Serway & Jewett — The Kinetic Theory of Gases: Problem 44.

Consider the particles in a gas centrifuge, a device used to separate particles of different mass by whirling them in a circular path of radius \( r \) at angular speed \( \omega \). The force acting on a gas molecule toward the center of the centrifuge is \( m_0 \omega^2 r \). (a) Discuss how a gas centrifuge can be used to separate particles of different mass. (b) Suppose the centrifuge contains a gas of particles of identical mass. Show that the density of the particles as a function of \( r \) is \( n(r) = n_0 e^{m_0 r^2 \omega^2 / 2 k_B T} \).