Question

If the uncertainties in the measurements of position and momentum are equal, then calculate the uncertainty in the measurement of velocity (in ${\text{ms}}^{-1}$) of particle of mass $1.21\times {10}^{-18}\text{kg}$. Given h = $6.6\times {10}^{-34}J.s\pi =3.1$

Answer 1

We know, according to Heisenberg uncertainty principle
$\Delta x.\Delta P\ge \frac{h}{4\pi }$
Here, the uncertainties in the measurements of position and momentum are equal, thus $\Delta x=\Delta p$
Thus, ${\Delta P}^2=\frac{h}{4\pi }$
$\Rightarrow \Delta P=\sqrt{\frac{h}{4\pi }}$
$\Rightarrow m\Delta V=\sqrt{\frac{h}{4\pi }}$
$\Rightarrow m\Delta V=\sqrt{\frac{6.6\times {10}^{-34}}{4\times 3.1}}$
$\Rightarrow \Delta V=\sqrt{\frac{6.6\times {10}^{-34}}{4\times 3.1}}\times \frac{1}{1.21\times {10}^{-18}}$
$\Rightarrow \Delta V=6.01$