JEE Main & Advanced Chemistry Structure of Atom Question Bank Uncertainty principle and Schrodinger wave equation

  • question_answer According to Heisenberg?s uncertainty principle, the product of uncertainties in position and velocities for an electron of mass \[9.1\times {{10}^{-31}}kg\] is                                         [BHU  2004]

    A)                 \[2.8\times {{10}^{-3}}{{m}^{2}}{{s}^{-1}}\]        

    B)                 \[3.8\times {{10}^{-5}}{{m}^{2}}{{s}^{-1}}\]

    C)                 \[5.8\times {{10}^{-5}}{{m}^{2}}{{s}^{-1}}\]        

    D)                 \[6.8\times {{10}^{-6}}{{m}^{2}}{{s}^{-1}}\]

    Correct Answer: C

    Solution :

               Given that mass of electron \[=9.1\times {{10}^{-31}}kg\]                    Planck?s constant \[=6.63\times {{10}^{-34}}kg\,{{m}^{2}}{{s}^{-1}}\]                    By using \[\Delta x\times \Delta p=\frac{h}{4\pi }\];     \[\Delta x\times \Delta v\times m=\frac{h}{4\pi }\]                    where : \[\Delta x\]= uncertainity in position                    \[\Delta v\]= uncertainity in velocity                    \[\Delta x\times \Delta v=\frac{h}{4\pi \times m}\]                   \[=\frac{6.63\times {{10}^{-34}}}{4\times 3.14\times 9.1\times {{10}^{-31}}}\] \[=5.8\times {{10}^{-5}}{{m}^{2}}{{s}^{-1}}\].

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