Problem 6.237

The mean path length of alpha-particles in air under standard conditions is defined by the formula \(R=0.98 \cdot 10^{-27} v_{0}^{3} \mathrm{~cm}\) where \(v_{0}(\mathrm{~cm} / \mathrm{s})\) is the initial velocity of an alpha-particle. Using this formula, find for an alpha-particle with initial kinetic energy \(7.0 \mathrm{MeV}:\) (a) its mean path length; (b) the average number of ion pairs formed by the given alphaparticle over the whole path \(R\) as well as over its first half, assuming the ion pair formation energy to be equal to \(34 \mathrm{eV}\).