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 $
