Question

Uncertainty in position is twice the uncertainty in momentum. Uncertainty in velocity is:

• A. $\sqrt{\frac{h}{\pi }}$
• B. $\frac{1}{2m}\sqrt{\frac{h}{\pi }}$
• C. $\frac{1}{2m}\sqrt{h}$
• D. $\sqrt{\frac{h}{4\pi }}$

Answer 1

Answer: (C)

$\Delta x=2\Delta p$
$\Delta x.\Delta p=\frac{h}{2}=\frac{h}{4\pi }$
$\Rightarrow 2\Delta p.\Delta p=\frac{h}{2}$
$2{\left(m\Delta V\right)}^2=\frac{h}{2};{\left(\Delta V\right)}^2=\frac{h}{4m^2}$
$\Rightarrow \Delta V=\frac{\sqrt{h}}{2m}.$