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  4. An α particle passes rapidly through the exact centre of a hydrogen molecule, moving on a line perpendicular to the internuclear 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.)

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Q. An $\alpha$ particle passes rapidly through the exact centre of a hydrogen molecule, moving on a line perpendicular to the internuclear 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.)Physics Question Image

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Solution:

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$E_p=\frac{2 K_{ ex }}{\left(x^2+\frac{b^2}{4}\right)^{3 / 2}}$
For maximum $E_P$
$\frac{d E_P}{d x}=0 \Rightarrow x=\frac{b}{2 \sqrt{2}}$