Question

A ball weighing $10g$ is moving with a velocity of $90m{s}^{-1}.$ If the uncertainty in its velocity is $5\%$, then the uncertainty in its position is $\times {10}^{-33}m.$ (Rounded off to the nearest integer)

[Given : $h=6.63\times {10}^{-34}Js$]

Answer 1

According to Heisenberg uncertainty principle
$\Delta x\Delta p\ge \frac{h}{4\pi }$

$\Delta x=\frac{h}{4\pi m\Delta V}(\Delta P=m\Delta V)$

$=\frac{6.63\times {10}^{-34}Js}{4\times 3.14\times 10\times {10}^{-3}kg\times 90m{s}^{-1}\times 0.05}$

$=1.173\times {10}^{-33}m$

$=1\times {10}^{-33}m$