2. *Scattering experiment. The figure is a generic illustration of an extremely common setup for an experiment. The cylindrical chamber of length / = 10 cm and radius r = 1 cm contains the measured molecules. A dye laser that can adjust its wavelength in order to excite an atomic transition in the interrogated molecule injects through a window at the end of the chamber (at r = 0). Once excited, the molecule radiates a photon isotropically. Some of the radiated photons are collected by the lens at the top of the chamber, where they are analyzed by a spectrometer. A photodetector at the opposite end of the chamber monitors the laser intensity. Assume the laser injects photons at the rate of 3 x 10"/s, that the cross section for scattering at the measured molecular transition is 5 x 10 2 m', that the density of all molecules in the chamber is 2 x 102 m " but the concentration of interrogated molecules is only 10- of the total density. Also assume thatLens Laser Photodetector the other molecules absorb some of the light with a total cross section of 4 x 10 2 m'. Finally, assume that the diameter of the spectrometer lens is 0.4 cm. (a) What is the laser light's mean free path in the apparatus? [Hint: Use a generalization of the equation that follows Eq. (14.12).] [Answer: 0.56 m] (b) What fraction of the injected photons emerge from the opposite end? (c) Approximately how many photons per second are scattered by inter- rogated molecules in the chamber? (d) Very roughly, what is the count rate at the spectrometer