A) \[5.79\,\,\times \,\,{{10}^{8}}\,m/s\]
B) \[5.79\,\,\times \,\,{{10}^{5}}\,m/s\]
C) \[5.79\,\,\times \,\,{{10}^{6}}\,m/s\]
D) \[5.79\,\,\times \,\,{{10}^{7}}\,m/s\]
Correct Answer: C
Solution :
According to Hisenberg uncertainty principle \[\Delta x\cdot \Delta p=\frac{h}{4\pi }\] \[\Delta x\times \,\,m\Delta v=\frac{h}{4\pi }\] \[\Delta x\times \,\,\Delta v=\frac{h}{4\pi m}\] \[\Delta v=\frac{h}{4\pi m\cdot \Delta x}\] \[=\,\,\,\,\frac{6.626\times {{10}^{-34}}}{4\times 3.14\times 9.11\times {{10}^{-}}^{31}\times 0.1\times {{10}^{-}}^{10}}\] \[=\,\,\,\,\frac{6.626\times {{10}^{-34}}}{4\times 3.14\times 0.1\times {{10}^{-}}^{41}}\] \[=\,\,\,\,\frac{6.626\times {{10}^{-34\,+\,41}}}{0.4\times 3.14}=\frac{6.626}{0.4\times 3.14}\times {{10}^{+7}}\] \[=\,\,\,5.79\times 1{{0}^{6}}m/s\]
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