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

Question

Aicharya · Accepted Answer

We know $\Delta p . \Delta x \geq \frac{h}{4 \pi}$
since $\Delta p=\Delta x$ (given) $\therefore \Delta p \cdot \Delta p=\frac{h}{4 \pi}$
or $m \Delta v m \Delta v .=\frac{h}{4 \pi}[\therefore \Delta p=m \Delta v]$
or $(\Delta v)^{2}=\frac{h}{4 \pi m^{2}}$
or $\Delta v=\sqrt{\frac{h}{4 \pi m^{2}}}=\frac{1}{2 m} \sqrt{\frac{h}{\pi}}$ *

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

Solution