Haryana PMT Haryana PMT Solved Paper-1999

  • question_answer
    An electron beam has a kinetic energy equal to 100 eV. Find the wavelength associated with the electron if the mass of electron is  \[9.1\times {{10}^{-31}}kg\] and \[1eV=1.6\times {{10}^{-}}^{19}J,h=6.6\times {{10}^{-34}}Js\]:

    A) \[2.4\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[4.6\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[0.6\overset{\text{o}}{\mathop{\text{A}}}\,\]                         

    D) \[1.2\overset{\text{o}}{\mathop{\text{A}}}\,\]

    Correct Answer: D

    Solution :

                    According to de Broglie \[\lambda =\frac{h}{\sqrt{2mE}}\]           ...(i) Here,                 \[E=100eV=100\times 1.6\times {{10}^{-19}}J\]                 \[=1.6\times {{10}^{-17}}J\] Substituting the given values in eq. (i) we get \[\lambda =\frac{6.6\times {{10}^{-34}}}{\sqrt{2\times 9.1\times {{10}^{-31}}\times 1.6\times {{10}^{-17}}}}\]                 \[=\frac{6.6}{\sqrt{2\times 9.1\times 1.6}}\times {{10}^{-10}}\] or            \[\lambda =1.22\times {{10}^{-10}}m\approx 1.2\overset{\text{o}}{\mathop{\text{A}}}\,\]


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