Education, The science
The half-life of radioactive elements - what is it and how is it determined? The half-life formula
The history of studying radioactivity began on March 1, 1896, when the famous French scientist Henri Becquerel accidentally discovered strangeness in the emission of uranium salts. It turned out that the photographic plates located in the same box with the sample were illuminated. This led to a strange, highly penetrating radiation, which possessed uranium. This property was found in the heaviest elements that complete the periodic table. He was given the name "radioactivity".
Introduce the characteristics of radioactivity
This process is the spontaneous transformation of the isotope atom of an element into another isotope with simultaneous separation of elementary particles (electrons, nuclei of helium atoms). The transformation of atoms turned out to be spontaneous, not requiring the absorption of energy from outside. The main quantity that characterizes the process of energy release during radioactive decay is called activity.
A = λN, where λ is the decay constant, N is the number of active atoms in the sample.
Separate α, β, γ-decays. The corresponding equations are called displacement rules:
name | What's happening | The reaction equation |
Α-decay | Transformation of the atomic nucleus X into the nucleus of Y with the liberation of the nucleus of the helium atom | Z A X → Z-2 Y A-4 + 2 He 4 |
Β - decay | Transformation of the atomic nucleus X into the nucleus Y with the liberation of the electron | Z A X → Z + 1 Y A + -1 e A |
Γ - decay | Is not accompanied by a change in the nucleus, the energy is released in the form of an electromagnetic wave | Z X A → Z X A + γ |
Time interval in radioactivity
The moment of disintegration of a particle can not be established for a given particular atom. For him, this is more of an "accident" than a regularity. The energy release characterizing this process is defined as the activity of the sample.
It is established that there is a time during which exactly half of the atoms in a given sample undergo disintegration. This time interval was called the "half-life". What is the point of introducing this concept?
What is the half-life?
It seems that in a time equal to a period, exactly half of all active atoms of a given sample break up. But does this mean that during a period of two half-lives, all the active atoms will completely decay? Not at all. After a certain moment, half of the radioactive elements remain in the sample, after a similar period of time, half of the remaining atoms break up, and so on. In this case, the radiation persists for a long time, considerably exceeding the half-life. Hence, the active atoms are conserved in the sample irrespective of the radiation
The half-life is a quantity that depends solely on the properties of the substance. The value of the value is determined for many known radioactive isotopes.
Table: "Half-period of decay of individual isotopes"
| Name | Designation | Type of decay | Half life |
Radium | 88 Ra 219 | alpha | 0.001 seconds |
Magnesium | 12 Mg 27 | beta | 10 minutes |
Radon | 86 Rn 222 | alpha | 3.8 days |
Cobalt | 27 Co 60 | Beta, gamma | 5.3 years |
Radium | 88 Ra 226 | Alpha, gamma | 1620 years old |
Uranus | 92 U 238 | Alpha, gamma | 4.5 billion years |
The determination of the half-life was carried out experimentally. In the course of laboratory tests, activity is repeatedly measured. Since laboratory samples of minimal dimensions (the safety of the researcher above all), the experiment is conducted with a different time interval, repeatedly repeating. It is based on the regularity of the change in the activity of substances.
To determine the half-life, the activity of a given sample is measured at specific intervals. Given that this parameter is related to the number of decaying atoms, using the law of radioactive decay, determine the half-life.
An example of a determination for an isotope
Let the number of active elements of the investigated isotope at a given instant of time be N, the time interval during which t 2 - t 1 is observed, where the moments of the beginning and the end of the observation are sufficiently close. Suppose that n is the number of atoms that decayed into a given time interval, then n = KN (t 2 - t 1 ).
In this expression, K = 0.693 / T1 is a coefficient of proportionality, called the decay constant. T1 is the half-life of the isotope.
We take the time interval for the unit. In this case, K = n / N indicates the fraction of the isotope nuclei present, decaying per unit time.
Knowing the value of the decay constant, we can also determine the half-period of the decay: T1 = 0.693 / K.
Hence it follows that for a unit of time there is not a definite number of active atoms, but a certain fraction of them that decays.
The law of radioactive decay (RDF)
The half-life is the basis of the ZRD. The regularity was deduced by Frederico Soddy and Ernest Rutherford on the basis of the results of experimental studies in 1903. Surprisingly, multiple measurements performed with instruments far from perfect in the early twentieth century have led to an accurate and justified result. It became the basis of the theory of radioactivity. We shall derive a mathematical notation for the law of radioactive decay.
Let N 0 be the number of active atoms at a given time. After expiration of the time interval t, N elements remain unbroken.
- By the time equal to the half-life, exactly half of the active elements will remain: N = N 0/2 .
- After one more half-life in the sample, N = N 0/4 = N 0/2 2 active atoms remain.
- After a time equal to one more half-life, the sample will retain only: N = N 0/8 = N 0/2 3 .
- By the time when n half-lives have passed, N = N 0/2 n active particles remain in the sample. In this expression, n = t / T1: the ratio of study time to half-life.
- ZRP has a slightly different mathematical expression, more convenient in solving problems: N = N 0 2 - t / T1 .
