There are certain naturally occurring isotopes that are unstable due to the imbalanced numbers of protons and neutrons they have in their nucleus of atoms. Therefore, in order to become stable, these isotopes undergo a spontaneous process called radioactive decay. The radioactive decay causes an isotope of a particular element to be converted into an isotope of a different element. However, the final product of radioactive decay is always stable than the initial isotope. The radioactive decay of a certain substance is measured by a special term known as the half life. The time taken by a substance to become half of its initial mass through radioactive decay is measured as the half life of that substance. This is the relationship between radioactive decay and half life.
Key Areas Covered
1. What is Radioactive Decay
â Definition, Mechanisms, Examples 2. What is Half Life â Definition, Explanation with Examples 3. What is the Relationship Between Radioactive Decay and Half Life â Radioactive Decay and Half Life
Key Terms: Half Life, Isotopes, Neutrons, Protons, Radioactive Decay
What is Radioactive Decay
Radioactive decay is the process in which unstable isotopes undergo decay through emitting radiation. Unstable isotopes are atoms having unstable nuclei. An atom can become unstable due to several reasons such as the presence of a high number of protons in the nuclei or a high number of neutrons in the nuclei. These nuclei undergo radioactive decay in order to become stable.
If there are too many protons and too many neutrons, the atoms are heavy. These heavy atoms are unstable. Therefore, these atoms can undergo radioactive decay. Other atoms also can undergo radioactive decay according to their neutron: proton ratio. If this ratio is too high, it is neutron rich and is unstable. If the ratio is too low, then it is proton rich atom and is unstable. The radioactive decay of substances may occur in three major ways.
Alpha Emission
An alpha particle is identical to a Helium atom. It is composed of 2 protons and 2 neutrons. Alpha particle bears a +2 electrical charge because there are no electrons to neutralize the positive charges of 2 protons. Alpha decay causes the isotopes to lose 2 protons and 2 neutrons. Hence, the atomic number of a radioactive isotope is decreased by 2 units and the atomic mass from 4 units. Heavy elements such as Uranium can undergo alpha emission.
Beta Emission
In the process of beta emission (β), a beta particle is emitted. According to the electrical charge of the beta particle, it can be either a positively charged beta particle or a negatively charged beta particle. If it is βâ emission, then the emitted particle is an electron. If it is β+ emission, then the particle is a positron. A positron is a particle having the same properties as an electron except for its charge. The charge of the positron is positive whereas the charge of the electron is negative. In the beta emission, a neutron is converted into a proton and an electron (or a positron). Hence, the atomic mass would be not changed, but the atomic number is increased by one unit.
Gamma Emission
Gamma radiation is not particulate. Therefore, gamma emissions do not change either the atomic number or the atomic mass of an atom. Gamma radiation is composed of photons. These photons carry only energy. Therefore, gamma emission causes the isotopes to release their energy.
Uranium-235 is a radioactive element that is found naturally. It can undergo all three types of radioactive decay at different conditions.
What is Half Life
The half life of a substance is the time taken by that substance in order to become half of its initial mass or concentration through radioactive decay. This term is given the symbol t1/2. The term half life is used because it is not possible to predict when an individual atom might decay. But, it is possible to measure the time taken to half the nuclei of a radioactive element.
The half life can be measure regarding either the number of nuclei or the concentration. Different isotopes have different half lives. Therefore, by measuring the half life, we can predict the presence or absence of a particular isotope. The half life is independent of the physical state of the substance, temperature, pressure or any other outside influence.
The half life of a substance can be determined using the following equation.
ln(Nt / No) = kt
where,
Nt is the mass of the substance after t time
No is the initial mass of the substance
K is the decay constant
t is the time considered
Figure 02: A Curve of
Radioactive Decay
The above image shows a curve of radioactive decay for a substance. The time is measured in years. According to that graph, the time taken by the substance to become 50% from initial mass (100%) is one year. Show open windows on taskbar. The 100% becomes 25% (one fourth of initial mass) after two years. Therefore, the half life of that substance is one year.
100% â 50% â 25% â 12.5% â â â
(1st half life) (2nd half life) (3rd half life)
The above chart has summarized the details given from the graph. Sims 4 installer download.
