Radioactive decay, constant half-life

Understand why radioactive decay is a first-order process and the meaning of half-life convert among units of radioactivity, and calculate specific activity, decay constant, half-life, and number of nuclei estimate the age of an object from its specific activity ( 23.2) (SPs 23.4, 23.5) (EPs 23.17-23.30)... 

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. 

Half-life is defined as the time required for a radioisotope to reduce its initial radioactivity (disintegration rate) to one-half (or 50%). The half-life is represented by the symbol, t a, and it is unique for a given radioisotope. The useful lifetimes of radiopharmaceuticals are usually determined by radioactive decay, which constantly decreases the amount of radioactivity present. The half-life is related to decay constant, X of a radioisotope (discussed in the subsequent section), as follows ... 

Thus the half-life is inversely proportional to the radioactive decay constant. Table 2.5 lists the most frequently used 0-emitting isotopes together with their half-lives and particle energies. 

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 ... 

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 ... 

If the radioactive decay following neutron capture is fairly slow, catalytic experiments can be done after the bombardment but before appreciable decay. In this way, the effect of the introduction of the impurity can subsequently be followed without interference from the radiation damage, which can either be removed by annealing or be treated as a constant background. This doping by decay can also be done by incorporating in a catalyst a radioactive isotope of half-life which will allow experiments to be done essentially before and after the decay. 

Any radionuclide, whatever the type of radiation emitted, is characterized by its half-life T (Table 17.1), which is the time taken for half of corresponding atom population in the sample to decompose (from initial time, t = 0). Calling A the radioactive decay constant, the law of radioactivity decay allows calculation of the number of atoms N present after time t for a population containing Nq atoms initially. The integrated form of this law is written as equation 17.4 ... 

Consider an emitter with an average neutron absorption cross section a exposed to a total neutron flux (f), and upon absorption of a neutron becoming radioactive with a half-life T [or decay constant A = (In2)/T]. The number of radioactive atoms NU) present after exposure for time t is (see Eq. 14.16)... 

The rate of radioactive decay is typically expressed in terms of either the radioactive half-life or the radioactive decay constant. They are related as follows ... 

In this problem is given the initial content of radionuchdes That is why equation (2.361) should be used. To solve it, first of all it is convenient to convert half-life values of radioactive isotopes into the radioactive decay constants X for Ih, 4.95-10, for 9.9-10 ° and for 1.54-10 °. 

SECTIONS 21.4 AND 21.5 The SI unit for the activity of a radioactive source is the becquerel (Bq), defined as one nuclear disintegration per second. A related unit, the curie (Ci), corresponds to 3.7 X 10 disintegrations per second. Nuclear decay is a first-order process. The decay rate (activity) is therefore proportional to the number of radioactive nuclei. The half-life of a radionuclide, which is a constant, is the time needed for one-half of the nuclei to decay. Some radioisotopes can be used to date objects C, for example, is used to date organic objects. Geiger counters and scintillation counters count the emissions from radioactive samples. The ease of detection of radioisotopes also permits their use as radiolracers to follow elements through reactions. 

Radioactivity. Radioactive decay is a process governed by statistics. At any given instant of time, each radioactive atom has a measurable probability of decaying. The rate of decay depends upon the number of original atoms present and upon the instantaneous fraction of atoms decaying per unit time, the decay constant. Another term used in discussing radioactivity is the half-life. This is defined as the amount of time it takes for... 

Since the half-life is independent of the number of radioactive atoms, it remains constant throughout the decay process. Thus, 50% of the radioactive atoms disintegrate in one half-life, 75% in two half-lives, and 87.5% in three half-lives. 

Radioactive waste is characterized by volume and activity, defined as the number of disintegrations per second, known as becquerels. Each radionucHde has a unique half-life,, and corresponding decay constant, A = 0.693/tj 2 For a component radionucHde consisting of JS1 atoms, the activity, M, is defined as... 

Predict the amount of a radioactive sample that will remain after a given time period, given the decay constant or half-life of the sample (Example 17.3). 

The decay constant, X, defines the probability that a particular atom will decay within a given time (X = In 2/t1/2). The half-life (t1/2) describes a time interval after which N = NJ2. The observed counting rate or activity (A) is equal to XN. Another way to describe radioactive decay is in terms of the mean life (t) of a... 

Radioactive decay is a stochastic process that occurs at random in a large number of atoms of an isotope (see Textbox 13). The exact time when any particular atom decayed or will decay can be neither established nor predicted. The average rate of decay of any radioactive isotope is, however, constant and predictable. It is usually expressed in terms of a half-life, the amount of time it takes for half of the atoms in a sample of a radioactive isotope to decay to a stable form. 

Chemical forms with at least one radioactive atomic nucleus are radioactive substances. The capability of atomic nuclei to undergo spontaneous nuclear transformation is called radioactivity. Nuclear transformations are accompanied by emission of nuclear radiation (Severa and Bar 1991). The average number of nuclei that disintegrate per unit time (= activity) is directly proportional to the total number of radioactive nuclei. The time for 50% of the original nuclei to disintegrate (= half-life or Tb 1/2) is equal to In 2/decay constant for that element (Kiefer 1990). Radiations... 

The degree of activation of the sample is measured by post-irradiation spectroscopy, usually performed with high-purity semiconductors. The time-resolved intensity measurements of one of the several spectral lines enables to get the half-life of the radioactive element and the total number of nuclear reactions occurred. In fact, the intensity of a given spectral line associated with the decay of the radioactive elements decreases with time as Aft) = Aoexp[—t/r], where Aq indicates the initial number of nuclei (at t = 0) and r is the decay time constant related to the element half-life (r = In2/ /2), which can be measured. Integrating this relation from t = 0 to the total acquisition time, and weighting it with the detector efficiency and natural abundance lines, the total number of reactions N can be derived. Then, if one compares this number with the value obtained from the convolution of... 

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