A speck of dust has a mass of 1.0 µg. (a) How fast would it have to move for its de Broglie…

Step 1. The speed. $v = \dfrac{h}{m\lambda} = \dfrac{6.63 \times 10^{-34}\ \text{J s}}{1.0 \times 10^{-9}\ \text{kg} \times 1.0 \times 10^{-9}\ \text{m}} = 6.63 \times 10^{-16}\ \text{m/s}$.

Step 2. The time for 1.0 mm. $t = \dfrac{1.0 \times 10^{-3}\ \text{m}}{6.63 \times 10^{-16}\ \text{m/s}} = 1.51 \times 10^{12}\ \text{s}$.

Step 3. In years. $\dfrac{1.51 \times 10^{12}\ \text{s}}{3.156 \times 10^{7}\ \text{s/year}} = 4.78 \times 10^{4}\ \text{years}$.