Constant, half

The constant half-life of a nuclide is used to determine the ages of archaeological artifacts. In isotopic dating, we measure the activity of the radioactive isotopes that they contain. Isotopes used for dating objects include uranium-238, potassium-40, and tritium. However, the most important example is radiocarbon dating, which uses the decay of carbon-14, for which the half-life is 5730 a. 

When an organism dies, it no longer exchanges carbon with its surroundings. However, carbon-14 nuclei already inside the organism continue to decay with a constant half-life, and so the ratio of carbon-14 to carbon-12 decreases. The ratio observed in a sample of dead tissue can therefore be used to estimate the time since death. 

Each radioactive nuclide has a characteristic, constant half-life. This means that it acts as a clock, ticking ... 

A quick glance at Equations (1) through (5) shows sources of error that contribute to error in age, presuming that the assumptions used in calculating the equations hold (initial condition assumptions and the closed-system assumption). These include errors in the decay constants/half-lives, errors in the measurement of the pertinent isotope ratios, and in the case of Equation (3), the error in our estimate of initial °Th/ Th. Relationships among error in half-lives, laboratory standardization procedures, and °Th age are discussed in detail by Cheng et al. (2000b). 

One consequence of a first-order reaction is that it takes a constant amount of time for half the remaining substrate to be converted to product—regardless of how much of the reactant is present. It takes the same amount of time to convert 100,000 A molecules to 50,000 P molecules as it takes to convert 10 A molecules to 5 P s. A first-order reaction has a constant half-time t1/2. 

We next look for a constant half-life, indicative of a first-order reaction. The initial concentration of 0.88 M decreases to one half of that value, 0.44 M, during the first 100 s, indicating a 100-s half-life. The concentration halves again to 0.22 M in the second 100 s, another 100-s half-life. Finally, we note that the concentration halves also from 0.62 M at 50 s to 0.31 M at 150 s, yet another 100-s half-life. The rate is established as first-order. 

Planck s constant half-thickness or thickness of a slice or a ribbon depth of scratch... 

TABLE 5.2 Relationships between the Rate Constant, Half-Lives, and Lifetimes for First-, Second-, and Third-Order Reactions... 

From this equation we see that in a first-order reaction the reactant has a constant half life, independent of initial concentration. 

Fig. 14. Plots of the average number, A, of aluminum neighbors for a silicon atom calculated for the truly random and the Loewensteinian distribution of Si and A1 in a range of compositions of synthetic zeolites X and Y (59). Experimental points were calculated from the first moment of the spectra assuming constant half-width and regular spacing of Si(nAl) signals.

The age of an art object can provide a valuable clue to whether it is real or a forgery. Because the half-life for a specific isotope is constant, half-life can be used to find the age of an object. The isotope put to use for radioactive dating is carbon-14. The half-life of carbon-14 is 5,730 years. The amount of carbon-14 in our atmosphere remains fairly constant. When an object such as a plant is alive, it absorbs C02. The carbon atoms in the C02 are made of a specific ratio of carbon-14 atoms to carbon-12 atoms. The carbon-14 atoms decay by emission of beta particles ... 

Bioconcentration, Uptake (k,) and Elimination (k2) Rate Constants Half-Lives in the Environment ... 

The results of a further examination of Operation Ranch Hand veterans was recently published (Burton et al. 1998). The cohort consisted of 930 exposed subjects and 1,200 comparison individuals who served in SEA during the same period but who were not involved with spraying herbicides. The authors examined the associations between serum dioxin levels and a) chloracne, b) occurrence of acne relative to the tour of duty in SEA, and c) anatomical location of acne after service in SEA. Initial dioxin levels were computed using a first-order pharmacokinetic model with a constant half-life of 8.7 years. Four exposure categories were defined 1) comparisons, with current dioxin levels of 10 ppt 2) background Operation Ranch Hand veterans, with current dioxin levels of 10 ppt 3) low category, with current dioxin levels exceeding 10... 

Charge number of an ion Conductivity Diffusion rate constant Electric current Electric current density Electric mobility Electrode potential Electrolytic conductivity Electromotive force (emf) Elementary charge Faraday constant Half-wave potential Ionic strength... 

Two commonly used properties of first-order kinetics are A plot of logarithm of concentration t>. time is a straight line and there is a constant half life. Thus, each time half life is treated as a constant or a straight line is drawn on semilog paper, one is assuming that first-order kinetics apply. The mathematical expressions appropriate to this rate law are given below ... 

For a number of years, computers have been successfully utilized in pharmacokinetics to 1) fit blood-level data to the appropriate model (single, two, or multiple compartments) and to calculate model parameters, such as absorption rate constant, elimination rate constant, half-life, and volume of distribution 2) evaluate... 

When a radioactive isotope undergoes nuclear decay, the concentration of the isotope decreases exponentially with a constant half-life. It can be determined from this that radioactive decay is a ... 

C is correct. A first order reaction has a constant half life. In the first 15 minutes, 16 out of 33 white dots (compound X) turned black, so 15 minutes represents approximately one half life. In the next 15 minutes, the second half life, half of the remaining 17 white dots should turn black. This represents choice C where there are 9 white dots left. Once you identify that 15 minutes is the half life, you should be able to eliminate answer A because there is no change and answer choice B and D because there are very few dots left. Even if you didn t know that a first order reaction has a constant half life, you should know that the reaction will be proportional to the concentration of white dots. In choice B and D, the rate of the reaction hasn t changed in the second 15 minutes even though the concentration of white dots has been reduced after the first 15 minutes, so this can t be right. 

Table 22 AG, Rate Constants, Half-Lives, and Completion Times of a Unimolecular Reaction at Room Temperature, 298 K (25°C)...

The potential at which the current is equal to one half of the limiting current is called the half-wave potential and is given the symbol 1/2. The half-wave potential is closely related to the standard potential for the half-reaction but is usually not identical to that constant. Half-wave potentials are sometimes useful for identification of the components of a solution. 

Compound Solution Nitrogen screening constant half-height width (Hz) Notes... 

The Cpep group, formed from the enol ether, has a rate of hydrolysis that is only 3.73 times slower at pH 3.75 than at pH 0.5. It is more stable than the Fpmp group at pH 0.5 and yet over twice as labile at pH 3.75. It has a nearly constant half-life between pH 0.5 and 2.5. ... 

When there is a constant source of a reacting chemical species in the water column or at its boundaries (e.g., water-air and/or water-sediment interface) then, by a rule of thumb, a steady-state may be attained within a period of time equal to a few half-lives of the species. In detail, a steady-state concentration is attained after infinitely long time. The time required for the concentration to come close to the steady-state value at any point in the water column depends on its distance from the source, transport properties of the medium (i.e., its diffu-sivity and distribution of advective velocities), and the rates of the reactions removing the species from the water. A concentration of 95% of a steady-state value may be arbitrarily taken as sufficiently close to a steady-state and indicating that the transient state has effectively come to an end. The time required to attain this concentration level (i.e., when C = 0.95C ) at some point of a concentration-depth profile will be referred to as the time to steady-state. By way of generalization, a chemical species with a constant half-life would attain a steady-state concentration at any point in the water column sooner when the distance... 

---