JEE Main & Advanced Chemistry Structure of Atom Question Bank Dual nature of electron

  • question_answer An electron has kinetic energy \[2.8\times {{10}^{-23}}J\]. de-Broglie wavelength will be nearly \[({{m}_{e}}=9.1\times {{10}^{-31}}kg)\]                                               [MP PET 2000]

    A)                 \[9.28\times {{10}^{-4}}\,m\]    

    B)                 \[9.28\times {{10}^{-7}}\,m\]

    C)                 \[9.28\times {{10}^{-8}}\,m\]    

    D)                 \[9.28\times {{10}^{-10}}\,m\]

    Correct Answer: C

    Solution :

               Formula for de-Broglie wavelength is            \[\lambda =\frac{h}{p}\] or \[\lambda =\frac{h}{mv}\Rightarrow eV=\frac{1}{2}m{{v}^{2}}\] or  \[\nu =\sqrt{\frac{2eV}{m}}\]            \[\lambda =\frac{h}{\sqrt{2meV}}\]\[=\frac{6.62\times {{10}^{-34}}}{\sqrt{2\times 9.1\times {{10}^{-31}}\times 2.8\times {{10}^{-23}}}}\]                 \[\lambda =9.28\times {{10}^{-8}}meter\].

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