Disintegration rate constant

The activity of a sample, expressed in curies, depends both on the number of atoms of the radioisotope (determined from the mass of the sample) and on the half-life (disintegration rate constant). See Problem 21.14. The subunits are millicurie (mCi), microcurie (p.Ci), and others. 

The activity of 30 ig of 247Cm is 1.8 nCi. Calculate the disintegration rate constant and the half-life of 247Cm. 

Calculate the rate constant for the radioactive disintegration of an isotope that has a half-life of 6930 years. 

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 ... 

Elementary reactions (also termed monomolecular reactions) that involve only a single entity in the formation of an activated complex. Unimolecular rate constants, k, are concentration-independent and are typically expressed in units of sUnimolecular reactions are expected to be first order (i.e., -dc/dt = kc where c is the concentration and t is time). Examples of unimolecular processes include radioactive disintegrations, isomeriza-tions, disassociations, and decompositions. Reactions in solution are unimolecular only if the solvent is not covalently incorporated into the product(s). 

It is further shown in Chapter 15 that the needed rate constant is traditionally provided in terms ofthe half-life (/ ), the time needed for one-half ofthe isotope to disintegrate. The needed relationship between k and is given by... 

The number of disintegrations emitted by a radioactive sample depends on the purity of the sample (number of radioactive atoms present) and the decay constant, A. Therefore, radioactive decay is also expressed in terms of specific activity, the disintegration rate per unit mass of radioactive atoms. Typical units for specific activity are mCi/mmole and /r,Ci//rmole. 

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... 

An empirical parameter that describes the temperature dependence of the rate constant, active site (1) The region of an enzyme molecule where the substrate reacts. (2) The effective catalytic site on the surface of a heterogeneous catalyst, activity (1) In thermodynamics, a, the effective concentration or pressure of a substance J. (2) In radioactivity, the number of nuclear disintegrations that occur per second. 

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-... 

Acid hydrolysis of these samples led to the results to be expected, i.e., a lowering of LODP and residue value by NH3 pretreatment and mercerization as well as by mechanical disintegration prior to the hydrolytic treatment (Table XII). With regard to residue value, an NH3 pretreatment again proved to be more efficient in enhancing accessibility than a mercerization, while the rate constant of chain-length degradation was increased somewhat more by mercerization. 

When the data are known for each of the contributing reactions it is easy, as shown in the table, to calculate what the sum total effect will be, but in laboratory practise the situation is reversed and we try to find out what reaction steps and what rate constants are operating to give us our observed facts. This is a much more difficult task and frequently the differential equation can not be solved by ordinary methods. Furthermore, if a set of reaction steps is found to reproduce the facts we can not be sure that it is the only set of reactions which will account for the over-all observed rate. Excellent examples of these consecutive reactions are found among the disintegrations of the radioactive elements. Frequently the kineticist has to work out intermediate steps in this way for ordinary chemical reactions. It is always to be hoped that one... 

Decay constant Measure of the probabihty of the decay of radioactive atoms [s ] Decay series Sequence of successive decay processes Disintegration Synonym of (radioactive) decay Disintegration rate Disintegrations per unit time [s ]... 

Radioactive equilibrium refers to that state in which the ratios between the amounts of successive members of the series remain constant. Under these conditions the disintegration rates of the parent and all the subsequent radioactive daughters will be the same. 

Here, F is the disintegration force at time t, F is the maximum force developed, k is an expansion rate constant, and n signifies which of the two mechanisms controls the disintegration. The interface controlled phenomenon involves tablet particles breaking apart from the interface of the tablet and the diffusion-controlled phenomenon involves particles diffusing... 

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