A) \[2.6\times {{10}^{-\,12}}J\]
B) \[2.6\times {{10}^{12}}J\]
C) \[2.6\times {{10}^{-\,12}}eV\]
D) \[2.6\times {{10}^{12}}eV\]
Correct Answer: A
Solution :
With \[\Delta x=5\times {{10}^{-15}}m,\] By uncertainty principle, we have \[\Delta p\cdot \Delta x\ge \frac{h}{4\pi }\] \[\Rightarrow \]\[\Delta p\ge \frac{\left( \frac{h}{2\pi } \right)}{2\Delta x}\ge \frac{1.054\times {{10}^{-\,34}}}{(2\times 5\times {{10}^{-15}})}\] \[\Rightarrow \]\[\Delta p\ge 1.1\times {{10}^{-\,20}}kg\,m{{s}^{-\,1}}\] Kinetic energy, \[K=\frac{1}{2}m{{c}^{2}}=\frac{1}{2}pc\] \[=\frac{1}{2}\times 1.1\times {{10}^{-\,20}}\times 3\times {{10}^{8}}\] \[=26\times {{10}^{-\,12}}J\]
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