Question

Uncertainty in position of a $0.25g$ particle is ${10}^{-5}$. Uncertainty in velocity of that particle is:
($h=6.6\times {10}^{-34}Js)$

• A. $1.2\times {10}^{-34}m{s}^{-1}$
• B. $2.1\times {10}^{-25}m{s}^{-1}$
• C. $1.6\times {10}^{-29}m{s}^{-1}$
• D. $1.7\times {10}^{-9}m{s}^{-1}$

Answer 1

The correct option is B $2.1\times {10}^{-25}m{s}^{-1}$

According to the Heisenberg uncertainty principle, the exact momentum and position of a particle can’t be calculated simultaneously.
Mathematically represented as:
$\Delta p.\Delta x\ge \frac{h}{4\pi }$
$\Delta x\times (m\times \Delta v)=\frac{h}{4\pi }$
⇒ $\Delta v=\frac{h}{\Delta x\times m\times 4\pi }$
$\Delta v=\frac{6.6\times {10}^{-34}}{{10}^{-5}\times (2.5\times {10}^{-4})\times 3.14\times 4}$
= $2.1\times {10}^{-25}m{s}^{-1}$