Atomic Structure Question 487

Question: A hydrogen atom in the ground state is excited by monochromatic radiation of wavelength $ \lambda \overset{o}{\mathop{A}}, $ . The resulting spectrum consists of maximum 15 different lines. What is the wavelength $ \lambda $ -

Options:

A) $ 937.3,\overset{o}{\mathop{A}}, $

B) $ 1025,\overset{o}{\mathop{A}}, $

C) $ 1236,\overset{o}{\mathop{A}}, $

D) None of these

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Answer:

Correct Answer: A

Solution:

  • Total number of spectral lines given by $ \frac{1}{2}[n-1]\times n=15 $ ;
    $ \therefore ,n=16 $ Thus, electron is excited upto 6th energy level from ground state. Therefore, $ \frac{1}{\lambda }=R_{H}[ \frac{1}{1^{2}}-\frac{1}{n^{2}} ]=109737\times \frac{35}{36} $ ; $ \lambda =9.373\times {10^{-6}},cm=937.3,\overset{o}{\mathop{A}}, $


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