A) \[{{10}^{-8}}\] m
B) \[{{10}^{-12}}\] m
C) \[{{10}^{-16}}\]m
D) \[{{10}^{-4}}\] m
Correct Answer: D
Solution :
The product of uncertainties in the simultaneous measurement of position and momentum, energy and time, angular momentum and angular displacement is of the order of h (or h). where, \[h=\frac{h}{2\pi }\] \[\therefore \] \[\Delta p.\,\Delta x\ge h\] where \[\Delta p\] is uncertainty in the measurement of momentum of particle. The minimum uncertainty in position of particle will be \[\,\Delta x=\frac{h}{\Delta p}\] Here, \[\,\Delta p={{10}^{-30}}kg\,\,m/s\] \[\therefore \] \[\Delta x=\frac{1.034\times {{10}^{-34}}}{{{10}^{-30}}}\] \[={{10}^{-4}}m\]
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