question_answer 16)

A microscope using suitable photons is employed to locate an electron in an atom within a distance of \[0.1\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. What is the uncertainty involved in the measurement of its velocity?

Answer:

Information shadow: Uncertainty in position. \[\Delta x=0.1\overset{{}^\circ }{\mathop{\text{A}}}\,\] \[=0.1\times {{10}^{-10}}m\] \[={{10}^{-11}}m\] Uncertainty in velocity \[\Delta \upsilon \] is required. Problem solving strategy: According to the Heisenberg's uncertainty principle \[\Delta x\,\,\Delta \upsilon \ge \frac{h}{4\pi m}\] \[\Delta \upsilon \ge \frac{h}{4\pi m\Delta x}\] Working it out: \[\Delta \upsilon =\frac{6.626\times {{10}^{-34}}}{4\times 3.14\times 9.1\times {{10}^{-31}}\times {{10}^{-11}}}\] \[=5.79\times {{10}^{6}}m{{s}^{-1}}\]