Rates emission

Einstein derived the relationship between spontaneous emission rate and the absorption intensity or stimulated emission rate in 1917 using a thennodynamic argument [13]. Both absorption intensity and emission rate depend on the transition moment integral of equation (B 1.1.1). so that gives us a way to relate them. The symbol A is often used for the rate constant for emission it is sometimes called the Einstein A coefficient. For emission in the gas phase from a state to a lower state j we can write... 

The fluorescence signal is linearly proportional to the fraction/of molecules excited. The absorption rate and the stimulated emission rate 1 2 are proportional to the laser power. In the limit of low laser power,/is proportional to the laser power, while this is no longer true at high powers 1 2 <42 j). Care must thus be taken in a laser fluorescence experiment to be sure that one is operating in the linear regime, or that proper account of saturation effects is taken, since transitions with different strengdis reach saturation at different laser powers. 

Note that negative Acoj (red detuning) produces a force attracting the atom to the intensity maximum while positive (blue detuning) repels the atom away from the intensity maximum. The spontaneous force or cooling force can also be written in tenns of the saturation parameter and the spontaneous emission rate. 

The light emitted in the spontaneous recombination process can leave tire semiconductor, be absorbed or cause additional transitions by stimulating electrons in tire CB to make a transition to tire VB. In tliis stimulated recombination process anotlier photon is emitted. The rate of stimulated emission is governed by a detailed balance between absorjDtion, and spontaneous and stimulated emission rates. Stimulated emission occurs when tire probability of a photon causing a transition of an electron from tire CB to VB witli tire emission of anotlier photon is greater tlian that for tire upward transition of an electron from tire VB to tire CB upon absorjDtion of tire photon. These rates are commonly described in tenns of Einstein s H and 5 coefficients [8, 43]. For semiconductors, tliere is a simple condition describing tire carrier density necessary for stimulated emission, or lasing. This carrier density is known as... 

Here, Ri f and Rf i are the rates (per moleeule) of transitions for the i ==> f and f ==> i transitions respeetively. As noted above, these rates are proportional to the intensity of the light souree (i.e., the photon intensity) at the resonant frequeney and to the square of a matrix element eonneeting the respeetive states. This matrix element square is oti fp in the former ease and otf ip in the latter. Beeause the perturbation operator whose matrix elements are ai f and af i is Hermitian (this is true through all orders of perturbation theory and for all terms in the long-wavelength expansion), these two quantities are eomplex eonjugates of one another, and, henee ai fp = af ip, from whieh it follows that Ri f = Rf i. This means that the state-to-state absorption and stimulated emission rate eoeffieients (i.e., the rate per moleeule undergoing the transition) are identieal. This result is referred to as the prineiple of microscopic reversibility. 

In this sequence the Cl also acts as a catalyst and two molecules are destroyed. It is estimated that before the Cl is finally removed from the atmosphere in 1—2 yr by precipitation, each Cl atom will have destroyed approximately 100,000 molecules (60). The estimated O -depletion potential of some common CFCs, hydrofluorocarbons, HFCs, and hydrochlorofluorocarbons, HCFCs, are presented in Table 10. The O -depletion potential is defined as the ratio of the emission rate of a compound required to produce a steady-state depletion of 1% to the amount of CFC-11 required to produce the 1% depletion. The halons, bromochlorofluorocarbons or bromofluorocarbons that are widely used in fire extinguishers, are also ozone-depleting compounds. Although halon emissions, and thus the atmospheric concentrations, are much lower than the most common CFCs, halons are of concern because they are from three to ten times more destmctive to O, than the CFCs. 

Source sampling of particulates requites isokinetic removal of a composite sample from the stack or vent effluent to determine representative emission rates. Samples are coUected either extractively or using an in-stack filter EPA Method 5 is representative of extractive sampling, EPA Method 17 of in-stack filtration. Other means of source sampling have been used, but they have been largely supplanted by EPA methods. Continuous in-stack monitors of opacity utilize attenuation of radiation across the effluent. Opacity measurements are affected by the particle size, shape, size distribution, refractive index, and the wavelength of the radiation (25,26). 

In research environments where the configuration and activity level of a sample can be made to conform to the desires of the experimenter, it is now possible to measure the energies of many y-rays to 0.01 keV and their emission rates to an uncertainty of about 0.5%. As the measurement conditions vary from the optimum, the uncertainty of the measured value increases. In most cases where the counting rate is high enough to allow collection of sufficient counts in the spectmm, the y-ray energies can stih be deterrnined to about 0.5 keV. If the configuration of the sample is not one for which the detector efficiency has been direcdy measured, however, the uncertainty in the y-ray emission rate may increase to 5 or 10%. 

