Step 1: Conceptual Understanding:
Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.
Step 2: Explanation in Detail:
$\Delta x = \Delta v$. $\Delta p = m \Delta v = m \Delta x$. So $(\Delta x)^2 \geq \frac{h}{4\pi m}$, $\Delta x = \sqrt{\frac{h}{4\pi m}}$. Then $\Delta p = m \Delta x = m \sqrt{\frac{h}{4\pi m}} = \sqrt{\frac{mh}{4\pi}} = \frac{1}{2}\sqrt{\frac{mh}{\pi}}$.
Step 3: Therefore, Stating the Final Answer
$\Delta p = \frac{1}{2}\sqrt{\frac{mh}{\pi}}$.