Question

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

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

Answer 1

The correct option is A

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

$\Delta x.\Delta p\ge \frac{h}{4\pi }$

$\Delta x=\Delta p$ (given)

$(\Delta p{)}^2=\frac{h}{4\pi }$

$(m.\Delta v{)}^2=\frac{h}{4\pi }$

$\Delta v^2=\frac{h}{4\pi m^2}$

$\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$