Radionuclides disintegration rates

Figure 6. Cosmic ray radionuclide disintegration rates in rainwater from two rain showers at Forks, Wash.

The mass at radionuclide disintegration rates commonly encountered in the laboratory is extremely small at a typical disintegration rate of 1 disintegration s or Bq, the mass may be about 1 x 10 g. Weighable amounts of radionuclides occur for radionuclides that have half-lives of billions of years. For such long-lived radionuclides, it has been commonplace to calculate the disintegration rate from the known half-life and measured mass, or the half-life from the measured... 

The decay rate of a given radionuclide is generally constant and independent of the past history of the nuclide and of the P, T (at least below 10 K), and chemistry of the system. The probability fP of the radionuclide disintegrating over time At is... 

The variation in 7Be with altitude and time at 46 °N was very similar to the variations in the activities of the bomb-produced radionuclides, except in the case of short lived fission products whose seasonal variations were obscured largely by debris from recent nuclear tests. Figure 3 shows the 137Cs disintegration rate plotted as function of time for several altitudes. As for 7Be, 137Cs reached a maximum at 40,000 feet and below on June 5, 1967 and then decreased. The activities of 137Cs and the other bomb-produced radionuclides increased sharply again from 20,000 to 40,000 feet after October 23. 

If the above explanation is correct, the rainwater disintegration rates of other airborne radionuclides should also decrease with increasing rainfall rate. However, the atmospheric activities of the longer lived radionuclides change with time, making it difficult to compare the activities in different rainwater samples. The 7Be activity in rainwater ap-... 

It is difficult to measure the half-life of a very long-lived radionuclide. Here variation in disintegration rate may not be noticeable within a reasonable length of time. In this case, the decay constant must be calculated from the absolute decay rate according to Equation (3.2). The absolute number of atoms of the radioisotope present (AO in a given sample can be calculated according to... 

In other words, 1 MBq of tritium contains about 3 ng of tritium. Thus, an important feature of radionuclides becomes apparent—we routinely work with extremely small quantities of material. Pure samples of radioisotopes are called carrier free. Unless a radionuclide is in a carrier-free state, it is mixed homogeneously with the stable nuclides of the same element. It is, therefore, desirable to have a simple expression to show the relative abundances of the radioisotope and the stable isotopes. This specification is readily accomplished by using the concept of specific activity, which refers to the amount of radioactivity per given mass or other similar units of the total sample. The SI unit of specific activity is Bq/kg. Specific activity can also be expressed in terms of the disintegration rate (Bq or dpm), or... 

The detection systems first must be calibrated for counting efficiency to permit conversion of the sample count rate to the disintegration rate. These systems are monitored periodically for their stability and performance by measuring the count rates of reliable radionuclide sources and the radiation background. Records are maintained for each instrument to comply with quality assurance specifications. Graphs of count rates recorded at frequent intervals for periods of months or years provide a visual record of detector and background stability and indicate deviations from the norm. 

The counting efficiency (e) of the proportional detector is calculated as the ratio of the net count rate, in s, to the activity (A), in Bq, of this standard radionuclide solution. The net count rate is the standard s gross count rate (RG) minus the detector s background count rate (RB). The reported disintegration rate (A) is the product of the radionuclide concentration, in Bq L 1, and the amount of counted sample, in L, adjusted for the radioactive decay of the radionuclide between standardization and measurement. Equation 2A.1 is the general form of this equation. 

Equation (2.3) indicates that the number of radioactive atoms present as well as the disintegration rate (activity) decrease exponentially with time. The time taken for half the radioactive atoms originally present to decay is called the half-life of the radionuclide. 

A radionuclide disintegrates at a rate which is a function only of the constitution of the nucleus unlike ordinary chemical processes, it cannot be influenced by any chemical or physical means, such as by changing the temperature. The disintegration of a nucleus, with the emission of radiation, is kinetically a first-order process in other words, the rate of disappearance of the isotope is proportional to the amount n present at any time ... 

Consider a sample containing a pure radionuclide with a disintegration rate of 10 dpm. For a of 1 h the number of atoms is ( 4.11) 8.7 X10 for a ti of 1 y it is 7.6 X10. If such a sample is dissolved in one liter of solution, the respective concentrations would be 1.4xl0 M and 1.3 X10" M. At such concentrations the chemical bdiavior may be quite different than it is at higher concentrations. Addition of macroscopic amounts (e.g. at the gram level) of non-radioactive (isotopic) atoms of the element results in concentrations of 10 to 10 M. The non-radioactive component is called a carrier as it "carries" the radioactive and ensures normal chemical behavior. Many applications of radiotracers involve mixing the tracer atoms with a much larger amount of nonradioactive isotopic atoms prior to use. 

Not all radionuclides disintegrate at the same rate. The disintegration of any radionuclide is a first-order process and follows Equation 19.1 ... 

Radioanalytical chemistry is devoted to analyzing samples for their radionuclide content. For this purpose, the strategies of identifying and purifying the radioelements of interest by chemical methods, and of identifying and measuring the disintegration rate ( activity ) of radionuclides by nuclear methods, are combined. Radioanalytical chemistry can be considered to be a specialty in the subdiscipline of nuclear and radiochemistry. 

Measurements of the slope of the line in Fig. 2.2 or the disintegration rate at two separate times can be used to calculate the half-life ti/2, i.e., the time period during which the radionuclide decays to one-half of a previous value. The half-life is In 2/k,i.e., ti/2 = 0.693/A,. 

The disintegration rate can be determined from the measured values of radionuclide mass m in grams and the half-life ti/2 in seconds. Equation (2.7) relates the decay rate to the mass in terms of Avogadro s number Ay of 6.02 x 10 atoms per mol and the isotope mass number A in g/mol ... 

In some instances, a radionuclide decays not to a stable nuclide but to a second radionuclide (or even an entire chain of radionuclides) before a stable nuclide is finally reached. In that case, when the second radionuclide is separated from the first, it immediately begins to grow into the first radionuclide while decaying in the separated portion. For two successive radionuclides, the disintegration rate of the daughter (subscript 2) is related to the disintegration rate at the time of separation, t = 0, of the parent (subscript 1) by... 

Calculations for longer decay chains under some conditions can be simplified by assuming that short-lived daughters and long-lived parents have the same disintegration rate. In some complex chains, the Bateman equation (in the same form as Eq. (2.8), but with terms added to describe further decays) can be used to determine the ingrowth and decay pattern of three or four successive radionuclides (Evans 1955). 

If the produced atom is radioactive, the rate of radionuclide production in terms of the disintegration rate [shown in Eq. (2.4)] is Rk. The disintegration rate of the accumulated atoms, balancing the production and decay rates, is then... 

The radionuclide standard must be accompanied by a certificate (see Section 11.2.6) with detailed descriptions of its chemical, physical, and radiological characteristics and the uncertainty of the reported disintegration rate. The uncertainty of calibration depends on the reported uncertainty of the standard, compounded by the uncertainty due to source preparation and measurement. 

Two internal counters facing each other and electronically combined to produce single pulses constitute a 4 r detector. A thin source deposited on a thin backing is placed between the two detectors. Measurements at near 100% counting efficiency approach the absolute disintegration rate of a radionuclide that emits beta particles. 

Radionuclides that are used as comparison sources, e.g., for determining instrument count rate stability and as tracers, must be of sufficient radiochemical purity and activity to eliminate interference in counting and permit correction for decay, but in most instances they need not have an accurately known disintegration rate. The absolute count rate also is unimportant for energy calibration because only the energy must be accurately known. 

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