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Alpha decay is one example type of radioactive decay, in which an atomic nucleus emits an alpha particle, and thereby transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. Many other types of decays are possible.

Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). There are many different types of radioactive decay (see table below). A decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide, transforms to an atom with a nucleus in a different state, or to a different nucleus containing different numbers of nucleons. Either of these products is named the daughter nuclide. In some decays the parent and daughter are different chemical elements, and thus the decay process results in nuclear transmutation (creation of an atom of a new element).

The first decay processes to be discovered were alpha decay, beta decay, and gamma decay. Alpha decay occurs when the nucleus ejects an alpha particle (helium nucleus). This is the most common process of emitting nucleons, but in rarer types of decays, nuclei can eject protons, or specific nuclei of other elements (in the process called cluster decay). Beta decay occurs when the nucleus emits an electron or positron and a type of neutrino, in a process that changes a proton to a neutron or vice versa. The nucleus may capture an orbiting electron, converting a proton into an neutron (electron capture). All of these processes result in nuclear transmutation.

By contrast, there exist radioactive decay processes that do not result in transmutation. The energy of an excited nucleus may be emitted as a gamma ray in gamma decay, or used to eject an orbital electron by interaction with the excited nucleus in a process called internal conversion. Radioisotopes occasionally emit neutrons, and this results in a change in an element from one isotope to another.

One type of radioactive decay results in products which are not defined, but appear in a range of "pieces" of the original nucleus. This decay is called spontaneous fission. This decay happens when a large unstable nucleus spontaneously splits into two (and occasionally three) smaller daughter nuclei, and usually emits gamma rays, neutrons, or other particles as a consequence.

Radioactive decay is a stochastic (i.e., random) process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay.^[1] However, the chance that a given atom will decay is constant over time. For a large number of atoms, the decay rate for the collection is computable from the measured decay constants of the nuclides (or equivalently from the half-lifes).

Natural Origin[link]

Primordial nuclides found in the earth are residues from ancient supernova explosions which occurred before the formation of the solar system. They are the long-lived fraction of radionuclides surviving in the primordial solar nebula through planet accretion until the present. The naturally-occurring short-lived radiogenic radionuclides found in rocks are the daughters of these radiactive primordial nuclides. Another minor source of naturally-occurring radioactive nuclides are cosmogenic nuclides, formed by cosmic ray bombardment of material in the Earth's atmosphere or crust. For a summary table showing the number of stable nuclides and of radioactive nuclides in each category, see radionuclide. Radionuclides can also be produced artificially e.g. using particle accelerators or nuclear reactors.

Decay phenomena[link]

The trefoil symbol is used to indicate radioactive material.

The neutrons and protons that constitute nuclei, as well as other particles that approach close enough to them, are governed by several interactions. The strong nuclear force, not observed at the familiar macroscopic scale, is the most powerful force over subatomic distances. The electrostatic force is almost always significant, and, in the case of beta decay, the weak nuclear force is also involved.

The interplay of these forces produces a number of different phenomena in which energy may be released by rearrangement of particles in the nucleus, or else the change of one type of particle into others. These rearrangements and transformations may be hindered energetically, so that they do not occur immediately. In certain cases, random quantum vacuum fluctuations are theorized to promote relaxation to a lower energy state (the "decay") in a phenomenon known as quantum tunneling. Radioactive decay half-life of nuclides has been measured over timescales of 55 orders of magnitude, from 2.3 x 10^-23 second (for hydrogen-7) to 6.9 x 10³¹ seconds (for tellurium-128)^[2]. The limits of these timescales are set by the sensitivity of instrumentation only, and there are no known natural limits to how brief or long a decay half life for radioactive decay of a radionuclide may be.

The decay process, like all hindered energy transformations, may be analogized by a snowfield on a mountain. While friction between the ice crystals may be supporting the snow's weight, the system is inherently unstable with regard to a state of lower potential energy. A disturbance would thus facilitate the path to a state of greater entropy: The system will move towards the ground state, producing heat, and the total energy will be distributable over a larger number of quantum states. Thus, an avalanche results. The total energy does not change in this process, but, because of the law of entropy, avalanches happen only in one direction and that is toward the "ground state" — the state with the largest number of ways in which the available energy could be distributed.

Such a collapse (a decay event) requires a specific activation energy. For a snow avalanche, this energy comes as a disturbance from outside the system, although such disturbances can be arbitrarily small. In the case of an excited atomic nucleus, the arbitrarily small disturbance comes from quantum vacuum fluctuations. A radioactive nucleus (or any excited system in quantum mechanics) is unstable, and can, thus, spontaneously stabilize to a less-excited system. The resulting transformation alters the structure of the nucleus and results in the emission of either a photon or a high-velocity particle that has mass (such as an electron, alpha particle, or other type).

Discovery[link]

Radioactivity was discovered in 1896 by the French scientist Henri Becquerel, while working on phosphorescent materials. These materials glow in the dark after exposure to light, and he suspected that the glow produced in cathode ray tubes by X-rays might be associated with phosphorescence. He wrapped a photographic plate in black paper and placed various phosphorescent salts on it. All results were negative until he used uranium salts. The result with these compounds was a blackening of the plate. These radiations were called Becquerel Rays.