The regularity makes it possible to determine, in addition to the half-life, the number of atoms of the active isotope that have not decayed at a given instant of time. Knowing the number of atoms in the sample at the beginning of the observation, after a while you can determine the lifetime of the drug.
Determine the half-life of the formula for the law of radioactive decay only helps in the presence of certain parameters: the number of active isotopes in the sample, which is difficult to know.
Consequences of the law
You can write down the ZRP formula using the concepts of activity and mass of the atoms of the drug.
The activity is proportional to the number of radioactive atoms: A = A 0 • 2 -t / T. In this formula, A 0 is the activity of the sample at the initial time, A is activity after t seconds, and T is the half-life.
The mass of the substance can be used in the regularity: m = m 0 • 2 -t / T
During any equally long intervals of time, an absolutely identical fraction of the radioactive atoms that are present in the preparation disintegrates.
Limits of applicability of the law
The law in all senses is statistical, determining the processes taking place in the microcosm. It is clear that the half-life of radioactive elements is a statistical one. The probabilistic nature of events in atomic nuclei suggests that an arbitrary nucleus can collapse at any time. Predict the event is impossible, you can only determine its probability at a given time. As a consequence, the half-life does not make sense:
- For an individual atom;
- For a sample of minimum mass.
The lifetime of an atom
The existence of an atom in its original state can last a second, maybe millions of years. It is also not necessary to talk about the lifetime of a given particle. Introducing a value equal to the average value of the lifetime of atoms, one can talk about the existence of atoms of a radioactive isotope, the consequences of radioactive decay. The half-life of an atomic nucleus depends on the properties of a given atom and does not depend on other quantities.
Is it possible to solve the problem: how to find the half-life, knowing the average lifetime?
Determine the half-life of the formula for the relationship between the average lifetime of the atom and the decay constant is no less important.
Τ = T 1/2 / ln2 = T 1/2 / 0.693 = 1 / λ.
In this record, τ is the mean lifetime, λ is the decay constant.
Use of half-life
The use of ZRP to determine the age of individual samples has become widespread in studies of the late twentieth century. The accuracy of determining the age of fossil artifacts has grown so much that it can give an idea of the lifetime of millennium BC.
Radiocarbon analysis of fossil organic samples is based on a change in the activity of carbon-14 (the radioactive carbon isotope) present in all organisms. It enters the living organism in the process of metabolism and is contained in it in a certain concentration. After death, the metabolism with the environment stops. The concentration of radioactive carbon falls due to natural decay, the activity decreases proportionally.
In the presence of such a value as the half-life, the formula of the law of radioactive decay helps determine the time from the moment of cessation of vital activity of the organism.
Chains of radioactive transformation
Radioactivity studies were carried out under laboratory conditions. The amazing ability of radioactive elements to maintain activity for hours, days and even years could not but surprise the physicists of the early twentieth century. Studies, for example, thorium, were accompanied by an unexpected result: in a closed ampoule, its activity was significant. At the slightest blow she fell. The conclusion was simple: the transformation of thorium is accompanied by the release of radon (gas). All elements in the process of radioactivity are transformed into a completely different substance, differing in both physical and chemical properties. This substance, in turn, is also unstable. At present, three series of similar transformations are known.
Knowledge of such transformations is extremely important in determining the time of inaccessibility of zones infected in the process of atomic and nuclear research or catastrophes. The half-life of plutonium, depending on its isotope, ranged from 86 years (Pu 238) to 80 Ma (Pu 244). Concentration of each isotope gives an idea of the period of disinfection of the territory.
The most expensive metal
It is known that in our time there are metals much more expensive than gold, silver and platinum. Plutonium also belongs to them. It is interesting that in nature plutonium created in the course of evolution does not occur. Most of the elements were obtained under laboratory conditions. The operation of plutonium-239 in nuclear reactors made it possible to become extremely popular these days. Getting enough of this isotope for use in reactors makes it almost invaluable.
Plutonium-239 is obtained under natural conditions as a consequence of the chain of transformations of uranium-239 into neptunium-239 (half-life - 56 hours). A similar chain allows the accumulation of plutonium in nuclear reactors. The speed of appearance of the required quantity exceeds the natural one in billions of times.
Application in power engineering
We can talk a lot about the shortcomings of nuclear energy and about the "oddities" of mankind, which almost any discovery uses to destroy their own kind. The discovery of plutonium-239, which is capable of taking part in a chain nuclear reaction, made it possible to use it as a source of peaceful energy. Uranium-235, which is an analog of plutonium, is extremely rare on Earth, it is much more difficult to separate it from uranium ore than to obtain plutonium.
Age of the Earth
Radioisotope analysis of isotopes of radioactive elements gives a more accurate picture of the lifetime of a given sample.
The use of the chain of transformations of "uranium - thorium" contained in the earth's crust makes it possible to determine the age of our planet. The percentage of these elements on average throughout the entire earth's crust lies at the basis of this method. According to the latest data, the Earth's age is 4.6 billion years.
Similar articles
Trending Now