Question

If uncertainties in the measurement of position and momentum of an electron are equal, calculate uncertainty in the measurement of velocity.

Answer 1

According to Heisenberg's uncertainty principle,

$\Delta x\cdot \Delta p\ge \frac{h}{4\pi }$

Given, $\Delta x=\Delta p=\sqrt{\frac{h}{4\pi }}=0.726\times {10}^{-17}$

$\Delta p=m\Delta V$

$\Rightarrow \Delta V=\frac{\Delta p}{m}=\frac{0.726\times {10}^{-17}}{9.1\times {10}^{-31}}=7.98\times {10}^{12}m{s}^{-1}$.

Hence, the uncertainty in the measurement of velocity will be $7.98\times {10}^{12}m{s}^{-1}$.