Atoms And Nuclei Question 292

Question: An $ \alpha $ particle passes rapidly through the exact center of a hydrogen molecule, moving on a line perpendicular to the inter nuclear axis. The distance between the nuclei is b. Where on its path does the $ \alpha $ particle experience the greatest force? (Assume that the nuclei do not move much during the passage of the $ \alpha $ particle. Also neglect the electric field of the electrons in the molecule.)

Options:

A) $ \frac{b}{2} $

B) $ \frac{b}{2\sqrt{2}} $

C) $ \frac{b}{\sqrt{2}} $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \frac{1}{{\lambda_{\alpha }}}=\frac{3R}{4}{{( Z-1 )}^{2}} $
    $ \Rightarrow ( Z-1 )=\sqrt{\frac{4}{3R{\lambda_{\alpha }}}}=\sqrt{\frac{4}{3\times 1.1\times 10^{7}\times 1.8\times {{10}^{-10}}}} $ $ =\frac{200}{3}\sqrt{\frac{5}{33}}=\frac{78}{3}=26 $
    $ \Rightarrow Z=26+1=27 $


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