Pierre and Marie Curie in their Paris laboratory, before 1907

It soon became clear that the blackening of the plate had nothing to do with phosphorescence, because the plate blackened when the mineral was in the dark. Non-phosphorescent salts of uranium and metallic uranium also blackened the plate. It was clear that there is a form of radiation that could pass through paper that was causing the plate to become black.

At first it seemed that the new radiation was similar to the then recently-discovered X-rays. Further research by Becquerel, Ernest Rutherford, Paul Villard, Pierre Curie, Marie Curie, and others discovered that this form of radioactivity was significantly more complicated. Different types of decay can occur, producing very different types of radiation. Rutherford was the first to realize that they all occur with the same mathematical exponential formula (see below), and Rutherford and his student Frederick Soddy were first to realize that many decay processes resulted in the transmutation of one element to another. Subsequently, the radioactive displacement law of Fajans and Soddy was formulated to describe the products of alpha and beta decay.

The early researchers also discovered that many other chemical elements besides uranium have radioactive isotopes. A systematic search for the total radioactivity in uranium ores also guided Marie Curie to isolate a new element polonium and to separate a new element radium from barium. The two elements' chemical similarity would otherwise have made them difficult to distinguish.

Danger of radioactive substances[link]

The danger classification sign of radioactive materials

Alpha particles may be completely stopped by a sheet of paper, beta particles by aluminum shielding. Gamma rays can only be reduced by much more substantial mass, such as a very thick layer of lead.

Different types of decay of a radionuclide. Vertical: atomic number Z, Horizontal: neutron number N

The dangers of radioactivity and radiation were not immediately recognized. Acute effects of radiation were first observed in the use of X-rays when electrical engineer and physicist Nikola Tesla intentionally subjected his fingers to X-rays in 1896.^[3] He published his observations concerning the burns that developed, though he attributed them to ozone rather than to X-rays. His injuries later healed.

The genetic effects of radiation, including the effect of cancer risk, were recognized much later. In 1927, Hermann Joseph Muller published research showing genetic effects, and in 1946 was awarded the Nobel prize for his findings.

Before the biological effects of radiation were known, many physicians and corporations began marketing radioactive substances as patent medicine, glow-in-the-dark pigments. Examples were radium enema treatments, and radium-containing waters to be drunk as tonics. Marie Curie protested this sort of treatment, warning that the effects of radiation on the human body were not well understood. Curie later died from aplastic anemia, likely caused by exposure to ionizing radiation. By the 1930s, after a number of cases of bone necrosis and death of enthusiasts, radium-containing medicinal products had been largely removed from the market (radioactive quackery).

Types of decay[link]

As for types of radioactive radiation, it was found that an electric or magnetic field could split such emissions into three types of beams. The rays were given the alphabetic names alpha, beta, and gamma, in order of their ability to penetrate matter. While alpha decay was seen only in heavier elements (atomic number 52, tellurium, and greater), the other two types of decay were seen in all of the elements. Spontaneous decay is evident in elements of atomic number ninety or greater.

In analyzing the nature of the decay products, it was obvious from the direction of electromagnetic forces induced upon the radiations by external magnetic and electric fields that alpha particles carried a positive charge, beta particles carried a negative charge, and gamma rays were neutral. From the magnitude of deflection, it was clear that alpha particles were much more massive than beta particles. Passing alpha particles through a very thin glass window and trapping them in a discharge tube allowed researchers to study the emission spectrum of the resulting gas, and ultimately prove that alpha particles are helium nuclei. Other experiments showed the similarity between classical beta radiation and cathode rays: They are both streams of electrons. Likewise gamma radiation and X-rays were found to be similar high-energy electromagnetic radiation.

The relationship between the types of decays also began to be examined: For example, gamma decay was almost always found associated with other types of decay, and occurred at about the same time, or afterward. Gamma decay as a separate phenomenon (with its own half-life, now termed isomeric transition), was found in natural radioactivity to be a result of the gamma decay of excited metastable nuclear isomers, which were in turn created from other types of decay.

Although alpha, beta, and gamma radiations were found most commonly, other types of decay were eventually discovered. Shortly after the discovery of the positron in cosmic ray products, it was realized that the same process that operates in classical beta decay can also produce positrons (positron emission). In an analogous process, instead of emitting positrons and neutrinos, some proton-rich nuclides were found to capture their own atomic electrons (electron capture), and emit only a neutrino (and usually also a gamma ray). Each of these types of decay involves the capture or emission of nuclear electrons or positrons, and acts to move a nucleus toward the ratio of neutrons to protons that has the least energy for a given total number of nucleons (neutrons plus protons).

A theoretical process of positron capture (analogous to electron capture) is possible in antimatter atoms, but has not been observed since the complex antimatter atoms are not available.^[4] This would required antimatter atoms at least as complex as beryllium-7, which is the lightest known isotope of normal matter to undergo decay by electron capture.

