Question

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

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

Answer 1

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

According to Heisenberg's uncertainity principle,

$\Delta x.\Delta p=\frac{h}{\pi }$

$\Delta x.m\Delta v=\frac{h}{4\pi }$

Given that $\Delta x=m\Delta v$

$\Rightarrow m\Delta v.m\Delta v=\frac{h}{4\pi }$

$m^2\Delta v^2=\frac{h}{4\pi }$

$\Delta v=\sqrt{\frac{h}{4\pi }}\times \frac{1}{m}$

$\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$

So, the correct option is $C$