Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

174 EXPERIMENTAL METHODS FOR FAST REACTIONSpumping arrangement could be dispensed with by enclosing the whole apparatusin a copper box attached to a large liquid-nitrogen trap. The background pressurewas maintained at about lo-’ mm Hg. Typically the beams were about 1 mmwide at the scattering centre.How the measured intensities of the products at different angles relative to thereactant beams may be correlated with the projected reaction mechanism has beendiscussed admirably by Herschbach”zl ’ 14. By applying various conservation lawsit is possible to derive relationships between the velocity vectors of reactant andproduct particles. Although some of the her points are modifled slightly in a fullquantum mechanical treatment, Newtonian mechanics still apply and it is instructiveto discuss the collisions in terms of classical behaviour. A so-called “NewtonDiagram” is constructed from which it is possible to compute the product distributionfor different final kinetic energies. In a collision between particles (1) and(2) to give (3) and (4) it is useful to think in terms of the movement of the centreof mass. Its velocity is given bywhere m, and m2 are the masses of the reactants and ul , u2 their velocities. If therelative velocity vector of the two particles is u (= ul - uz), it follows thatu and (uz-vc) = -These follow from the linear momentum conservation relationship. Similar expressionsrelate the recoil velocities u3 and u4(u3-uc)= (A)u’ and (u4-uc) = - (-m3 ) 0’.m1+ mz m1+ mzThe magnitude of the final relative velocity vector u’ is determined by the energyconservation restrictionwhere p‘ is the reduced mass of the products. E’, the final relative translationalkinetic energy, is restricted by the relationshipE’+ W = E+ W+AD,