Explanation

(a)
Given, $\mathrm{\Delta}x = \mathrm{\Delta}P$ or $\mathrm{\Delta}x = m \bullet \mathrm{\Delta}v$
Heisenberg’s uncertainty principle,
$\mathrm{\Delta}x \bullet m \bullet \mathrm{\Delta}v = \frac{h}{4\pi}$
$m \bullet \mathrm{\Delta}v \bullet m\mathrm{\Delta}v = \frac{h}{4\pi}$
$(\mathrm{\Delta}v)^{2} = \frac{h}{4\pi m^{2}}$
$\mathrm{\Delta}v = \frac{1}{2m}\sqrt{\frac{h}{\pi}}$
$= \frac{1}{2 \times 9.1 \times 10^{- 31}}\ \sqrt{\frac{6.63 \times 10^{- 34}}{3.14}}$
$= 7.98 \times 10^{12}ms^{- 1} \approx 8 \times 10^{12}ms^{- 1}$