A dust particle has a mass of 10^{-11} , g,a | vedclass

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(D) Given: Mass $m = 10^{-11} \, g$,Velocity $u = 10^{-4} \, cm \, sec^{-1}$,Error in velocity $= 0.1 \%$.Uncertainty in velocity $\Delta u = \frac{0.

Vedclass · Accepted Answer

$5.27 	imes 10^{-10} \, cm$

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(D) Given: Mass $m = 10^{-11} \, g$,Velocity $u = 10^{-4} \, cm \, sec^{-1}$,Error in velocity $= 0.1 \%$.Uncertainty in velocity $\Delta u = \frac{0.1}{100} 	imes 10^{-4} = 10^{-7} \, cm \, sec^{-1}$.According to Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p = \frac{h}{4 \pi}$ or $\Delta x \cdot m \Delta u = \frac{h}{4 \pi}$.$\Delta x = \frac{h}{4 \pi m \Delta u}$.Substituting the values: $\Delta x = \frac{6.626 	imes 10^{-27} \, erg \cdot sec}{4 	imes 3.1416 	imes 10^{-11} \, g 	imes 10^{-7} \, cm \, sec^{-1}}$.$\Delta x = \frac{6.626 	imes 10^{-27}}{1.2566 	imes 10^{-17}} = 5.27 	imes 10^{-10} \, cm$.

$A$ dust particle has a mass of $10^{-11} \, g$,a diameter of $10^{-4} \, cm$,and a velocity of $10^{-4} \, cm \, sec^{-1}$. If the error in the measurement of velocity is $0.1 \%$,what is the uncertainty in its position?

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