Energy thresholds

Figure A3.4.5. Simple models for effeetive eollision eross seetions a hard sphere without tlireshold (dotted line) hard sphere with tlireshold (dashed line) and hyperbolie threshold (full eiirve). is the (translational) eollision energy and is the threshold energy. Oq is the hard sphere eollision eross seetion. The dashed-dotted eurve is of the generalized type E > q) Oq (1 - q/ j) exp[(l - j/ q)/(<3 q)] with the parameter...

Reactive scattering or a chemical reaction is characterized by a rearrangement of the component particles within the collision system, thereby resulting in a change of the physical and chemical identity of the original collision reactants A + B into different collision products C + D. Total mass is conserved. The reaction is exothemiic when rel(CD) > (AB) and is endothermic when rel(CD) < (AB). A threshold energy is required for the endothemiic reaction. 

Clearly, the value of -12 kcal/mol for the threshold energy is not accidental. Buried water molecules are in equilibrium with water nioh cules in the... 

This discussion of threshold energy causes us to wonder what energies are possessed by molecules at a given temperature. We have already compared the molecules of a gas with billiard balls rebounding on a billiard table. When billiard balls bounce around, colliding with each other, some of them move rapidly and some slowly. Do molecules behave this way Experiment provides the answer. 

We can apply these curves to our reaction rate problem. Suppose a reaction can proceed only if two molecules collide with kinetic energy exceeding a certain threshold energy, E. Figure 8-4 shows us a typical situation. At Tx the darkly shaded area is proportional to the number of the molecules which possess this energy or more. Since only a small number of molecules have as... 

Describe the life and death of an ordinary, empty water glass. Utilize the concept threshold energy. ... 

Theory. The requirement of a threshold energy for an endothermic ion-molecule reaction can be used together with the described model to calculate the exact position within the dark space where an ion can undergo reaction having gained from the field at least the necessary... 

If at any point x (Figure 2) away from the cathode but within the dark space 8N(E,X) denotes the number of ions per unit volume with energy between E and E + dE, such that E > E0, the threshold energy for the reaction, then as the ions move toward the cathode, the total amount of a bimolecular reaction they will undergo with neutral reactant species of density p, to yield Ns secondary ions per cc. at the cathode is given by ... 

The threshold energy of potassium metal, 3.7x10 J, is given in the problem. To determine whether the red and blue photons will eject electrons, we convert the frequencies of these photons to their... 

Figure 9. Potential energy diagram (in kJ mol ) showing energetically allowed photodissociation channels for CH3CHO. Note the similar threshold energies for the four energetically allowed channels. Reprinted with permission from Dr. Scott Kable, University of Sydney.

It will be necessary to provide quantitative criteria for studies of photoelectrochemical phenomena. These phenomena are a function of photon energy and appear only at energies above a particular threshold energy hv (or below a particular threshold wavelength, of the light). The threshold energy is an important characteristic of any given phenomenon. 

Acronym Electron impact reaction Threshold energy (eV Reference ) Comment... 

The experimental approaches described above are examples of relative methods, wherein a thermochemical property is measured with respect to that of a standard, or an anchor. The quality of these measurements ultimately depends on the quality of the anchor. Alternatively, there are methods of determining thermochemical properties, in which the energy for a chemical process is measured on an absolute basis. Among the more common of these are the appearance energy measurements, in which the threshold energy for formation of an ionic fragment from an activated precursor is measured. There are mauy differeut methods of activation that can be used. Some of these are discussed here. 

S.3.4.2. Collision-induced Dissociation/Translationally-driven Reactions Tandem-mass spectrometry can be used to determine the threshold energy for collision-induced dissociation (CID),... 

Similarly, Ervin and co-workers have measured acidities of organic molecules by measuring the energy for endothermic proton transfer reactions between acids and anionic bases." " Alternatively, it is possible to use competitive CID of proton-bound dimer ions." Nominally, these are relative approaches for measuring acidities, as the measured acidities depend on the properties of the reference acids or bases. However, it is usually possible to select references with very accurately known acidities (such as HE, HCN, or HCl), such that the accuracy of the final measurement depends predominantly on the accuracy of the threshold energy determination. 

The threshold energies for these processes correspond directly to the electron affinity (EA) or ionization energy (IE). 

Merged-beam measurements 23-26 have consistently shown that the measured recombination cross section depends on conditions in the ion source. The authors have ascribed the effect to differing vibrational distributions. In one of the later measurements,16 the Hj vibrational state was inferred from the threshold energy for electron-ion dissociative excitation,... 

Figure 9. Energy levels of an ammonia molecule showing the states investigated in the pump-probe experiments. Also shown are the threshold energies where H atoms can be produced. The upper hatched region denotes the ionization limit. Taken with permission from, NATOASI Series on Large Clusters of Atoms and Molecules Kluwer Academic Dordrecht, 1996, pp 371-404.

The threshold curves obtained when the accelerating potential between OR and Q2 was changed over a wide range from the onset of a given production to its maximum intensity were fitted with the theoretical cross section program, CRUNCH, developed by Armenrout and coworkers,67-69 which leads to a determination of the threshold energies (see Section IV.C). 

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