Shortly after the discovery of the neutron in 1932, it was realized by Enrico Fermi that certain rare decay reactions yield neutrons as a decay particle (neutron emission). Isolated proton emission was eventually observed in some elements. It was also found that some heavy elements may undergo spontaneous fission into products that vary in composition. In a phenomenon called cluster decay, specific combinations of neutrons and protons other than alpha particles (helium nuclei) were found to be spontaneously emitted from atoms.

Other types of radioactive decay that emit previously seen particles were found, but by different mechanisms. An example is internal conversion, which results in electron and sometimes high-energy photon emission, even though it involves neither beta nor gamma decay. This type of decay (like isomeric transition gamma decay) does not transmute one element to another.

Rare events that involve a combination of two beta-decay type events happening simultaneously (see below) are known. Any decay process that does not violate conservation of energy or momentum laws (and perhaps other particle conservation laws) is permitted to happen, although not all have been detected. An interesting example (discussed in a final section) is bound state beta decay of rhenium-187. In this process, an inverse of electron capture, beta electron-decay of the parent nuclide is not accompanied by beta electron emission, because the beta particle has been captured into the K-shell of the emitting atom. An antineutrino, however, is emitted.

Decay modes in table form[link]

Radionuclides can undergo a number of different reactions. These are summarized in the following table. A nucleus with mass number A and atomic number Z is represented as (A, Z). The column "Daughter nucleus" indicates the difference between the new nucleus and the original nucleus. Thus, (A − 1, Z) means that the mass number is one less than before, but the atomic number is the same as before.

Radioactive decay results in a reduction of summed rest mass, once the released energy (the disintegration energy) has escaped in some way (for example, the products might be captured and cooled, and the heat allowed to escape). Although decay energy is sometimes defined as associated with the difference between the mass of the parent nuclide products and the mass of the decay products, this is true only of rest mass measurements, where some energy has been removed from the product system. This is true because the decay energy must always carry mass with it, wherever it appears (see mass in special relativity) according to the formula E = mc². The decay energy is initially released as the energy of emitted photons plus the kinetic energy of massive emitted particles (that is, particles that have rest mass). If these particles come to thermal equilibrium with their surroundings and photons are absorbed, then the decay energy is transformed to thermal energy, which retains its mass.

Decay energy therefore remains associated with a certain measure of mass of the decay system invariant mass. The energy of photons, kinetic energy of emitted particles, and, later, the thermal energy of the surrounding matter, all contribute to calculations of invariant mass of systems. Thus, while the sum of rest masses of particles is not conserved in radioactive decay, the system mass and system invariant mass (and also the system total energy) is conserved throughout any decay process.

Decay chains and multiple modes[link]

The daughter nuclide of a decay event may also be unstable (radioactive). In this case, it will also decay, producing radiation. The resulting second daughter nuclide may also be radioactive. This can lead to a sequence of several decay events. Eventually, a stable nuclide is produced. This is called a decay chain (see this article for specific details of important natural decay chains).

Gamma-ray energy spectrum of uranium ore (inset). Gamma-rays are emitted by decaying nuclides, and the gamma-ray energy can be used to characterize the decay (which nuclide is decaying to which). Here, using the gamma-ray spectrum, several nuclides that are typical of the decay chain of ²³⁸U have been identified: ²²⁶Ra, ²¹⁴Pb, ²¹⁴Bi.

An example is the natural decay chain of ²³⁸U, which is as follows:

• decays, through alpha-emission, with a half-life of 4.5 billion years to thorium-234
• which decays, through beta-emission, with a half-life of 24 days to protactinium-234
• which decays, through beta-emission, with a half-life of 1.2 minutes to uranium-234
• which decays, through alpha-emission, with a half-life of 240 thousand years to thorium-230
• which decays, through alpha-emission, with a half-life of 77 thousand years to radium-226
• which decays, through alpha-emission, with a half-life of 1.6 thousand years to radon-222
• which decays, through alpha-emission, with a half-life of 3.8 days to polonium-218
• which decays, through alpha-emission, with a half-life of 3.1 minutes to lead-214
• which decays, through beta-emission, with a half-life of 27 minutes to bismuth-214
• which decays, through beta-emission, with a half-life of 20 minutes to polonium-214
• which decays, through alpha-emission, with a half-life of 160 microseconds to lead-210
• which decays, through beta-emission, with a half-life of 22 years to bismuth-210
• which decays, through beta-emission, with a half-life of 5 days to polonium-210
• which decays, through alpha-emission, with a half-life of 140 days to lead-206, which is a stable nuclide.

Some radionuclides may have several different paths of decay. For example, approximately 36% of bismuth-212 decays, through alpha-emission, to thallium-208 while approximately 64% of bismuth-212 decays, through beta-emission, to polonium-212. Both the thallium-208 and the polonium-212 are radioactive daughter products of bismuth-212, and both decay directly to stable lead-208.

