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:

  • 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 $



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