Question

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

• A. $\sqrt{\frac{h}{\pi }}$
• B. $\sqrt{\frac{h}{2\pi }}$
• C. $\frac{1}{2m}\sqrt{\frac{h}{\pi }}$
• D. none of these

Answer 1

Answer: (C)

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

Uncertainity principle:
$△x△p=\frac{h}{4\pi }\Rightarrow △p^2=\frac{h}{4\pi }$
$\Rightarrow m^2△v^2=\frac{h}{4\pi }\Rightarrow △v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$