Occurrence and applications[link]

According to the Big Bang theory, stable isotopes of the lightest five elements (H, He, and traces of Li, Be, and B) were produced very shortly after the emergence of the universe, in a process called Big Bang nucleosynthesis. These lightest stable nuclides (including deuterium) survive to today, but any radioactive isotopes of the light elements produced in the Big Bang (such as tritium) have long since decayed. Isotopes of elements heavier than boron were not produced at all in the Big Bang, and these first five elements do not have any long-lived radioisotopes. Thus, all radioactive nuclei are, therefore, relatively young with respect to the birth of the universe, having formed later in various other types of nucleosynthesis in stars (in particular, supernovae), and also during ongoing interactions between stable isotopes and energetic particles. For example, carbon-14, a radioactive nuclide with a half-life of only 5730 years, is constantly produced in Earth's upper atmosphere due to interactions between cosmic rays and nitrogen.

Nuclides that are produced by radioactive decay are called radiogenic nuclides, whether they themselves are stable or not. There exist stable radiogenic nuclides that were formed from short-lived extinct radionuclides in the early solar system.^[5][6] The extra presence of these stable radiogenic nuclides (such as Xe-129 from primordial I-129) against the background of primordial stable nuclides can be inferred by various means.

Radioactive decay has been put to use in the technique of radioisotopic labeling, which is used to track the passage of a chemical substance through a complex system (such as a living organism). A sample of the substance is synthesized with a high concentration of unstable atoms. The presence of the substance in one or another part of the system is determined by detecting the locations of decay events.

On the premise that radioactive decay is truly random (rather than merely chaotic), it has been used in hardware random-number generators. Because the process is not thought to vary significantly in mechanism over time, it is also a valuable tool in estimating the absolute ages of certain materials. For geological materials, the radioisotopes and some of their decay products become trapped when a rock solidifies, and can then later be used (subject to many well-known qualifications) to estimate the date of the solidification. These include checking the results of several simultaneous processes and their products against each other, within the same sample. In a similar fashion, and also subject to qualification, the rate of formation of carbon-14 in various eras, the date of formation of organic matter within a certain period related to the isotope's half-life may be estimated, because the carbon-14 becomes trapped when the organic matter grows and incorporates the new carbon-14 from the air. Thereafter, the amount of carbon-14 in organic matter decreases according to decay processes that may also be independently cross-checked by other means (such as checking the carbon-14 in individual tree rings, for example).

Radioactive decay rates[link]

The decay rate, or activity, of a radioactive substance are characterized by:

Constant quantities:

• The half-life — t_1/2, is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value; see List of nuclides.
• The mean lifetime — τ, "tau" the average lifetime of a radioactive particle before decay.
• The decay constant — λ, "lambda" the inverse of the mean lifetime.

Although these are constants, they are associated with statistically random behavior of populations of atoms. In consequence predictions using these constants are less accurate for small number of atoms.

In principle the reciprocal of any number greater than one — a half-life, a third-life, or even a (1/√2)-life — can be used in exactly the same way as half-life; but the half-life t_1/2 is adopted as the standard time associated with exponential decay.

Time-variable quantities:

• Total activity — A, is number of decays per unit time of a radioactive sample.
• Number of particles — N, is the total number of particles in the sample.
• Specific activity — S_A, number of decays per unit time per amount of substance of the sample at time set to zero (t = 0). "Amount of substance" can be the mass, volume or moles of the initial sample.

These are related as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): t_{1/2} = \frac{\ln(2)}{\lambda} = \tau \ln(2)

Failed to parse (Missing texvc executable; please see math/README to configure.): A = - \frac{\mathrm{d}N}{\mathrm{d}t} = \lambda N

Failed to parse (Missing texvc executable; please see math/README to configure.): S_A a_0 = - \frac{\mathrm{d}N}{\mathrm{d}t}\bigg|_{t=0} = \lambda N_0

where N₀ is the initial amount of active substance — substance that has the same percentage of unstable particles as when the substance was formed.

Units of radioactivity measurements[link]

The SI unit of radioactive activity is the becquerel (Bq), in honor of the scientist Henri Becquerel. One Bq is defined as one transformation (or decay or disintegration) per second. Since sensible sizes of radioactive material contains many atoms, a Bq is a tiny measure of activity; amounts giving activities on the order of GBq (gigabecquerel, 1 x 10⁹ decays per second) or TBq (terabecquerel, 1 x 10¹² decays per second) are commonly used.

Another unit of radioactivity is the curie, Ci, which was originally defined as the amount of radium emanation (radon-222) in equilibrium with one gram of pure radium, isotope Ra-226. At present it is equal, by definition, to the activity of any radionuclide decaying with a disintegration rate of 3.7 × 10¹⁰ Bq, so that 1 curie (Ci) = 3.7 × 10¹⁰ Bq. The use of Ci is currently discouraged by the SI. Low activities are also measured in disintegrations per minute (dpm).

Mathematics of radioactive decay[link]

Universal law of radioactive decay[link]

Radioactivity is one very frequent example of exponential decay. The law describes the statistical behavior of a large number of nuclides, rather than individual ones. In the following formalism, the number of nuclides or nuclide population N, is of course a discrete variable (a natural number) - but for any physical sample N is so large (amounts of L = 10^23, avagadro's constant) that it can be treated as a continuous variable. Differential calculus to set up differential equations for modelling the behaviour of the nuclear decay.

