A) \[5.79\times {{10}^{8}}\,m\,{{s}^{-1}}\]
B) \[5.79\times {{10}^{5}}\,m\,{{s}^{-1}}\]
C) \[5.79\times {{10}^{6}}\,m\,{{s}^{-1}}\]
D) \[5.79\times {{10}^{7}}\,m\,{{s}^{-1}}\]
Correct Answer: C
Solution :
By Heisenberg?s uncertainty principle, \[\Delta p\times \Delta x=\frac{h}{4\pi }\]or \[\Delta r\times \Delta x=\frac{h}{4\pi m}\] Given that, \[\Delta x=0.1\overset{\text{o}}{\mathop{\text{A}}}\,=0.1\times {{10}^{-10}}m\] \[m=9.11\times {{10}^{-31}}kg\] \[h=\]planck?s constant \[=6.626\times {{10}^{-34}}\,Js\] \[\pi =3.14\] Thus, \[\Delta r\times 0.1\times {{10}^{-10}}=\frac{6.626\times {{10}^{-31}}}{4\times 3.14\times 9.11\times {{10}^{-31}}}\] \[=5.785\times {{10}^{6}}m{{s}^{-1}}=5.79\times {{10}^{6}}\,m{{s}^{-1}}\]
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