First order kinetics radioactive decay

The rate of decay, or activity, for a radioactive isotope follows first-order kinetics... 

All radioactive decay processes follow first-order kinetics. The half-life of the radioactive isotope tritium (3H, or T) is 12.3 years. How much of a 25.0-mg sample of tritium would remain after 10.9 years ... 

State whether the following statements are true or false. If false, explain why. (a) The dose equivalent is lower than the actual dose of radiation because it takes into account the differential effects of different types of radiation, (b) Exposure to 1 X 1 ()x Bq of radiation would be much more hazardous than exposure to 10 Ci of radiation, (c) Spontaneous radioactive decay follows first-order kinetics, (d) Fissile nuclei can undergo fission when struck with slow neutrons, whereas fast neutrons are required to split fissionable nuclei. 

The important phenomenon of exponential decay is the prototype first-order reaction and provides an informative introduction to first-order kinetic principles. Consider an important example from nuclear physics the decay of the radioactive isotope of carbon, carbon-14 (or C). This form of carbon is unstable and decays over time to form nitrogen-14 ( N) plus an electron (e ) the reaction can be written as... 

C15-0058. Radioactive isotopes decay according to first-order kinetics. For one particular isotope, 1.00 nmol registers 1.2x10 decays in 1.00 min. (a) How many decays will occur in 1.00 min if 5.00 nmol of this isotope are present (b) What fraction of the isotope decays per minute in each case (c) Explain the relationship between your answers to (a) and (b). 

Equation (8.33) suggests the half-life is independent of the amount of material initially present, so radioactive decay follows the mathematics of first-order kinetics. 

When species i disappears by either radioactive decay or chemical reaction with first-order kinetics, the mass balance equation must be changed according to... 

This radioactive decay process follows first-order kinetics. Substitute the value of k into the appropriate equation ... 

A radioactive isotope may be unstable, but it is impossible to predict when a certain atom will decay. However, if we have a statistically large enough sample, some trends become obvious. The radioactive decay follows first-order kinetics (see Chapter 13 for a more in-depth discussion of first-order reactions). If we monitor the number of radioactive atoms in a sample, we observe that it takes a certain amount of time for half the sample to decay it takes the same amount of time for half the remaining sample to decay, and so on. The amount of time it takes for half the sample to decay is the half-life of the isotope and has the symbol t1/2. The table below shows the percentage of the radioactive isotope remaining versus half-life. 

First-order kinetic behavior is observed throughout Nature. One familiar example is radioactive decay ... 

In Chapter 12, the concept of half-life was used in connection with the time it took for reactants to change into products during a chemical reaction. Radioactive decay follows first order kinetics (Chapter 12). First order kinetics means that the decay rate... 

Such a reaction is described as first order and the proportionality constant k is known as the rate constant. Such first-order kinetics is observed for unimolecular processes in which a molecule of A is converted into product P in a given time interval with a probability that does not depend on interaction with another molecule. An example is radioactive decay. Enzyme-substrate complexes often react by unimolecular processes. In other cases, a reaction is pseudo-first order compound A actually reacts with a second molecule such as water, which is present in such excess that its concentration does not change during the experiment. Consequently, the velocity is apparently proportional only to [A]. 

The spontaneous disintegration of a nucleus is a first-order kinetic process. That is, the rate of radioactive decay of TV atoms (—dN/dt, the change of TV with time, t) is proportional to the number of radioactive atoms present (Equation 6.4). 

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-... 

As deduced from the section on kinetics, the radioactive decay follows first-order kinetics because the activity A depends upon N raised to the power one. Solving this equation as discussed there, the following expression can be obtained ... 

The radioactive decay follows first order kinetics with a half-life of the radionuclide. Theoretically, after one half-life, 50% of the labeled protein should remain intact in the stored sample. In practice, this is not the case. Some radioactive molecule of the protein change their identity and in this manner they are converted to impurities during the preparation of the radioactively labeled protein. Radiochemical conversions f H He, - N, - C1, 1 - Te, - Xe) cause destruc-... 