One-decay process[link]

Consider the case of a nuclide A decaying into another B by some process A → B (emission of other particles, like electron neutrinos ν
e and electrons e^– in beta decay, are irrelevant in what follows). The decay of an unstable nucleus is entirely random and it is impossible to predict when a particular atom will decay.^[1] However, it is equally likely to decay at any time. Therefore, given a sample of a particular radioisotope, the number of decay events −dN expected to occur in a small interval of time dt is proportional to the number of atoms present N, that is

Failed to parse (Missing texvc executable; please see math/README to configure.): -\frac{\mathrm{d}N}{\mathrm{d}t} \propto N.

Particular radionuclides decay at different rates, so each has its own decay constant λ. The expected decay −dN/N is proportional to an increment of time, dt:

Failed to parse (Missing texvc executable; please see math/README to configure.): -\frac{\mathrm{d}N}{N} = \lambda \mathrm{d}t

The negative sign indicates that N decreases as time increases, as each decay event follows one after another. The solution to this first-order differential equation is the function:

Failed to parse (Missing texvc executable; please see math/README to configure.): N(t) = N_0\,e^{-{\lambda}t} = N_0\,e^{-t/ \tau}, \,\!

where N₀ is the value of N at time t = 0.

This equation is of particular interest; the behaviour of numerous important quantities can be found from it (see below). Although the parent decay distribution follows an exponential, observations of decay times will be limited by a finite integer number of N atoms and follow Poisson statistics as a consequence of the random nature of the process.

We have for all time t:

Failed to parse (Missing texvc executable; please see math/README to configure.): N_A + N_B = N_\mathrm{total} = N_{A0},

where N_total is the constant number of particles throughout the decay process, clearly equal to the initial number of A nuclides since this is the initial substance.

If the number of non-decayed A nuclei is:

Failed to parse (Missing texvc executable; please see math/README to configure.): N_A = N_{A0}e^{-{\lambda}t} \,\!

then the number of nuclei of B, i.e. number of decayed A nuclei, is

Failed to parse (Missing texvc executable; please see math/README to configure.): N_B = N_{A0} - N_A = N_{A0} - N_{A0}e^{-{\lambda}t} = N_{A0} \left ( 1 - e^{-{\lambda}t} \right ).

Chain-decay processes[link]

Chain of two decays

Now consider the case of a chain of two decays: one nuclide A decaying into another B by one process, then B decaying into another C by a second process, i.e. A → B → C. The previous equation cannot be applied to a decay chain, but can be generalized as follows. The decay rate of B is proportional to the number of nuclides of B present, so again we have:

Failed to parse (Missing texvc executable; please see math/README to configure.): -\frac{\mathrm{d}N_B}{\mathrm{d}t} \propto N_B,

but care must be taken. Since A decays into B, then B decays into C, the activity of A adds to the total number of B nuclides in the present sample, before those B nuclides decay and reduce the number of nuclides leading to the later sample. In other words, the number of second generation nuclei B increases as a result of the first generation nuclei decay of A, and decreases as a result of its own decay into the third generation nuclei C.^[7] The proportionality becomes an equation:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\mathrm{d}N_B}{\mathrm{d}t} = - \lambda_B N_B,

adding the increasing (and correcting) term obtains the law for a decay chain for two nuclides:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\mathrm{d}N_B}{\mathrm{d}t} = -\lambda_B N_B + \lambda_A N_A.

The equation is not

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\mathrm{d}N_B}{\mathrm{d}t} = - \left ( \lambda_B N_B + \lambda_A N_A \right ) ,

since this implies the number of atoms of B is only decreasing as time increases, which is not the case. The rate of change of N_B, that is dN_B/dt, is related to the changes in the amounts of A and B, N_B can increase as B is produced from A and decrease as B produces C.

Re-writing using the previous results:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\mathrm{d}N_B}{\mathrm{d}t} = - \lambda_B N_B + \lambda_A N_{A0} e^{-\lambda_A t}

The subscripts simply refer to the respective nuclides, i.e. N_A is the number of nuclides of type A, N_A0 is the initial number of nuclides of type A, λ_A is the decay constant for A - and similarly for nuclide B. Solving this equation for N_B gives:

Failed to parse (Missing texvc executable; please see math/README to configure.): N_B = \frac{N_{A0}\lambda_A}{\lambda_B - \lambda_A} \left ( e^{-\lambda_A t} - e^{-\lambda_B t}\right ) .

Naturally this equation reduces to the previous solution, in the case B is a stable nuclide (λ_B = 0):

Failed to parse (Missing texvc executable; please see math/README to configure.): \lim_{\lambda_B\rightarrow 0} \left [ \frac{N_{A0}\lambda_A}{\lambda_B - \lambda_A} \left ( e^{-\lambda_A t} - e^{-\lambda_B t}\right ) \right ] = \frac{N_{A0}\lambda_A}{0 - \lambda_A} \left ( e^{-\lambda_A t} - 1 \right ) = N_{A0} \left ( 1- e^{-\lambda_A t} \right ),

as shown above for one decay. The solution can be found by the integration factor method, where the integrating factor is e^λ_Bt. This case is perhaps the most useful, since it can derive both the one-decay equation (above) and the equation for multi-decay chains (below) more directly.

