A) \[5.79\times {{10}^{6}}m{{s}^{-1}}\]
B) \[5.79\times {{10}^{7}}m{{s}^{-1}}\]
C) \[5.79\times {{10}^{8}}m{{s}^{-1}}\]
D) \[5.79\times {{10}^{5}}m{{s}^{-1}}\]
Correct Answer: A
Solution :
By Heisenberg's uncertainty principle \[\Delta p\times \Delta x\ge \frac{h}{4\pi }\] or \[\Delta v\times \Delta x\ge \frac{h}{4\pi m}\] \[\Delta x=\]uncertainty in position \[0.1\overset{o}{\mathop{\text{A}}}\,=0.1\times {{10}^{-10}}m\] \[m=\]mass of particle \[9.11\times {{10}^{-31}}kg\] \[h=\]Planck constant\[=6.626\times {{10}^{-34}}Js\] \[\pi =3.14\] \[\Delta v=\]uncertainty in velocity = ? In uncertain position, \[\Delta v\times \Delta x=\frac{h}{4\pi m}\] \[\Delta v\times 0.1\times {{10}^{-10}}=\frac{6.626\times {{10}^{-34}}}{4\times 3.14\times 9.11\times {{10}^{-31}}}\] \[\Delta v=\frac{6.626\times {{10}^{-34}}}{4\times 3.14\times 9.11\times {{10}^{-31}}\times 0.1\times {{10}^{-10}}}m{{s}^{-1}}\] \[=5.785\times {{10}^{6}}m{{s}^{-1}}\] \[=5.79\times {{10}^{6}}m{{s}^{-1}}\]
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