Question

The diameter of a dust particle of mass $10^{-3}$ gm is $2\stackrel{o}{A}$. If the uncertainty in the speed of this particle is $\frac{3.31}{\pi }\times 10^{-3}m/s$,then find minimum uncertainty in position.

Answer 1

$\Delta x.\Delta P\ge \frac{h}{4\pi }$

$\therefore \Delta x\ge \frac{h}{4\pi \left(\Delta P\right)}$

$\therefore \Delta x\ge \frac{h}{4\pi m.\left(\Delta V\right)}$

$\therefore \Delta x\ge \frac{6.626\times {10}^{-34}\times \pi }{4\times 3.14\times {10}^{-3}\times {10}^{-3}\times 3.31\times {10}^{-3}}m$

$\therefore \Delta x\ge 5\times {10}^{-26}m$

Therefore the minimum uncertainity in position is $5\times {10}^{-26}m$