A) \[8.0\times {{10}^{12}}m{{s}^{-1}}\]
B) \[4.2\times {{10}^{10}}m{{s}^{-1}}\]
C) \[8.5\times {{10}^{10}}m{{s}^{-1}}\]
D) \[6.2\times {{10}^{10}}m{{s}^{-1}}\]
Correct Answer: A
Solution :
Given, \[\Delta \,x=\Delta P\]or \[\Delta \,x=m\cdot \Delta v\] From Heisenbergs uncertainty principle, \[\Delta \,x\cdot m\cdot \Delta v=\frac{h}{4\pi }\] \[\Rightarrow \] \[m\cdot \Delta v\cdot m\Delta v=\frac{h}{4\pi }\] \[{{(\Delta v)}^{2}}=\frac{h}{4\pi {{m}^{2}}}\] \[\Rightarrow \] \[\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}\] \[=\frac{1}{2\times 9.1\times {{10}^{-31}}}\sqrt{\frac{6.63\times {{10}^{-34}}}{3.14}}\] \[=7.98\times {{10}^{12}}m{{s}^{-1}}\] \[=8\times {{10}^{12}}m{{s}^{-1}}\]
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