Question

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

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

Answer 1

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

From Heisenberg uncertainty principle,
$\Delta p.\Delta x\ge \frac{h}{4\pi }$ or $m\Delta v\times \Delta x\ge \frac{h}{4\pi }$
Given: uncertainty in position and uncertainty in momentum is equal
⇒ $\Delta x=\Delta p$
or $(m\Delta v{)}^2\ge \frac{h}{4\pi }$
or $\Delta v\ge \frac{1}{2m}\sqrt{\frac{h}{\pi }}$