Radioactive decay processes

Carbon-14 (C-14) with a half-life of 5730 years decays to nitrogen-14 (N-14). A sample of carbon dioxide containing carbon in the form of C-14 only is sealed in a vessel at 1.00-atmosphere pressure. Over time, the CO2 becomes NO2 through the radioactive decay process. The following equilibrium is established ... 

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 ... 

The process of radioactive decay (also known as radioactivity) involves the ejection from a nucleus of one or more nuclear particles and ionizing radiation. Nuclear fission is a reaction in which the nucleus splits into smaller nuclei, with the simultaneous release of energy. Most radioisotopes undergo radioactive decay processes and are converted into different smaller atoms. 

What is the difference between radioactive decay processes and other types of nuclear reactions ... 

Ans. Other types of reactions require a small particle to react with a nucleus to produce a nuclear reaction radioactive decay processes are spontaneous with only the one nucleus as reactant. 

The classic example of reactions of this type is a sequence of radioactive decay processes that result in nuclear transformations. The differential equations that govern kinetic systems of this type are most readily solved by working in terms of concentration derivatives. For the first reaction,... 

He is found in natural gas deposits principally because alpha particles are produced during natural radioactive decay processes. These alpha particles are 4 He nuclei they obtain two electrons from the surrounding material to become helium atoms. This gaseous helium then accumulates with the natural gas trapped beneath the earth. Although other noble gases are produced by radioactive decay—notably 40 Ar—they are not produced in the large quantities that helium is. 

We use expression (26.12), substituting the disintegration rate for the number of atoms, since we recognize that in this first-order reaction the rate is directly proportional to the amount of reactant, that is, the number of atoms. (All radioactive decay processes follow... 

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

In the meantime, E. Rutherford (NLC 1908 ) studied the radioactivity discovered by Becquerel and the Curies. He determined that the emanations of radioactive materials include alpha particles (or rays) which are positively charged helium atoms, beta particles (or rays) which are negatively charged electrons, and gamma rays which are similar to x-rays. He also studied the radioactive decay process and deduced the first order rate law for the disappearance of a radioactive atom, characterized by the half-life, the time in which 50% of a given radioactive species disappears, and which is independent of the concentration of that species. 

Given that all isotopes of francium are radioactive with relatively short half-lives, there are few practical uses for it—except as a source of radiation to study the radioactive decay process. 

Various radium isotopes are derived through a series of radioactive decay processes. For example, Ra-223 is derived from the decay of actinium. Ra-228 and Ra-224 are the result of the series of thorium decays, and Ra-226 is a result of the decay of the uranium series. 

Chemists of the early twentieth century tried to find the existence of element 85, which was given the name eka-iodine by Mendeleev in order to fill the space for the missing element in the periodic table. Astatine is the rarest of all elements on Earth and is found in only trace amounts. Less than one ounce of natural astatine exists on the Earth at any one time. There would be no astatine on Earth if it were not for the small amounts that are replenished by the radioactive decay process of uranium ore. Astatine produced by this uranium radioactive decay process soon decays, so there is no long-term build up of astatine on Earth. The isotopes of astatine have very short half-lives, and less than a gram has ever been produced for laboratory study. 

Equation (8.3) is the basic equation that describes all radioactive decay processes. It gives the number of atoms (N) of a radioactive parent isotope remaining at any time t from a starting number N0 at time t = 0. 

In this section we shall present a few of the elementary type reactions that have been solved exactly. By elementary we mean unimolecular and bimolecular reactions, and simple extensions of them. In a more classical stochastic context, these reactions may be thought of as birth and death processes, unimolecular reactions being linear birth and death processes and bimolecular being quadratic. These reactions may be described by a finite or infinite set of states, (x), each member of which corresponds to a specified number of some given type of molecule in the system. One then describes a set of transition probabilities of going from state x to x — i, which in unimolecular reactions depend linearly upon x and in bimolecular reactions depend quadratically upon x. The simplest example is that of the unimolecular irreversible decay of A into B, which occurs particularly in radioactive decay processes. This process seems to have been first studied in a chemical context by Bartholomay.6... 

Exercise. Find the stationary distribution for the radioactive decay process described by the master equation (V.1.7). 

Exercise. In the radioactive decay process the state n = 0 is an absorbing state. Show that the equations for the remaining pn (n = 1,2,...) constitute a master equation with absorbing boundary. The state n = 0 functions as limbo state. 

Exercise. Compute (1.6) and (1.7) for the M-equation of the radioactive decay process. 

Before going on to these alternative procedures, however, we should consider a special way by which true (not pseudo) first-order reactions are often considered. In these cases,/ = k. This consideration is especially applicable to radioactive decay processes. It is common practice to describe these true first-order reactions in terms of the time required for one-half of the material to decompose (this time is called the half-life, t ). In this special circumstance [A] = i[A]0 when t = t , and Equation 15-9 becomes... 

First-order Differential Equations in Radioactive Decay Processes... 

Consider the following radioactive / decay processes, involving two sequential first-order steps, in which 2i and A2 are decay constants... 

Characteristics of the different kinds of radioactive decay processes are summarized in Table 22.1. 

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