Relationship Between Radioactive Decay and Half Life
There is a direct relationship between radioactive decay and half life of a radioactive substance. The rate of radioactive decay is measured in half life equivalents. From the above equation, we can derive another important equation for the calculation of the rate of radioactive decay.
ln(Nt / No) = kt
since the mass (or the number of nuclei) is half of its initial value after one half life,
Nt = No/2
Then,
ln({No/2}/ No) = kt1/2
ln({1/2}/ 1) = kt1/2
ln(2) = kt1/2
Therefore,
t1/2 = ln2 / k
The value of ln2 is 0.693. Then,
t1/2 = 0.693 / k
Here, t1/2 is the half life of a substance and k is the radioactive decay constant. The above-derived expression tells that highly radioactive substances are spent quickly, and the weakly radioactive substances take a longer time to decay completely. Therefore, a long half life indicates fast radioactive decay while a short half life indicates a slow radioactive day. The half life of some substances cannot be determined since it may take millions of years to undergo radioactive decay.
Half Life 1Conclusion
Radioactive decay is the process where unstable isotopes undergo decay through emitting radiation. There is a direct relationship between the radioactive decay of a substance and half life since the rate of the radioactive decay is measured by the equivalents of half life.
References:
1. âHalf-Life of Radioactive Decay â Boundless Open Textbook.â Boundless. 26 May 2016. Web. Available here. 01 Aug. 2017.
2.âThe Process of Natural Radioactive Decay.â Dummies. N.p., n.d. Web. Available here. 01 Aug. 2017. Image Courtesy:
1. âRadioactive decayâ By Kurt Rosenkrantz from PDF.(CC BY-SA 3.0) via Commons Wikimedia
The biological half-life of a biological substance is the time it takes for half to be removed by biological processes when the rate of removal is roughly exponential.[1] It is often denoted by the abbreviation t12{displaystyle t_{frac {1}{2}}}. Examples include metabolites, drugs, and signalling molecules. Typically, this refers to the body's cleansing through the function of kidneys and liver in addition to excretion functions to eliminate a substance from the body. In a medical context, half-life may also describe the time it takes for the blood plasma concentration of a substance to halve (plasma half-life) its steady-state. The relationship between the biological and plasma half-lives of a substance can be complex depending on the substance in question, due to factors including accumulation in tissues (protein binding), active metabolites, and receptor interactions.[2]
Examples[edit]Water[edit]
The biological half-life of water in a human is about 7 to 14 days. It can be altered by behavior. Drinking large amounts of alcohol will reduce the biological half-life of water in the body.[3][4] This has been used to decontaminate humans who are internally contaminated with tritiated water (tritium). The basis of this decontamination method (used at Harwell)[citation needed] is to increase the rate at which the water in the body is replaced with new water.
Alcohol[edit]
The removal of ethanol (drinking alcohol) through oxidation by alcohol dehydrogenase in the liver from the human body is limited. Hence the removal of a large concentration of alcohol from blood may follow zero-order kinetics. Also the rate-limiting steps for one substance may be in common with other substances. For instance, the blood alcohol concentration can be used to modify the biochemistry of methanol and ethylene glycol. In this way the oxidation of methanol to the toxicformaldehyde and formic acid in the human body can be prevented by giving an appropriate amount of ethanol to a person who has ingested methanol. Note that methanol is very toxic and causes blindness and death. A person who has ingested ethylene glycol can be treated in the same way. Half life is also relative to the subjective metabolic rate of the individual in question.
Common prescription medications[edit]
Metals[edit]
The biological half-life of caesium in humans is between one and four months. This can be shortened by feeding the person prussian blue. The prussian blue in the digestive system acts as a solid ion exchanger which absorbs the caesium while releasing potassium ions.
For some substances, it is important to think of the human or animal body as being made up of several parts, each with their own affinity for the substance, and each part with a different biological half-life (physiologically-based pharmacokinetic modelling). Attempts to remove a substance from the whole organism may have the effect of increasing the burden present in one part of the organism. For instance, if a person who is contaminated with lead is given EDTA in a chelation therapy, then while the rate at which lead is lost from the body will be increased, the lead within the body tends to relocate into the brain where it can do the most harm.[8]
Peripheral half-life[edit]
Some substances may have different half-lives in different parts of the body. For example, oxytocin has a half-life of typically about three minutes in the blood when given intravenously. Peripherally administered (e.g. intravenous) peptides like oxytocin cross the blood-brain-barrier very poorly, although very small amounts (< 1%) do appear to enter the central nervous system in humans when given via this route.[11] In contrast to peripheral administration, when administered intranasally via a nasal spray, oxytocin reliably crosses the bloodâbrain barrier and exhibits psychoactive effects in humans.[12][13] In addition, also unlike the case of peripheral administration, intranasal oxytocin has a central duration of at least 2.25 hours and as long as 4 hours.[14][15] In likely relation to this fact, endogenous oxytocin concentrations in the brain have been found to be as much as 1000-fold higher than peripheral levels.[11]
Rate equations[edit]First-order elimination[edit]
Half-times apply to processes where the elimination rate is exponential. If C(t){displaystyle C(t)} is the concentration of a substance at time t{displaystyle t}, its time dependence is given by
where k is the reaction rate constant. Such a decay rate arises from a first-order reaction where the rate of elimination is proportional to the amount of the substance:[16]
The half-life for this process is[16]
Half-life is determined by clearance (CL) and volume of distribution (VD) and the relationship is described by the following equation:
In clinical practice, this means that it takes 4 to 5 times the half-life for a drug's serum concentration to reach steady state after regular dosing is started, stopped, or the dose changed. So, for example, digoxin has a half-life (or t½) of 24â36 h; this means that a change in the dose will take the best part of a week to take full effect. For this reason, drugs with a long half-life (e.g., amiodarone, elimination t½ of about 58 days) are usually started with a loading dose to achieve their desired clinical effect more quickly.
