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Calculate the uncertainty in velocity of an electron if the uncertainty in its position is of the order of $1A^{\large\circ}$

$\begin{array}{1 1}(a)\;4.8\times 10^5m/s&(b)\;5.8\times 10^5m/s\\(c)\;5.8\times 10^2m/s&(d)\;2.3\times 10^5m/s\end{array}$

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According to Heisenberg's uncertainty principle
$\Delta u\Delta x\approx \large\frac{h}{4\pi m}$
$\Delta u\approx \large\frac{h}{4\pi m\Delta x}$
$\Rightarrow \large\frac{6.625\times 10^{\Large-34}}{4\times 22/7\times 9.108\times 10^{\Large-31}\times 10^{-10}}$
$\Rightarrow 5.8\times 10^5m/s$
Hence (b) is the correct answer.
answered Jan 17, 2014 by sreemathi.v

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