Chain of any number of decays

For the general case of any number of consecutive decays in a decay chain, i.e. A₁ → A₂ ··· → A_i ··· → A_D, where D is the number of decays and i is a dummy index (i = _{1, 2, 3, ...D}), each nuclide population can be found in terms of the previous population. In this case N₂ = 0, N₃ = 0,..., N_D = 0. Using the above result in a recursive form:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\mathrm{d}N_j}{\mathrm{d}t} = - \lambda_j N_j + \lambda_{j-1} N_{(j-1)0} e^{-\lambda_{j-1} t}.

The general solution to the recursive problem are given by Bateman's equations^[8] :

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathrm{N_D} = \frac{N_1(0)}{\lambda_D} \sum_{i=1}^D \lambda_i c_i e^{-\lambda_i t} Failed to parse (Missing texvc executable; please see math/README to configure.): c_i = \prod_{j=1, i\neq j}^D \frac{\lambda_j}{\lambda_j - \lambda_i}

Alternative decay modes[link]

In all of the above examples, the initial nuclide decays into only one product. Consider the case of one initial nuclide which can decay into two products, that is A → B + C. We have for all time t:

Failed to parse (Missing texvc executable; please see math/README to configure.): N_A + N_B + N_C = N_\mathrm{total} = N_{A0},

in which,

Failed to parse (Missing texvc executable; please see math/README to configure.): - \frac{\mathrm{d}N_A}{\mathrm{d}t} = \lambda_A N_A,

Failed to parse (Missing texvc executable; please see math/README to configure.): - \frac{\mathrm{d}N_B}{\mathrm{d}t} = \lambda_B N_A,

Failed to parse (Missing texvc executable; please see math/README to configure.): - \frac{\mathrm{d}N_C}{\mathrm{d}t} = \lambda_C N_A,

so the relations follow in parallel:

Failed to parse (Missing texvc executable; please see math/README to configure.): - \frac{\mathrm{d}N_A}{\mathrm{d}t} = - \frac{\mathrm{d}N_B}{\mathrm{d}t} - \frac{\mathrm{d}N_C}{\mathrm{d}t} = \lambda_A N_A = N_A \left ( \lambda_B + \lambda_C \right ) = N_A \lambda_A = \lambda_A \left [ N_{A0} - \left ( N_B + N_C \right ) \right ],

indicating that the total decay constant is that of A, given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \lambda_A = \lambda_B + \lambda_C .

Solving this equation for N_A:

Failed to parse (Missing texvc executable; please see math/README to configure.): N = N_{A0} e^{-\lambda_A t} .

When measuring the production of one nuclide, one can only observe the total decay constant λ_A. The decay constants λ_B and λ_C determine the probability for the decay to result in products B or C as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): N_B = \frac{\lambda_B}{\lambda_A} N_{A0} \left ( 1 - e^{-\lambda_A t} \right ),

Failed to parse (Missing texvc executable; please see math/README to configure.): N_C = \frac{\lambda_C}{\lambda_A} N_{A0} \left ( 1 - e^{-\lambda_A t} \right ).

These perhaps seemingly disjionted results are consistent:

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} N_B + N_C & = \frac{\lambda_B}{\lambda_A} N_{A0} \left ( 1 - e^{-\lambda_A t} \right ) + \frac{\lambda_C}{\lambda_A} N_{A0} \left ( 1 -e^{-\lambda_A t} \right ) \\ & = \left ( \frac{\lambda_B}{\lambda_B + \lambda_C} + \frac{\lambda_C}{\lambda_B + \lambda_C} \right ) N_{A0} \left ( 1 -e^{-\lambda_A t} \right ) = N_{A0} \left ( 1 -e^{-\lambda_A t} \right ) \\ & = N_{A0} - N_{A0} e^{-\lambda_A t} = N_\mathrm{total} - N_A . \end{align}

Corollaries of the decay laws[link]

The solutions to the above differential equations are sometimes written using quantities related to the number of nuclide particles N in a sample, where L is Avagadro's constant,6.023×10²³, and A_r is the relative atomic mass number, and the amount of the substance is in moles.

• The activity: A = λN.
• The amount of substance: n = N/L.
• The mass: M = A_rn = A_rN/L.

Collecting these results together for convenience: N = A/λ = Ln = LM/A_r.

Equivalent ways to write the decay solutions, then, are as follows:

One-decay processes

The solution

Failed to parse (Missing texvc executable; please see math/README to configure.): N = N_0\,e^{-\lambda t} , \,\!

can be written:

Failed to parse (Missing texvc executable; please see math/README to configure.): A = A_0\,e^{-\lambda t} , \,\!

Failed to parse (Missing texvc executable; please see math/README to configure.): n = n_0\,e^{-\lambda t} , \,\!

Failed to parse (Missing texvc executable; please see math/README to configure.): M = M_0\,e^{-\lambda t} , \,\!

Notice how we can simply replace each quantity (on both sides of the equation), since they are directly proportional to N and so the constants cancel (constant at least for a particular nuclide).

