A) \[\frac{1}{2m}\sqrt{\frac{h}{\pi }}\]
B) \[\sqrt{\frac{h}{2\pi }}\]
C) \[\frac{1}{m}\sqrt{\frac{h}{\pi }}\]
D) \[\sqrt{\frac{h}{\pi }}\]
Correct Answer: A
Solution :
| Key Idea: According to Heisenberg's uncertainty principle, it is impossible to determine simultaneously the position and momentum of c moving microscopic particle, i.e., \[\Delta x\times \Delta p\ge \frac{h}{4\pi }\] |
| \[\because \] \[\Delta x\times \Delta p\ge \frac{h}{4\pi }\] |
| Here \[\Delta x=\Delta p\] and \[\Delta p=m.\Delta v\] |
| \[\therefore \] \[\Delta {{v}^{2}}=\frac{h}{{{m}^{2}}4\pi }\] or \[\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}\] |
| Note: The uncertainty principle, in terms of energy and time is given as \[\Delta E.\Delta t\ge \frac{h}{4\pi }\]. |
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