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

$\begin{array}{1 1}(a)\;7.98\times 10^{12}m/s&(b)\;6.98\times 10^{12}m/s\\(c)\;7.98\times 10^6m/s&(d)\;5.83\times 10^{12}m/s\end{array}$

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Heisenberg's uncertainty principle
$\Delta x.\Delta p\geq \large\frac{h}{4\pi}$
$\Delta x=\Delta p$,hence
$\Delta x=\Delta p=\sqrt{\large\frac{h}{4\pi}}$
$\Rightarrow 0.726\times 10^{-17}$
Also $\Delta x.\Delta v\geq \large\frac{h}{4\pi m}$
Thus $\Delta v=\large\frac{\Large\frac{h}{4\pi m}}{\Delta x}$
$\Rightarrow \large\frac{4/4\pi m}{\sqrt{h/4\pi}}$
$\Rightarrow \sqrt{\large\frac{h}{4\pi}}\times \large\frac{1}{m}$
$\Rightarrow \large\frac{0.726\times 10^{-17}}{9.1\times 10^{-31}}$
$\Rightarrow 7.98\times 10^{12}m/s$
Hence (a) is the correct answer.
answered Jan 16, 2014 by sreemathi.v

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