A) \[2.8\times {{10}^{-3}}{{m}^{2}}{{s}^{-1}}\]
B) \[3.8\times {{10}^{-5}}{{m}^{2}}{{s}^{-1}}\]
C) \[5.8\times {{10}^{-5}}{{m}^{2}}{{s}^{-1}}\]
D) \[6.8\times {{10}^{-6}}{{m}^{2}}{{s}^{-1}}\]
Correct Answer: C
Solution :
Key Idea: We will use formula\[\Delta x\times \Delta p=\frac{h}{4\pi }\]to solve problem. \[\Delta x\times \Delta p=\frac{h}{4\pi }\] \[\Delta x\times m\Delta v=\frac{h}{4\pi }\] \[\Delta x\times \Delta v=\frac{h}{4\pi m}\] \[\Delta x=\]uncertainty in position \[\Delta v=\]uncertainty in velocity h = Planck's constant\[=6.63\times {{10}^{-34}}kg\text{ }{{m}^{2}}{{s}^{-1}}\] m= mass of electron\[=9.1\times {{10}^{-31}}kg\] \[\therefore \] \[\Delta x\times \Delta v=\frac{6.63\times {{10}^{-34}}}{4\times 3.14\times 9.1\times {{10}^{-31}}}\] \[=5.8\times {{10}^{-5}}{{m}^{2}}{{s}^{-1}}\]
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