Question

In a vacuum of 10¬3 Torr at room temperature (20 °C). This number is a useful one for the experimentalist to know by heart (10¬³ Torr=1 µ).

Answer 1

We know that

$$PV=nkT,\\\space\\ N=\frac NV=\frac{P}{kT}=\frac{10^{-3}·133}{1.38·10^{-23}·(273+20)}=3.29·10^{-19}\text{ m}^{-3}.$$