Biphasic half-life[edit]
Many drugs follow a biphasic elimination curve â first a steep slope then a shallow slope:
The longer half-life is called the terminal half-life and the half-life of the largest component is called the dominant half-life.[16] For a more detailed description see Pharmacokinetics--Multi-compartmental_models.
Sample values and equations[edit]
See also[edit]
References[edit]
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Biological_half-life&oldid=887343924'
Half-life (symbol t1â2) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay. The term is also used more generally to characterize any type of exponential or non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life is doubling time.
The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s.[1] Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.
Probabilistic nature[edit]
Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note the consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.
A half-life usually describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states 'half-life is the time required for exactly half of the entities to decay'. For example, if there is just one radioactive atom, and its half-life is one second, there will not be 'half of an atom' left after one second.
Instead, the half-life is defined in terms of probability: 'Half-life is the time required for exactly half of the entities to decay on average'. In other words, the probability of a radioactive atom decaying within its half-life is 50%.
For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the process. Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.
There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.[2][3][4]
Formulas for half-life in exponential decay[edit]
An exponential decay can be described by any of the following three equivalent formulas:
N(t)=N0(12)tt1/2N(t)=N0eâtÏN(t)=N0eâλt{displaystyle {begin{aligned}N(t)&=N_{0}left({frac {1}{2}}right)^{frac {t}{t_{1/2}}}N(t)&=N_{0}e^{-{frac {t}{tau }}}N(t)&=N_{0}e^{-lambda t}end{aligned}}}
where
The three parameters t1â2, Ï, and λ are all directly related in the following way:
t1/2=lnâ¡(2)λ=Ïlnâ¡(2){displaystyle t_{1/2}={frac {ln(2)}{lambda }}=tau ln(2)}
where ln(2) is the natural logarithm of 2 (approximately 0.693).
Decay by two or more processes[edit]
Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T1â2 can be related to the half-lives t1 and t2 that the quantity would have if each of the decay processes acted in isolation:
For three or more processes, the analogous formula is:
For a proof of these formulas, see Exponential decay § Decay by two or more processes.
Examples[edit]
Half life demonstrated using dice in a classroom experiment
There is a half-life describing any exponential-decay process. For example:
In non-exponential decay[edit]
The term 'half-life' is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below). In a decay process that is not even close to exponential, the half-life will change dramatically while the decay is happening. In this situation it is generally uncommon to talk about half-life in the first place, but sometimes people will describe the decay in terms of its 'first half-life', 'second half-life', etc., where the first half-life is defined as the time required for decay from the initial value to 50%, the second half-life is from 50% to 25%, and so on.[5]
In biology and pharmacology[edit]
A biological half-life or elimination half-life is the time it takes for a substance (drug, radioactive nuclide, or other) to lose one-half of its pharmacologic, physiologic, or radiological activity. In a medical context, the half-life may also describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value (the 'plasma half-life').
The relationship between the biological and plasma half-lives of a substance can be complex, due to factors including accumulation in tissues, active metabolites, and receptor interactions.[6]
While a radioactive isotope decays almost perfectly according to so-called 'first order kinetics' where the rate constant is a fixed number, the elimination of a substance from a living organism usually follows more complex chemical kinetics.
For example, the biological half-life of water in a human being is about 9 to 10 days,[7] though this can be altered by behavior and various other conditions. The biological half-life of caesium in human beings is between one and four months.
The concept of a half-life has also been utilized for pesticides in plants,[8] and certain authors maintain that pesticide risk and impact assessment models rely on and are sensitive to information describing dissipation from plants.[9]
See also[edit]References[edit]
External links[edit]
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