The radioactive isotope j2P decays by first-order kinetics and has a half-life of 14.3 days. How long does it take for 95.0% of a given sample of j2P to decay ... 

The half-life of is 5730 years. A sample taken for radiocarbon dating was found to contain 56% of its original " C. What was the age of the sample (Radioactive decay of follows first-order kinetics.)... 

Such a chemical reaction, in which molecules are not colliding with other atoms or molecules, is called a first-order reaction because the rate at which chemical concentration changes at any instant in time is proportional to the concentration raised to the first power. Certain chemical processes, such as radioactive decay, are described by first-order kinetics. In the absence of any other sources of the chemical, first-order kinetics may lead to exponential decay or first-order decay of the chemical concentration (i.e., the concentration of the parent compound decreases exponentially with time) ... 

Since radioactive decay follows first-order kinetics, the rate of loss of X is d[X]... 

Radionuclides have different stabilities and decay at different rates. Some decay nearly completely in a fraction of a second and others only after millions of years. The rates of all radioactive decays are independent of temperature and obey first-order kinetics. In Section 16-3 we saw that the rate of a first-order process is proportional only to the concentration of one substance. The rate law and the integrated rate equation for a first-order process (Section 16-4) are... 

The conceptual approach is particularly effective when solving problems that have half-lives that are whole number values. For more complex problems, we need to use some ideas borrowed from chemical kinetics. Radioactive decay can be described as a first order processes, which means it can be described with the following equation ... 

Earth s atmosphere is constantly being bombarded by cosmic rays of extremely high penetrating power. These rays, which originate in outer space, consist of electrons, neutrons, and atomic nuclei. One of the important reactions between the atmosphere and cosmic rays is the capture of neutrons by atmospheric nitrogen (nitrogen-14 isotope) to produce the radioactive carbon-14 isotope and hydrogen. The unstable carbon atoms eventually form C02, which mixes with the ordinary carbon dioxide ( C02) in the air. As the carbon-14 isotope decays, it emits f3 particles (electrons). The rate of decay (as measured by the number of electrons emitted per second) obeys first-order kinetics. It is customary in the study of radioactive decay to write the rate law as... 

In the nuclear industry, workers use a rule of thumb that the radioactivity from any sample will be relatively harmless after ten half-lives. Calculate the fraction of a radioactive sample that remains after this time period. Hint Radioactive decays obey first-order kinetics.)... 

Half-life is defined in Section 13.3. Recall that radioactive decays obey first-order kinetics. 

The driving force for the development of chemiluminescence-based assays (as well as any other optical or electrical detection methodology) is the replacement of radiolabels both for safety reasons and because of their intrinsic instability. Because the earliest high sensitivity immunoassays utilized antibodies with covalently attached as the label, this has served as a yardstick against which all subsequent assay technologies are measured. For this reason, it is important to understand the detection limits for I. Radioactive iodine is a y-emitter that eventually decays to a stable isotope of lead. The decay process exhibits first-order kinetics so that we can write... 

Fig. 2.4 Radioactive decay follows first order kinetics and a plot of the number of nuclides against time is an exponential decay curve. The graph shows a decay curve for radon-222, which has a half-life of 3.82 days.

Radioactive decay follows first-order kinetics (Chapter 22) hence the two contributions to the rate of change of the number of helium atoms are... 

Here, v denotes the mean velocity of advection, and k is a rate constant of a reaction with first order kinetics. The last term in the equation R(x) is an unspecified source or sink related term which is determined by its dependence on the depth coordinate x. Instead of R(x), one might occasionally find the expression (ERj) which emphasizes that actually the sum of different rates originating from various diagenetic processes should be considered (e.g. Berner 1980). Such reactions, still rather easy to cope with in mathematics, frequently consist of adsorption and desorption, as well as radioactive decay (first-order reaction kinetics). Sometimes even solubility and precipitation reactions, albeit the illicit simplification, are concealed among these processes of sorption, and sometimes even reactions of microbial decomposition are treated as first order kinetics. 

Radioactive decay foiiows first-order kinetics... 

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