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

  • question_answer Calculate de-Broglie wavelength of an electron travelling at 1% of the speed of light        [DPMT 2004]

    A)                 \[2.73\times {{10}^{-24}}\]         

    B)                 \[2.42\times {{10}^{-10}}\]

    C)                 \[242.2\times {{10}^{10}}\]         

    D)                 None of these

    Correct Answer: B

    Solution :

               One percent of the speed of light is                    \[v=\left( \frac{1}{100} \right)\,\,(3.00\times {{10}^{8}}m{{s}^{-1}})\] = \[3.00\times {{10}^{6}}m{{s}^{-1}}\]                    Momentum of the electron \[(p)\] = \[m\nu \]                    = \[(9.11\times {{10}^{-31}}kg)\,(3.00\times {{10}^{6}}m{{s}^{-1}})\]                    = \[2.73\times {{10}^{-24}}kg\,m{{s}^{-1}}\]                    The de-broglie wavelength of this electron is                    \[\lambda =\frac{h}{p}=\frac{6.626\times {{10}^{-34}}}{2.73\times {{10}^{-24}}kgm{{s}^{-1}}}\]                                 \[\lambda =2.424\times {{10}^{-10}}m\].

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