Question

A microscope using suitable photons is employed to locate an electron in an atom within the distance of ${0.1}^{o}A$.

What is the Uncertainty involved in the measurement of its velocity?

Answer 1

$\Delta x.\Delta p\ge \frac{h}{4\pi }$, $\Delta p=m\Delta v$,

$\Delta v=\frac{\Delta p}{m}$

$\therefore \Delta v\ge \frac{h}{4\pi m\Delta x}$

$\Rightarrow \Delta v\ge \frac{6.626\times {10}^{-34}}{4\times 3.14\times 9.11\times {10}^{-31}\times 0.1\times {10}^{-10}}$

$\Rightarrow \Delta v\ge 5.79\times {10}^{6}m/s$