Radius collision

For 1, de Broglie s wavelength is small enough compared to the classical collision radius b so that a wave packet can be constructed which, approximately, follows the classical Coulomb trajectory [3]. The opposite limit, where the Sommerfeld parameter Zie hv<, denotes the case of weak Coulomb interaction where the Born approximation may be expected to be valid. 

On the other hand, if the rate constant for the quenching step exceeds that expected for a diffusion-controlled process, a modification of the parameters in the Debye equation is indicated. Either the diffusion coefficient D as given by the Stokes-Einstein equation is not applicable because the bulk viscosity is different from the microviscosity experienced, by the quencher (e.g. quenching of aromatic hydrocarbons by O, in paraffin solvents) or the encounter radius RAb is much greater than the gas-kinetic collision radius. In the latter case a long-range quenching... 

Since the collision radius for two particles of equal size is two times the particle radius, the effective volume swept out will be four times that given by Eq. 9-33. Since both particles are diffusing, the effective diffusion constant will be twice that used in obtaining Eq. 9-28. Thus, the effective volume swept out by the particle in a second will be eight times that given by Eq. 9-33. The volume swept out by one mole of particles is equal to /cD (recall that the second-order rate constant has dimensions of liter mol-1 s 1). Thus, when converted to a moles per liter basis and multiplied by 8, Eq. 9-33 should (and does) become identical with the Smolu-chowski equation (Eq. 9-30). 

The rate constant for reaction of the electron with biological polymers such as nucleic acids (11) and proteins (7) have been examined. When calculated on a per mole basis the rate constants can be quite high— e.g., ribonuclease (pH 6.8) k = 1.3 X 1010 M l sec.-1, lysozyme (pH 6.2) k = 7.5 X 1010 M l sec.""1), but they are much less than if the constituent units were in free solution. For ribonuclease an attempt has been made to estimate the rate constant from the rate constants for the constituent units (6). Allowance was made for the decrease in collision radius in going from the constituent units to the protein, and for the number of positive charges on the protein molecule. The estimated value agreed with the measured value to within a factor of two or three. If this approach is accepted, one can conclude that the strongest contribution to the reactivity arises from —SS groups, and this conclusion is in line with other evidence from radiation chemistry. 

Here d = 2r, where r is the radius of the colliding particles. For two different particles in a gas mixture d = rx + r2. d is sometimes called the collision radius (RM) to denote an active sphere of radius R and active cross-section nR2. ... 

H. Termolecular Collisions Collision Complexes. Having defined a collision radius o-a for the hard sphere molecule M of core diameter o-r, it is possible to define a collision complex M M as a pair of molecules whose centers are a distance o- apart, where o-a [Pg.156]

In the classical picture, the short range interaction is described by the classical Rutherford scattering theory, which is parameterized in terms of b being the impact parameter and b = Ze /mv the classical collision radius. Instead, in the quantum perturbation theory, the short-range behavior is related to high momentum transfers. In the Bethe and Lindhard theories... 

The rate of diffusion-controlled coalescence of spherical particles in a disperse system as a result of collisions has been shown by von Smoluchowski to be proportional to the collision radius of the particles, the diffusion coefficient, and the square of the concentration of the particles ... 

In liquids as contrasted with gases there is a nonnegligible probability that the collision of the two molecules is prevented by the intervention of a third molecule. In the papers under discussion here, this " shielding effect is taken into account by the introduction of a correction factor A which depends only on the local number density and the collision radius cr. 

Particle shape can also have a large effect. Anisometric particles have an increased collision radius as compared to spheres see the discussion in relation to Figure 5.3. Moreover, capture efficiency is affected, but prediction of the effect is far from easy. 

Wavelength of maximum absorption Extinction coefficient at 7200A. Width at half-height Oscillator strength Diffusion Constant Equivalent Conductance Effective Collision Radius Ion Atmosphere Relaxation Time at /x = 0.24M Partial Molal Volume Standard Free Energy of Solvation G (e m), y-Radiation Yield Lifetime with respect to H30+ at pH 7 Lifetime with respect to H20... 

In this equation we have introduced the collision radius, r, defined as... 

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