section is defined as the reaction probability of a ray of A particles per areal density of B targets, which makes the definition independent from the nature of the interaction between A and B. Consequently, the radius is related to the length scale of their interaction potential.) From kinetic theory it is known that a molecule of A has an average velocity (different from root mean square velocity) of , where is the Boltzmann constant, and is the mass of the molecule. The solution of the two-body problem states that two different moving bodies can be treated as one body which has the reduced mass of both and moves with the velocity of the center of mass, so, in this system must be used instead of . Thus, for a given molecule A, it travels before hitting a molecule B if all B is fixed with no movement, where is the average traveling distance. Since B also moves, the relative velocity can be calculated using the reduced mass of A and B. Therefore, the total collision frequency, of all A molecules, with all B molecules, is From Maxwell–Boltzmann distribution it can be deduced that the fraction of collisions with more energy than the activation energy is . Therefore, the rate of a bimolecular reaction for ideal gases will be in unit number of molecular reactions s−1⋅m−3, where: Z is the collision frequency with unit s−1⋅m−3. The z is Z without [A][B]. is the steric factor, which will be discussed in detail in the next section, Ea is the activation energy (per mole) of the reaction in unit J/mol, T is the absolute temperature in unit K, R is the gas constant in unit J/mol/K. [A] is molar concentration of A in unit mol/L, [B] is molar concentration of B in unit mol/L. The product zρ is equivalent to the preexponential factor of the Arrhenius equation. Validity of the theory and steric factor Once a theory is formulated, its validity must be tested, that is, compare its predictions with the results of the experiments. When the expression form of the rate constant is compared with the rate equation for an elementary bimolecular reaction, , it is noticed that unit M−1⋅s−1 (= dm3⋅mol−1⋅s−1), with all dimension unit dm including kB. This expression is similar to the Arrhenius equation and gives the first theoretical explanation for the Arrhenius equation on a molecular basis.