Question

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

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

Answer 1

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

If uncertainty in the measurement of position and momentum are equal then uncertainly in the measurement of velocity is equal to $\frac{1}{2m}\sqrt{\frac{h}{\pi }}$.
$\Delta x\Delta P=\frac{h}{4\pi }$
But $\Delta x=\Delta P$
Hence, $\Delta x=\Delta P=\sqrt{\frac{h}{4\pi }}$
But $\Delta P=m\Delta u$
Hence,
$\Delta u=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$