Answer
a. $1.6\times10^{4}m/s$.
b. $2.3\times10^{-4}m$.
Work Step by Step
a. The Heisenberg uncertainty principle limits our knowledge of its velocity.
$$\Delta y \Delta p_y \geq\frac{\hbar}{2}$$
$$\Delta y\;m \Delta v_y \geq\frac{\hbar}{2}$$
Find the minimum uncertainty.
$$ \Delta v_y =\frac{\hbar}{2m \Delta y}=1.6\times10^{4}m/s$$
b. The Heisenberg uncertainty principle limits our knowledge of its position.
$$\Delta z \Delta p_z \geq\frac{\hbar}{2}$$
$$\Delta z \;m \Delta v_z \geq\frac{\hbar}{2}$$
Find the minimum uncertainty.
$$ \Delta z =\frac{\hbar}{2m \Delta v_z}=2.3\times10^{-4}m$$