Question

If uncertainity in position and momentum are equal, then uncertainity in velocity is:

• A. $\sqrt{\frac{h}{\pi }}$
• B. $\frac{1}{2}\sqrt{\frac{h}{\pi }}$
• C. $\frac{1}{2m}\sqrt{\frac{h}{\pi }}$
• D. $2m\frac{1}{2}\sqrt{\frac{h}{\pi }}$

Answer 1

Answer: (C)

$\frac{1}{2m}\sqrt{\frac{h}{\pi }}$

Use,
$\Delta x\Delta p=\frac{h}{4\pi }$
Since, $\Delta x=\Delta p$, therefore $\Delta p=\frac{h}{2\sqrt{\pi }}=\Delta x,\Delta p=m\Delta v$,
Therefore, $\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$