SATHEE: Atoms And Nuclei Question 292

Atoms And Nuclei Question 292

Question: An $α$ 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 $α$ particle experience the greatest force? (Assume that the nuclei do not move much during the passage of the $α$ 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:

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

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Atoms And Nuclei Question 292

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