Growth and decay curves

Figure 3. Growth and decay curves for radon and its short-lived decay products.

Figure 1. Growth and decay curves for progeny originating from 2 Es. Reproduced with permission from Ref. 2, copyright 1978, Elsevier Sequoia, S.A.

Figure 8 shows the growth and decay curves (the kinetics) of these three phenomena—photoconductivity, light induced polarization and the electron spin resonance signal. All of them have the same unimole-cular time constants at 25°C. When the system is cooled to —100°, which has been done for the photoconductivity and the spin signal, they decay faster at the lower temperature but again they are parallel they have the same kinetic behavior. 

For longer decay chains or for a situation of a continuous production of a mother isotope the reader may be referred to the classical system of radioactive growth and decay curves as given in textbooks of radiochemistry. (See also Eqs. [38.29] and [ 38.30] in Chap. 38, Vol. 4.)... 

Fig. 1.8. Consecutive first-order reactions with p0 = 0.1 mol dm-3, fcu = 5 x 10-3 s and k2 = 10"2s (a) the exponential decay of precursor reactant concentration, p (b) growth and decay of intermediate concentrations a(t) and b(t). Also shown in (b), as broken curves, are the pseudo-stationary-state loci, a (t) and b (t), given by eqns (1.31) and...

To describe the long-term trend we use an exponential growth or decay curve and characterize it by the rate constant a [T1] ... 

Growth and Decay of the Transients Formed in Neutral 0.01M KC1 Matrix. The growth of the transients was followed at 330 nm., at 2 to 10 /xsec. sweep rates, and at gold concentrations of 25fiM and 50fiM. From the growth curves the rate constants for the reactions ... 

The growth and decay of the transient which we shall designate by (Au°)e-a(i was followed at 410 n.m. in ImM alkaline solutions at different concentrations of Au(CN)2". From the growth curves obtained at Au1 concentrations in the range from 20 to 100pM, at low sweep rates, the rate constants for the reactions ... 

Growth and decay of Ra after isolation of radium from 4n series at secular equilibrium. The top curve gives the decay of Ra after the first isolation relative to the secular rate. The growth curve shows the time dependence of Ra that comes from Ra (via Ac and Th). The middle decay curve shows Ra that decays (with the clock restarted) after thorium is removed when growth and decay are equal (about 22 days from t = 0). The bottom decay curve shows decay following a third purification (about 10 days after the second]... 

Reactions that are catalyzed by a product can often be treated with Equation (12). Many growth and decay processes also give sigmoidal curves. Higher-order au-tocatalytic reactions may likewise be fitted into this scheme. For reactions of the type... 

Concentration-time curves. Much of Sections 3.1 and 3.2 was devoted to mathematical techniques for describing or simulating concentration as a function of time. Experimental concentration-time curves for reactants, intermediates, and products can be compared with computed curves for reasonable kinetic schemes. Absolute concentrations are most useful, but even instrument responses (such as absorbances) are very helpful. One hopes to identify characteristic features such as the formation and decay of intermediates, approach to an equilibrium state, induction periods, an autocatalytic growth phase, or simple kinetic behavior of certain phases of the reaction. Recall, for example, that for a series first-order reaction scheme, the loss of the initial reactant is simple first-order. Approximations to simple behavior may suggest justifiable mathematical assumptions that can simplify the quantitative description. 

The data used were obtained from the reversibility experiment given above. The data give linear plots as required. The value of kt can now be calculated independently from either the growth or the decay curves. The results give k = 1.05 X 10-8 1/sec. and 1.08 X 10-8 1/sec., respectively. We can now also obtain k7 by use of the value of... 

During the stationary phase, the growth rate is zero as a result of the depletion of nutrients and essential metabolites. Several important fermentation products (including most antibiotics) are produced in the stationary phase. The stationary phase is followed by a phase where cells die or sporulate. During the death phase, there is a decrease in live cell concentration, which results from the toxic byproducts coupled with the depletion of the nutrient. The number of viable cells usually follows an exponential decay curve during this period. 

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