The space between stars in the universe contains a mixture of gases at very low pressure as well as some dust. The gas is mainly hydrogen with a little helium, but many other molecules. have also been detected in tiny amounts (see Chapter 4, p.168). For a hellum atom, the collision cross-section $\sigma=0.21 \mathrm{~nm}^{2}$. The conditions in interstellar space are around $T=10 \mathrm{~K}$ and $p=1 \times$ $10^{-18} \mathrm{~atm}$. (Section 8.5)
(a) Calculate the mean free path, $\lambda$, of helium atoms at SATP.
(b) Estimate the value of $\lambda$ for a helium atom in interstellar space. (Hint. For a given gas, $\lambda \propto \frac{I}{p}$.)
(c) Estimate the time between collisions for helium atoms in interstellar space. (For the atoms at $10 \mathrm{~K}, \bar{c}=230 \mathrm{~ms}^{-1}$ )