A) \[1\times {{10}^{9}}cm\,{{s}^{-1}}\]
B) \[1\times {{10}^{6}}cm\,{{s}^{-1}}\]
C) \[1\times {{10}^{5}}cm\,{{s}^{-1}}\]
D) \[1\times {{10}^{11}}cm\,{{s}^{-1}}\]
Correct Answer: A
Solution :
Key Idea: \[\Delta x\times \Delta p\ge \frac{h}{4\pi }\]where, \[\Delta p=\] uncertainty in momentum and \[\Delta v=\]uncertainty in velocity Here, \[\Delta p=1\times {{10}^{-18}}g\,cm\,{{s}^{-1}}\] \[m=9\times {{10}^{-28}}\]g \[\Delta v=\frac{\Delta p}{m}=\frac{1\times {{10}^{-18}}}{9\times {{10}^{-28}}}\] \[=1.1\times {{10}^{9}}\] \[\approx 1.0\times {{10}^{9}}\,cm\,{{s}^{-}}\]
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