Rate constant for radioactive decay

In this case, k is the rate constant for radioactive decay, and Sr is the intensity of the recorded radiation. Although in both processes the molecules (atoms) exhibit an exponential decay, the radioactive decay signal is produced by the radiation emitted by each decay event and hence Eq. 60 is a measurement of the rate of decay, while Eq. 59 is proportional to the number of reactant molecules remaining. 

The balance of 14C atoms in the same reservoir (14C = /. T. ) will reflect the rate of loss from decomposition, kh as well as the rate constant for radioactive decay of 14C, X (k = 1.210 x 10 4yr ), and the rate of inputs (in this case, from the atmosphere) ... 

Americium-241 is used in smoke detectors. It has a first order rate constant for radioactive decay of k = 1.6 X 10" yr . By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay otk = 0.011 day", (a) What are the half-lives of these two isotopes (b) Which one decays at a faster rate (c) How much of a 1.00-mg sample of each isotope remains after 3 half-lives (d) How much of a 1.00-mg sample of each isotope remains after 4 days ... 

Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of fc = 1.6 X 10 r . ... 

Here AT, is the number of radioactive nuclei at time t, and k is the radioactive decay constant, or rate constant for radioactive decay. This rate constant is a characteiislic of the radioactive nuclide, each nuclide having a different value. ... 

Radioactive decay constant (k) rate constant for radioactive decay. (204)... 

In these equations, In is the natural logarithm, Nt is the amount of isotope radioactive at some time t, N0 was the amount of isotope radioactive initially, and k is the rate constant for the decay. If you know initial and final amounts and if you are looking for the half-life, you would use equation (1) to solve for the rate constant and then use equation (2) to solve for t1/2. 

The rate constant for the decay can be found from (20-2). Ninety percent decay corresponds to 10% or 0.10, survival. In dealing with radioactive decay, the total population of radioactive element is used in place of its concentration. (Remember that in first-order reactions, the rate constant and the half-life, as well, are independent of the concentration units.) So, in place of the concentration ratio [A]/[A]o, put the ratio of the numbers of atoms N/Nq, or moles, or masses, of radioactive element. The mass of radioactive element encountered in the laboratory is exceedingly small a typical sample can be measured only by its activity. Since its activity is proportional to its population, the observed ratio of activities, A/Aq, can be used in place of the number ratio, N/Nq. 

All radioactive decays occur with first-order kinetics, with the exception of electron capture, which is a two-particle collision. The differential rate law for radioactive decay is given by Equation (2.7). After integration, an alternative and more useful form of the rate law is shown by Equation (2.8). The half-life of radioactive decay is defined as the length of time it takes for the number of unstable nuclides to decrease to exactly one-half of their original value. The half-life, t can be calculated using Equation (2.9), where k is the first-order rate constant... 

Question The half-life for the radioactive decay of carbon-14 is 5730 years. Calculate the rate constant for this decay reaction. 

Solution (a) Analyze and Plan We are asked to calculate a half-life, fj/2, based on data that teU us how much of a radioactive nucleus has decayed in a given period of time (Nq = 1.000 g, A4 = 0.953 g, and t = 2.00 yr). We do this by first calculating the rate constant for the decay, k, then using that to compute fj/2. 

One of the most familiar examples of a first-order process is radioactive decay. For example, the radioactive isotope iodine-131, used in treating thyroid disorders, has a half-life of 8.04 days. Whatever number of iodine-131 atoms are in a sample at a given moment, there will be half that number in 8.04 days one-quarter of that number in 8.04 + 8.04 = 16.08 days and so on. The rate constant for the decay isk = 0.693/fi/2, and in equation (20.13) we can use numbers of atoms, that is, Nt for [A]t and No for [A]o- Table 20.4 lists several examples of first-order processes. Note the great range of values of fi/2 and k. The processes range from very slow to ultrafast. 

Table 13.1 provides a list of several isotopes commonly used as tracers. The half-lives for these isotopes also are listed. What is the rate constant for the radioactive decay of each isotope ... 

Since S/t has units of moles per volume per time and a has units of moles per volume, the rate constant for a first-order reaction has units of reciprocal time e.g., s. The best example of a truly first-order reaction is radioactive decay for example,... 

The rate constant for the radioactive decay of thorium-232 is 5.0 X 10 u/year. Determine the half-life of thorium-232. 

You know that radioactive decay is first-order, so it is necessary only to find the rate constant for decay, from which the half-life may be calculated by means of Equation 15-11. To make the first-order plot, first convert cpm to log cpm to get... 

This is the same model process that we described above for radioactive decay of if we substitute decay constants by rate constants, and amount of substance by concentration, and assume that [A]0 = 1 mol dm-3, we can adapt equation (7.40) derived in Problem 7.5(c) to describe how [B] varies with time ... 

A reaction of this type is said to follow first-order kinetics because the rate is proportional to the concentration of a single species raised to the first power (fig. 7.2). An example is the decay of a radioactive isotope such as 14C. The rate of decay at any time (the number of radioactive disintegrations per second) is simply proportional to the amount of l4C present. The rate constant for this extremely slow nuclear reaction is 8 x 10-12 s l. Another example is the initial electron-transfer reaction that occurs when photosyn-... 

XDa and XDu will depend on the air movement in the room, the area and nature of the surfaces, and the strength of any electrostatic fields. For XDa, the size distribution of the nuclei in the air, and the presence or absence of thermal gradients near surfaces may also be important. Despite the variables, some experimental and observational data are available which allow XDa andXDu to be compared in order of magnitude with the radioactive decay constants and with the rate constant for ventilation. 

Here A represents the amount of decaying radionuclide of interest remaining after some time t, and Aq is the amount present at the beginning of the observation. The k is the rate constant, which is different for each radionuclide. Each atom decays independently of the others, so the stoichiometric coefScient a is always 1 for radioactive decay. We can therefore drop it from the calculations in this chapter and write the integrated rate equation as... 

First-order rates are proportional to the concentrations of a reactant or product. An important example is radioactive decay (Section 2.7.2), which generally is irreversible and has only a forward rate and rate constant, for which... 

The increase is caused by the sudden reduction in the overall removal rate constant for xenon when the reactor is shut down, whereas the rate of production of xenon from its main source, the decay of 1, decreases only slowly with time as the iodine decays. For low neutron fluxes ( < 10 ) prior to shutdown the xenon buildup after shutdown is less important because the xenon burnout by neutron capture is then small relative to xenon removal by radioactive decay. 

Aii radioactive decay processes foiiow first-order kinetics. What does this mean What happens to the rate of radioactive decay as the number of nuciides is haived Write the first-order rate law and the integrated first-order rate law. Define the terms in each equation. What is the half-life equation for radioactive decay processes How does the half-life depend on how many nuclides are present Are the half-life and rate constant k directly related or inversely related ... 

Supported is based on the average measurement of °Pb activity determined by measuring the activity of a °Pb as a decay product such as Pb in the lowest section of the sediment profile where °Pb activity is constant. Sedimentation or accretion rates are estimated from the excess (unsupported) °Pb profiles in the sediment profile using the constant initial concentration method (Goldberg et al., 1977). Linear regression analysis is used to solve for (X/s) in the log-transformed equation for radioactive decay ... 

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