Chain-decay processes

For the two-decay chain,

Failed to parse (Missing texvc executable; please see math/README to configure.): N_B = \frac{N_{A0}\lambda_A}{\lambda_B - \lambda_A} \left ( e^{-\lambda_A t} - e^{-\lambda_B t}\right ) ,

its almost as simple:

Failed to parse (Missing texvc executable; please see math/README to configure.): A_B = \frac{A_{A0}\lambda_B}{\lambda_B - \lambda_A} \left ( e^{-\lambda_A t} - e^{-\lambda_B t}\right ) ,

Failed to parse (Missing texvc executable; please see math/README to configure.): M_B = \frac{A_r \left ( \mathrm{B} \right ) M_{A0}\lambda_A}{ A_r \left ( \mathrm{A} \right ) \left ( \lambda_B - \lambda_A \right )} \left ( e^{-\lambda_A t} - e^{-\lambda_B t}\right ) ,

Failed to parse (Missing texvc executable; please see math/README to configure.): n_B = \frac{n_{A0}\lambda_A}{\lambda_B - \lambda_A} \left ( e^{-\lambda_A t} - e^{-\lambda_B t}\right ) .

Decay timing: definitions and relations[link]

Time constant and mean-life[link]

For the one-decay solution A → B:

Failed to parse (Missing texvc executable; please see math/README to configure.): N = N_0\,e^{-{\lambda}t} = N_0\,e^{-t/ \tau}, \,\!

the equation indicates that the decay constant λ has units of t^-1, and can thus also be represented as 1/τ, where τ is a characteristic time of the process called the time constant.

In a radioactive decay process, this time constant is also the mean lifetime for decaying atoms. Each atom "lives" for a finite amount of time before it decays, and it may be shown that this mean lifetime is the arithmetic mean of all the atoms' lifetimes, and that it is τ, which again is related to the decay constant as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): \tau = \frac{1}{\lambda}.

This form is also true for two-decay processes simultaneously A → B + C, inserting the equivalent values of decay constants (as given above)

Failed to parse (Missing texvc executable; please see math/README to configure.): \lambda = \lambda_B + \lambda_C \,

into the decay solution leads to:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{\tau} = \lambda = \lambda_B + \lambda_C = \frac{1}{\tau_B} + \frac{1}{\tau_C}\,

Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms (left) or 400 (right). The number at the top indicates how many half-lives have elapsed. Note the law of large numbers: with more atoms, the overall decay is less random.

Half-life[link]

A more commonly used parameter is the half-life. Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. For the case of one-decay nuclear reactions:

Failed to parse (Missing texvc executable; please see math/README to configure.): N = N_0\,e^{-{\lambda}t} = N_0\,e^{-t/ \tau}, \,\!

the half-life is related to the decay constant as follows: set N = N₀/2 and t = T_1/2 to obtain

Failed to parse (Missing texvc executable; please see math/README to configure.): t_{1/2} = \frac{\ln 2}{\lambda} = \tau \ln 2.

This relationship between the half-life and the decay constant shows that highly radioactive substances are quickly spent, while those that radiate weakly endure longer. Half-lives of known radionuclides vary widely, from more than 10¹⁹ years, such as for the very nearly stable nuclide ²⁰⁹Bi, to 10⁻²³ seconds for highly unstable ones.

The factor of ln(2) in the above relations results from the fact that concept of "half-life" is merely a way of selecting a different base other than the natural base e for the lifetime expression. The time constant τ is the e -1 -life, the time until only 1/e remains, about 36.8%, rather than the 50% in the half-life of a radionuclide. Thus, τ is longer than t_1/2. The following equation can be shown to be valid:

Failed to parse (Missing texvc executable; please see math/README to configure.): N(t) = N_0\,e^{-t/ \tau} =N_0\,2^{-t/t_{1/2}}. \,\!

Since radioactive decay is exponential with a constant probability, each process could as easily be described with a different constant time period that (for example) gave its "(1/3)-life" (how long until only 1/3 is left) or "(1/10)-life" (a time period until only 10% is left), and so on. Thus, the choice of τ and t_1/2 for marker-times, are only for convenience, and from convention. They reflect a fundamental principle only in so much as they show that the same proportion of a given radioactive substance will decay, during any time-period that one chooses.

Mathematically, the n^th life for the above situation would be found in the same way as above — by setting N = N₀/n, and substituting into the decay solution to obtain

Failed to parse (Missing texvc executable; please see math/README to configure.): t_{1/n} = \frac{\ln n}{\lambda} = \tau \ln n.

Example[link]

A sample of ¹⁴C, whose half-life is 5730 years, has a decay rate of 14 disintegration per minute (dpm) per gram of natural carbon. An artefact is found to have radioactivity of 4 dpm per gram of its present C, how old is the artefact?

Using the above equation, we have:

Failed to parse (Missing texvc executable; please see math/README to configure.): N = N_0\,e^{-t/ \tau},

where: Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{N}{ N_0} = 4/14 \approx 0.286,

Failed to parse (Missing texvc executable; please see math/README to configure.): \tau = \frac{T_{1/2}}{\ln 2} \approx 8267

years,

Failed to parse (Missing texvc executable; please see math/README to configure.): t = -\tau\,\ln\frac{N}{ N_0} \approx 10360

years.