Table 15 shows data for several radionucHdes the y-rays of which are often used to caHbrate the efficiency of y-ray detectors. For a number of these y-rays the very high accuracy arises because the y-ray occurs in essentially 100% of the decays of the nucHde, and only small corrections ate needed to deduce the y-emission probabiHty. In other cases the accuracy is high because a number of careful measurements have been made. The y-emission rate from a caHbration source also depends on the decay rate of the source, and for these nucHdes the uncertainty in the source activity is often the larger uncertainty. 

Nonattamment. EPA issued final rules for the Emission Offset PoHcy governing development in nonattainment areas. A new source must apply the lowest achievable emission rate (LAER) for the problem poUutant and must obtain a more than equivalent offsetting emission reduction from existing sources. Either the existing sources can be owned by the same company, or the reduction can be bought from other companies. In this way, new growth is ahowed while air quahty improvement is achieved. 

Empirical—statistical models ate based on estabUshing a relationship between historically observed air quaUty and the corresponding emissions. The linear rollback model is simple to use and requites few data, and for these reasons has been widely appHed (3,4). Linear rollback models assume that the highest measured pollutant concentration is proportional to the basinwide emission rate, plus the background value that is,... 

Moisture Content EPA Method 4 is the reference method for determining the moisture content of the stack gas. A value for moisture content is needed in some of the calculations for determining pollution-emission rates. 

For determination of the total mass-emission rate of SO9, the moisture content and the volumetric flow rate of the exhaust gas stream must also be measured. 

A samphng probe is placed at any location in the stack, and a grab sample is collected in an evacuated flask. This flask contains a solution of siilfiiric acid and hydrogen peroxide, which reacts with the NO. The volume and moisture content of the exhaust-gas stream must be determined for calculation of the total mass-emission rate. The sample is sent to a laboratoiy, where the concentration of nitrogen oxides, except nitrons oxide, is determined colorimetrically. 

SW-846, is used to measure emissions of semivolatile principal organic constituents. Method 0010 is designed to determine destruction and removal efficiency (DRE) of POHCs from incineration systems. The method involves a modification of the EPA Method 5 sampling train and may be used to determine particulate emission rates from stationary sources. The method is applied to semivolatile compounds, including polychlorinated biphenyls (PCBs), chlorinated dibenzodioxins and dibenzofurans, polycyclic organic matter, and other semivolatile organic compounds. 

Q = continuous dense vapor emission rate, mVs at 25°C Xl = distance to momentaiy LFL in centerhne of cloud, m u = wind speed, iti/s... 

Assume a continuous release of pressurized, hquefied cyclohexane with a vapor emission rate of 130 g moLs, 3.18 mVs at 25°C (86,644 Ib/h). (See Discharge Rates from Punctured Lines and Vessels in this sec tion for release rates of vapor.) The LFL of cyclohexane is 1.3 percent by vol., and so the maximum distance to the LFL for a wind speed of 1 iti/s (2.2 mi/h) is 260 m (853 ft), from Fig. 26-31. Thus, from Eq. (26-48), Vj 529 m 1817 kg. The volume of fuel from the LFL up to 100 percent at the moment of ignition for a continuous emission is not equal to the total quantity of vapor released that Vr volume stays the same even if the emission lasts for an extended period with the same values of meteorological variables, e.g., wind speed. For instance, in this case 9825 kg (21,661 lb) will havebeen emitted during a 15-min period, which is considerablv more than the 1817 kg (4005 lb) of cyclohexane in the vapor cloud above LFL. (A different approach is required for an instantaneous release, i.e., when a vapor cloud is explosively dispersed.) The equivalent weight of TNT may be estimated by... 

Providing quantitative estimates of NHj emissions is necessarily rather uncertain, because of the wide range of variability in the sources as well as in factors affecting the emission rate. In the case of livestock emissions, the obvious scaling parameter is the number of animals in a particular area and emissions estimates... 

Soil Temperature. In temperate climates, NO and NjO emission rates increase with increasing soil temperature and a response to diurnal and seasonal temperature variations has been reported freqnently." Activation energies for both soil NO and NjO emissions are usually in the range of 30-150 kJ mol ... 

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