A) \[\frac{1}{2}\sqrt{\frac{mh}{\pi }}\]
B) \[\frac{1}{2}\sqrt{\frac{h}{\pi m}}\]
C) \[\frac{h}{4\pi m}\]
D) \[\frac{mh}{4\pi }\]
Correct Answer: A
Solution :
\[\because \] \[\Delta x=\Delta v\] \[\Delta x\times \Delta p\ge \frac{h}{4\pi }\] \[\Delta x\times m.\Delta v=\frac{h}{4\pi }\] \[{{(\Delta v)}^{2}}=\frac{h}{4\pi m}\] \[(\because \Delta x=\Delta v)\] \[\therefore \] \[\Delta p=m.\Delta v\] \[=m\sqrt{\frac{h}{4\pi m}}=\sqrt{\frac{mh}{4\pi }}\] \[\Delta p=\frac{1}{2}\sqrt{\frac{mh}{\pi }}\]
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