac{20}{27}\times 6561=4860\overset{\text{o}}{\mathop{\text{A}}}\,\]
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