Answer
a. 19.3 m/s.
b. 11 mm/s.
Work Step by Step
a. The Heisenberg uncertainty principle limits our knowledge.
$$\Delta x \Delta p_x \geq \frac{\hbar}{2}$$
$$\Delta x\;m \Delta v_x \geq \frac{\hbar}{2}$$
We are told that $\ \Delta v_x = (0.010)v_x$
Set the product of uncertainties to its minimum value.
$$\Delta x\;m \Delta v_x = \frac{\hbar}{2}$$
$$\Delta x\;m (0.010)v_x = \frac{\hbar}{2}$$
$$ v_x =\frac{\hbar}{2m (0.010) \Delta x}=19.3m/s$$
b. Repeat, using the mass of a proton, to find 11 mm/s.
