Question

Calculate the uncertainty in the velocity of a wagon of mass, $3000\mathrm{Kg}$ whose position is known to an accuracy of $10\mathrm{pm}.$

Answer 1

Step 1: Given data

Mass of the wagon =$3000\mathrm{kg}$

Accuracy = $10\mathrm{pm}$

Step 2: Formula used

By Heisenberg’s Uncertainty Principle,

$\mathrm{\Delta x}\times \mathrm{m\Delta v}\ge \frac{\mathrm{h}}{4\mathrm{\pi }}$

Where, $∆\mathrm{v}$ is the error in the measurement of velocity, $∆\mathrm{x}$ is the error in the measurement of position, $\mathrm{m}$ is the mass of the particle, and, $\mathrm{h}$ is the Plank's constant.

Step 3: Calculation of uncertainty principle

Substitute the given values in the formula.

$\mathrm{\Delta x}\times \mathrm{m\Delta v}\ge \frac{\mathrm{h}}{4\mathrm{\pi }}$

$\Rightarrow \mathrm{\Delta v}=\frac{\mathrm{h}}{4\mathrm{\pi m\Delta x}}$

$\Rightarrow 1.75\times {10}^{-27}{\mathrm{ms}}^{-1}$

Therefore, the uncertainty principle is $1.75\times {10}^{-27}{\mathrm{ms}}^{-1}$.