• # 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)                 $6.8\times {{10}^{-6}}{{m}^{2}}{{s}^{-1}}$

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                    $\Delta x\times \Delta v=\frac{h}{4\pi \times m}$                   $=\frac{6.63\times {{10}^{-34}}}{4\times 3.14\times 9.1\times {{10}^{-31}}}$ $=5.8\times {{10}^{-5}}{{m}^{2}}{{s}^{-1}}$.