# 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. thuthuy

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

Explanation:

We know by Heisenberg Uncertainty principal :

$$\Delta p\times \Delta x=\dfrac{h}{4\pi}\\\\m\Delta v\times \Delta x=\dfrac{h}{4\pi}\\\\\Delta v\times \Delta x=\dfrac{h}{4\pi m}$$  ….equation 1.

Putting value of $$\Delta x$$, m ,h in above equation we get :

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

Hence, this is the required solution.