Find the minimum uncertainty in the speed of a bacterium having mass 3.0 × 10−15 kg if we know the position of the bacterium to within its l

Find the minimum uncertainty in the speed of a bacterium having mass 3.0 × 10−15 kg if we know the position of the bacterium to within its length of 1.0 µm

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  1. Answer:

    The minimum uncertainty in the speed of a bacterium is [tex]5.27\times 10^{-29}\ m/s.[/tex]

    Explanation:

    We know by Heisenberg Uncertainty principal :

    [tex]\Delta p\times \Delta x=\dfrac{h}{4\pi}\\\\m\Delta v\times \Delta x=\dfrac{h}{4\pi}\\\\\Delta v\times \Delta x=\dfrac{h}{4\pi m}[/tex]  ….equation 1.

    Putting value of [tex]\Delta x[/tex], m ,h in above equation we get :

    [tex]\Delta v\times 10^{-6}\ m=\dfrac{6.626\times 10^{-34}}{4\times \dfrac{22}{7}}\\\\\Delta v=\dfrac{6.626\times 10^{-34}}{4\times \dfrac{22}{7}\times 10^{-6}}=5.27\times 10^{-29}\ m/s.[/tex]

    Hence, this is the required solution.

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