Question

The uncertainty in the momentum of a particle is $3.3\times {10}^{-2}kgm{s}^{-1}$. Calculate the uncertainty in its position:

• A. $1.6\times {10}^{-33}m$
• B. $1.6\times {10}^{-32}m$
• C. $16\times {10}^{-30}m$
• D. $1.6\times {10}^{-30}m$

Answer 1

The correct option is A $1.6\times {10}^{-33}m$

Given :

$\Delta P$ = $3.3\times {10}^{-2}kg$

According to uncertainty principle,

$\Delta x\times \Delta P\approx \frac{h}{4\pi }$

$\Delta x=\frac{h}{4\pi \Delta P}=\frac{6.625\times {10}^{-34}}{4\times 3.14\times 3.3\times {10}^{-2}}\approx 1.6\times {10}^{-33}$