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

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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.

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