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JEE Main & Advanced Physics Atomic Physics Question Bank Self Evaluation Test - Atoms

  • question_answer
    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.)

    A)  \[\frac{b}{2}\] 

    B)                     \[\frac{b}{2\sqrt{2}}\]

    C)  \[\frac{b}{\sqrt{2}}\]                

    D)         None of these

    Correct Answer: A

    Solution :

    [a] \[\frac{1}{{{\lambda }_{\alpha }}}=\frac{3R}{4}{{\left( Z-1 \right)}^{2}}\] \[\Rightarrow \left( Z-1 \right)=\sqrt{\frac{4}{3R{{\lambda }_{\alpha }}}}=\sqrt{\frac{4}{3\times 1.1\times {{10}^{7}}\times 1.8\times {{10}^{-10}}}}\]\[=\frac{200}{3}\sqrt{\frac{5}{33}}=\frac{78}{3}=26\] \[\Rightarrow Z=26+1=27\]


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