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Half-life
Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, 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 (in exponential growth) 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. Rutherford applied the principle of a radioactive element's half-life in 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 ...
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Biological Half-life
Biological half-life (also known as elimination half-life, pharmacologic half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration ( Cmax) to half of Cmax in the blood plasma, and is denoted by the abbreviation t_. This is used to measure the removal of things such as metabolites, drugs, and signalling molecules from the body. Typically, the biological half-life refers to the body's natural cleansing through the function of the liver and through the excretion of the measured substance through the kidneys and intestines. This concept is used when the rate of removal is roughly exponential. In a medical context, half-life explicitly describes the time it takes for the blood plasma concentration of a substance to halve (''plasma half-life'') its steady-state when circulating in the full blood of an organism. This measurement is useful in medicine, pharmacology and pharmacokinetics because it helps ...
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Radioactive Decay
Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay ( ), beta decay ( ), and gamma decay ( ), all of which involve emitting one or more particles. The weak force is the mechanism that is responsible for beta decay, while the other two are governed by the electromagnetism and nuclear force. A fourth type of common decay is electron capture, in which an unstable nucleus captures an inner electron from one of the electron shells. The loss of that electron from the shell results in a cascade of electrons dropping down to that lower shell resulting in emission of discrete X-rays from the transitions. A common example is iodine-125 commonly used in medical settings. Radioactive decay is a stochastic (i.e. random) pro ...
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List Of Nuclides
This list of nuclides shows observed nuclides that either are stable or, if radioactive, have half-lives longer than one hour. This represents isotopes of the first 105 elements, except for elements 87 (francium) and 102 (nobelium). At least 3,300 nuclides have been experimentally characterized (see List of radioactive nuclides by half-life for the nuclides with decay half-lives less than one hour). A nuclide is defined conventionally as an experimentally examined bound collection of protons and neutrons that either is stable or has an observed decay mode. Introduction There are 251 known so-called stable nuclides. Many of these in theory could decay through spontaneous fission, alpha decay, double beta decay, etc. with a very long half-life, but no radioactive decay has yet been observed. Thus, the number of stable nuclides is subject to change if some of these 251 are determined to be very long-lived radioactive nuclides in the future. In this article, the "stable" nuclides ar ...
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Mean Lifetime
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and ( lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: :\frac = -\lambda N. The solution to this equation (see derivation below) is: :N(t) = N_0 e^, where is the quantity at time , is the initial quantity, that is, the quantity at time . Measuring rates of decay Mean lifetime If the decaying quantity, ''N''(''t''), is the number of discrete elements in a certain set, it is possible to compute the average length of time that an element remains in the set. This is called the mean lifetime (or simply the lifetime), where the exponential time constant, \tau, relates to the decay rate constant, λ, in the following way: :\tau = \frac. The mean lifetime can be looked at as ...
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Decay Constant
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: :\frac = -\lambda N. The solution to this equation (see derivation below) is: :N(t) = N_0 e^, where is the quantity at time , is the initial quantity, that is, the quantity at time . Measuring rates of decay Mean lifetime If the decaying quantity, ''N''(''t''), is the number of discrete elements in a certain set, it is possible to compute the average length of time that an element remains in the set. This is called the mean lifetime (or simply the lifetime), where the exponential time constant, \tau, relates to the decay rate constant, λ, in the following way: :\tau = \frac. The mean lifetime can be looked at as ...
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Exponential Decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: :\frac = -\lambda N. The solution to this equation (see derivation below) is: :N(t) = N_0 e^, where is the quantity at time , is the initial quantity, that is, the quantity at time . Measuring rates of decay Mean lifetime If the decaying quantity, ''N''(''t''), is the number of discrete elements in a certain set, it is possible to compute the average length of time that an element remains in the set. This is called the mean lifetime (or simply the lifetime), where the exponential time constant, \tau, relates to the decay rate constant, λ, in the following way: :\tau = \frac. The mean lifetime can be looked at as ...
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Radium
Radium is a chemical element with the symbol Ra and atomic number 88. It is the sixth element in group 2 of the periodic table, also known as the alkaline earth metals. Pure radium is silvery-white, but it readily reacts with nitrogen (rather than oxygen) upon exposure to air, forming a black surface layer of radium nitride (Ra3N2). All isotopes of radium are radioactive, the most stable isotope being radium-226 with a half-life of 1600 years. When radium decays, it emits ionizing radiation as a by-product, which can excite fluorescent chemicals and cause radioluminescence. Radium, in the form of radium chloride, was discovered by Marie and Pierre Curie in 1898 from ore mined at Jáchymov. They extracted the radium compound from uraninite and published the discovery at the French Academy of Sciences five days later. Radium was isolated in its metallic state by Marie Curie and André-Louis Debierne through the electrolysis of radium chloride in 1911. In nature, radi ...
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Atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small, typically around 100 picometers across. They are so small that accurately predicting their behavior using classical physics, as if they were tennis balls for example, is not possible due to quantum effects. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, then the atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively – such atoms are called ions. The electrons of an atom ...
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Chemical Element
A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler substances by any chemical reaction. The number of protons in the nucleus is the defining property of an element, and is referred to as its atomic number (represented by the symbol ''Z'') – all atoms with the same atomic number are atoms of the same element. Almost all of the baryonic matter of the universe is composed of chemical elements (among rare exceptions are neutron stars). When different elements undergo chemical reactions, atoms are rearranged into new compounds held together by chemical bonds. Only a minority of elements, such as silver and gold, are found uncombined as relatively pure native element minerals. Nearly all other naturally occurring elements occur in the Earth as compounds or mixtures. Air is primarily a mixture ...
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Lead-206
Lead (82Pb) has four stable isotopes: 204Pb, 206Pb, 207Pb, 208Pb. Lead-204 is entirely a primordial nuclide and is not a radiogenic nuclide. The three isotopes lead-206, lead-207, and lead-208 represent the ends of three decay chains: the uranium series (or radium series), the actinium series, and the thorium series, respectively; a fourth decay chain, the neptunium series, terminates with the thallium isotope 205Tl. The three series terminating in lead represent the decay chain products of long-lived primordial 238U, 235U, and 232Th, respectively. However, each of them also occurs, to some extent, as primordial isotopes that were made in supernovae, rather than radiogenically as daughter products. The fixed ratio of lead-204 to the primordial amounts of the other lead isotopes may be used as the baseline to estimate the extra amounts of radiogenic lead present in rocks as a result of decay from uranium and thorium. (See lead–lead dating and uranium–lead dating). The l ...
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Rate Law
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders). For many reactions, the initial rate is given by a power law such as :v_0\; =\; k mathrmx mathrmy where and express the concentration of the species and usually in moles per liter ( molarity, ). The exponents and are the partial ''orders of reaction'' for and and the ''overall'' reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The constant is the reaction rate constant or ''rate coefficient'' of the reaction. Its value may depend on conditions such as temperature, ionic strength, surface area of an adsorbent, or light irradiation. If the reaction goes to completion, the rate equation for the reaction rate v\; =\; k cex cey applies throu ...
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Chemical Kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction. History In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.C.M. Guldberg and P. Waage,"Studies Concerning Affinity" ''Forhandlinger i Videnskabs-Selskabet i Christiania'' (1864), ...
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