Browse Questions

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

$\begin{array}{1 1}(a)\;6.634\times 10^{12}ms^{-1}&(b)\;7.2\times 10^{11}ms^{-1}\\(c)\;7.98\times 10^{12}ms^{-1}&(d)\;7.98\times 10^{10}ms^{-1}\end{array}$

According to Heisenberg's uncertainty principle
$\Delta x\Delta p\geq \large\frac{h}{4\pi}$
$\Delta x=\Delta p=\sqrt{\large\frac{h}{4\pi}}$
$\Rightarrow 0.726\times 10^{-17}$
$\Delta p=m\Delta v$
$\Delta v=\large\frac{\Delta p}{m}$
$\Rightarrow \large\frac{0.726\times 10^{-17}}{9.1\times 10^{-31}}$
$\Rightarrow7.98\times 10^{12}ms^{-1}$
Hence (c) is the correct answer.