Structure of Atom - Result Question 26
####28. If uncertainty in position and momentum are equal, then uncertainty in velocity is : [2008]
(a) $\frac{1}{2 m} \sqrt{\frac{h}{\pi}}$
(b) $\sqrt{\frac{h}{2 \pi}}$
(c) $\frac{1}{m} \sqrt{\frac{h}{\pi}}$
(d) $\sqrt{\frac{h}{\pi}}$
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Solution:
- (a) We know $\Delta p \cdot \Delta x \geq \frac{h}{4 \pi}$
or $m \cdot \Delta v \cdot \Delta x=\frac{h}{4 \pi} \quad[\therefore \Delta p=m \Delta v]$
since $\Delta p=\Delta x$ (given)
$\therefore \Delta p \cdot \Delta p=\frac{h}{4 \pi}$ or $m \Delta v m \Delta v=\frac{h}{4 \pi}$
or $(\Delta v)^{2}=\frac{h}{4 \pi m^{2}}$
or $\Delta v=\sqrt{\frac{h}{4 \pi m^{2}}}=\frac{1}{2 m} \sqrt{\frac{h}{\pi}}$
