Question

If uncertanity in the measurement of position and momentum are equal, calculate uncertainity in the measurement of velocity:-

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

Answer 1

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

let,$\Delta x$ = uncertainity in position
$\Delta P$ = uncertainity in momentum
$\Delta x$ = $\Delta P$ [According to question]
$\Delta x\times \Delta P=\frac{h}{4\pi }\Rightarrow (\Delta P{)}^2=\frac{h}{4\pi }⟹\Delta P=\frac{1}{2}.\sqrt{\frac{h}{\pi }}$$\Rightarrow m\times \Delta v=\frac{1}{2}\sqrt{\frac{h}{\pi }}$
$\therefore \Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$