Atoms And Nuclei Question 447
Question: The first line in the Lyman series has wavelength l. The wavelength of the first line in Balmer series is
Options:
A) $ \frac{2}{9}\lambda $
B) $ \frac{9}{2}\lambda $
C) $ \frac{5}{27}\lambda $
D) $ \frac{27}{5}\lambda $
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Answer:
Correct Answer: D
Solution:
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For first line in Lyman series $ {\lambda_{L_{1}}}=\frac{4}{3\ R} $
For first line in Balmer series $ {\lambda_{B_{1}}}=\frac{36}{5\ R} $
From equation (i) and (ii) $ \frac{{\lambda_{B_{1}}}}{{\lambda_{L_{1}}}}=\frac{27}{5}\Rightarrow {\lambda_{B_{1}}}=\frac{27}{5}{\lambda_{L_{1}}}\Rightarrow {\lambda_{B_{1}}}=\frac{27}{5}\lambda $
