Effective half-life is the time it takes for the amount of a specific radionuclide in the body to decrease to half of its initial value of radioactive decay and elimination by biological processes.
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Jetzt kostenlos anmeldenEffective half-life is the time it takes for the amount of a specific radionuclide in the body to decrease to half of its initial value of radioactive decay and elimination by biological processes.
The effective half-life is calculated by determining the biological half-life, which will be discussed later on. But what does half-life actually mean?
An atom with an unstable nucleus undergoes radioactive decay to achieve stability by releasing either alpha, beta, or gamma radiation. A nuclide with an unstable nucleus is referred to as a radionuclide or radioisotope. The timing of the decay cannot be accurately predicted as it is a random process, and so it is impossible to predict when any single unstable nucleus will decay. There are several radioisotopes that exist naturally in nature, but the others are artificially created in nuclear reactors.
However, if we have a large number of atoms, we can predict that decay will occur somewhere within the sample. So, if we can somehow time how long it takes for half of the number of atoms in the sample to decay, we have a measure of its half-life.
Plotting the time it takes for our sample to halve each time, we get a graph similar to the one below:
N is the number of nuclei left in the sample, while T is the number of halves. In the graph, there are a total of 5 half-lives, T1/2 being the symbol for half-life, and nT being the number of half-lives passed. 2T, therefore, means after two half-lives.
It is also important to keep in mind that the rate of radioactive decay has no relationship with the radionuclide’s physical state, its chemical composition in which the nucleus is bonded, and exterior factors like temperature or pressure. The graph below indicates the amount of a radioactive sample in pink remaining after several half-lives have passed.
The half-life can be used to calculate the time it would take for half of the atoms that have not yet changed to decay. Consider the equation below:
\[N = N_0 (\frac{1}{2})^{\frac{t}{t_{1/2}}}\]
The choice of radionuclides for medical imaging and therapy primarily depends on their chemical, biological, and physical properties.
Radionuclides need to be chemically suitable in order for them to bond with the molecules as a pharmaceutical product. From a biological standpoint, the radiopharmaceutical must be acceptable so that it does not hinder the body's everyday functions while building up in the organ to be assessed. Finally, the radionuclide needs to have the correct physical properties, such as the type of radiation, the duration of half-life, and its energy.
In medicine, the half-life of a radionuclide T1/2 is referred to as its physical half-life Tp. The half-life values for some commonly used medical radionuclides that can be used are listed in the table below.
Radionuclide | Physical half-life TP |
Technetium-99 | 6.01 hours |
Indium-111 | 2.81 days |
Iodine-123 | 13.27 hours |
Iodine-125 | 59.41 days |
Tritium | 12.3 years |
Radium-226 | 1600 years |
Fluorine-18 | 109.8 minutes |
Yttrium-90 | 2.69 days |
The radionuclide is merged into a chemical compound that results in a radiopharmaceutical. Radiopharmaceuticals are radioisotopes that combine with biological molecules that target specific organs, tissues, or cells within the body. Via the everyday processes of respiration, urination, or defecation, a radiopharmaceutical’s concentration in the body will naturally decrease exponentially with time, which is known as the biological half-life TB.
The effective half-life is the biological excretion along with the radioactive decay after a radiopharmaceutical enters a body. The effective half-life can be represented as:
\[\frac{1}{T_E} = \frac{1}{T_B} + \frac{1}{T_P}\]
Rearranging the above yields:
\[T_E = \frac{T_P \cdot T_B}{T_P + T_B}\]
When comparing the effective half-life and physical half-life, keep in mind that the effective half-life consists of both the physical half-life and the biological half-life.
The effective half-life can change depending on the biological half-life as it depends on the person’s health and overall metabolism. With that being said, the effective half-life will always be less than the physical half-life because the nuclide is removed from the body quickly due to the biological processes of respiration, urination, and defecation.
The physical half-life of a radionuclide, however, remains the same and is unaffected.
The biological half-life of Iodine-123 is 5.5 hours, and the physical half-life is 13.27 hours. What is the effective half-life of Iodine-123 in the body?
Entering the values into the formula gives us:
\(T_E = \frac{T_P \cdot T_B}{T_P + T_B}\)
\(T_E = \frac{5.5 \cdot 13.27}{5.5 + 13.27} = 3.89 \space hours\)
Half-life can be calculated by using the formula N = N0(1/2)t/half-life
where N is the quantity remaining, N0 is the initial amount of that quantity, and t is the elapsed time.
Half-life is the time it takes for half of the number of atoms in a sample to decay.
An exponential decay graph is an example of a half-life graph.
An atom with an unstable nucleus that undergoes radioactive decay to achieve stability by releasing either alpha, beta, or gamma radiation is referred to as ….
Radioactivity.
A nuclide with an unstable nucleus is known as a ….
Radionuclide.
Is radioactive decay a random process?
Yes.
Do all radioisotopes exist naturally?
No.
If we can time how long it takes for half of the number of atoms in a sample to decay, what can we calculate from the sample?
Its half-life.
Which type of graph depicts half-life?
Exponentially decreasing.
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