## Half life

Radiopharmaceutical preparations are characterized by their shelf-life (expiration date) by the physical half-life of the radioisotopes, their radiochemical stability, and the radio-nuclidic impurities they contain. Radiopharmaceutical preparations usually contain radioisotopes with very short half-lives, so the shelf-life of such preparations is very limited. Expiration dates and times are so indicated with these preparations.N = N0λ −2t

A radionuclide's characteristic disintegration constant is the number of atoms at a given temperature, and a radionuclide's number of atoms N0 is its atomic number at a given time.. As a function of disintegration constant, half-lives are related by the equation:

N1/2 = 0.693/ λ

For radioactive decay corrections, one can either use the exponential equation or decay tables, or obtain a decay curve for the given radionuclide associated with the correction.

### Physical half life

Radiation decays one-half of its original value within the physical half-life of a radionuclide (T1/2 p). Even though the decay time of an individual atom cannot be determined, the decay rate of a large number of atoms can be calculated based on statistical considerations. It is constant and characteristic for each individual radionuclide to decay at a constant rate for a collection of atoms (N). Here's what is known about exponential decay:N = N0 e −µt

The number of nuclei at time t equals N, while N0 represents the number of nuclei at zero time, and denotes the decay constant. A decay law equation is commonly used to describe this relationshipBy using the decay law relationship, one can determine the activity of a quantity of radioactive substance at any other point in time if the activity of the quantity is known at one time. Half-life and decay constant are generally interconnected in the following way:

T1/2 = 0.693/µ

Along with the use of decay law formulas, radioactivity can also be measured by plotting decay curves for the specified radionuclide or using decay tables.

### Biological half life

Radiopharmaceutical half-life (T1/2b) can be defined as the period between when the concentration in a tissue, organ, or entire body drops 50% of its maximum level, without taking into account radioactive decay.### Effective half life

The half-life of a radiopharmaceutical (T1/2e) is determined by how the radioactive substance interacts with its physical and biological half-lives within tissues, organs, or all the body. In order to determine what dose of radiopharmaceutical to administer and to monitor the level of radiation exposure, the effective half-life is essential. Here is how it is calculated:T1/2e = T1/2p × T1/2b/T1/2p × T1/2b

Physical half-lives T1/2p and biological half-lives T1/2b are the respective half-lives.

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