Question

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

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

Answer 1

The correct option is B $\frac{1}{2m}\sqrt{\frac{h}{\pi }}$

According to Heisenberg uncertainty principle,

$\Delta x.\Delta p=\frac{h}{4\pi }$
Given,
$\Delta p=\Delta x$
Hence,
$\Delta p^2=\frac{h}{4\pi }\Delta p=\frac{1}{2}\sqrt{\frac{h}{\pi }};\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$