Changing decay rates[link]

The radioactive decay modes of electron capture and internal conversion are known to be slightly sensitive to chemical and environmental effects which change the electronic structure of the atom, which in turn affects the presence of 1s and 2s electrons that participate in the decay process. A small number of mostly light nuclides are affected. For example, chemical bonds can affect the rate of electron capture to a small degree (in general, less than 1%) depending on the proximity of electrons to the nucleus in beryllium. In ⁷Be, a difference of 0.9% has been observed between half-lives in metallic and insulating environments.^[9] This relatively large effect is because beryllium is a small atom whose valence electrons are in 2s atomic orbitals, which are subject to electron capture in ⁷Be because (like all s atomic orbitals in all atoms) they naturally penetrate into the nucleus.

Rhenium-187 is a more spectacular example. ¹⁸⁷Re normally beta decays to ¹⁸⁷Os with a half-life of 41.6 × 10⁹ y,^[10] but studies using fully ionised ¹⁸⁷Re atoms (bare nuclei) have found that this can decrease to only 33 y. This is attributed to "bound-state β^- decay" of the fully ionised atom — the electron is emitted into the "K-shell" (1s atomic orbital), which cannot occur for neutral atoms in which all low-lying bound states are occupied.^[11]

A number of experiments have found that decay rates of other modes of artificial and naturally-occurring radioisotopes are, to a high degree of precision, unaffected by external conditions such as temperature, pressure, the chemical environment, and electric, magnetic, or gravitational fields.^{[citation needed]} Comparison of laboratory experiments over the last century, studies of the Oklo natural nuclear reactor (which exemplified the effects of thermal neutrons on nuclear decay), and astrophysical observations of the luminosity decays of distant supernovae (which occurred far away so the light has taken a great deal of time to reach us), for example, strongly indicate that decay rates have been constant (at least to within the limitations of small experimental errors) as a function of time as well.

Recent results suggest the possibility that decay rates might have a weak dependence (0.5% or less) on environmental factors. It has been suggested that measurements of decay rates of silicon-32, manganese-54, and radium-226 exhibit small seasonal variations (of the order of 0.1%), proposed to be related to either solar flare activity or distance from the sun.^[12][13][14] However, such measurements are highly susceptible to systematic errors, and a subsequent paper^[15] has found no evidence for such correlations in six other isotopes, and sets upper limits on the size of any such effects.

See also[link]

Notes[link]

References[link]

• "Radioactivity", Encyclopædia Britannica. 2006. Encyclopædia Britannica Online. December 18, 2006
• Radio-activity by Ernest Rutherford Phd, Encyclopædia Britannica Eleventh Edition

External links[link]

Look up radioactivity in Wiktionary, the free dictionary.

• The Lund/LBNL Nuclear Data Search – Contains tabulated information on radioactive decay types and energies.
• NUCLEONICA Nuclear Science Portal
• NUCLEONICA wiki: Decay Engine
• Nomenclature of nuclear chemistry
• Some theoretical questions of nuclear stability
• Specific activity and related topics.
• The Karlsruhe Nuclide Chart
• Monte Carlo Simulation of Radioactive Decay
• The Live Chart of Nuclides – IAEA
• Health Physics Society Public Education Website
• Beach, Chandler B., ed. (1914). " Becquerel Rays". The New Student's Reference Work. Chicago: F. E. Compton and Co.. Wikisource 
• Annotated bibliography for radioactivity from the Alsos Digital Library for Nuclear Issues
• Stochastic Java applet on the decay of radioactive atoms by Wolfgang Bauer
• Stochastic Flash simulation on the decay of radioactive atoms by David M. Harrison

Marina and the Diamonds
Marina and the Diamonds performing in Edinburgh on 2 November 2010
Background information
Birth name	Marina Lambrini Diamandis
Born	(1985-10-10) 10 October 1985 (age 26) Abergavenny, Monmouthshire, Wales
Genres	indie pop, pop, New Wave, electropop
Occupations	Singer-songwriter, musician poet,
Instruments	Vocals, keyboard, piano, glockenspiel, casio VL-tone, organ
Years active	2007–present
Labels	Neon Gold, 679, Chop Shop
Website	marinaandthediamonds.com

Marina Lambrini Diamandis^[1] (Greek: Μαρίνα-Λαμπρινή Διαμάντη, pronounced [ðʝaˈmadi];^[2] born 10 October 1985), better known by her stage name Marina and the Diamonds (sometimes stylised as Marina & the Diamonds), is a Welsh singer-songwriter.^[3][4] She rose to fame after reaching number two on the BBC Sound of 2010 poll list, coming second to Ellie Goulding. After releasing one private EP, Diamandis released her second extended play, The Crown Jewels EP, with help from Neon Gold Records, in 2009.^[5] Now signed to 679 Recordings, she released her debut full length studio album, The Family Jewels, followed by her third extended play, The American Jewels EP, in 2010. In 2011, Diamandis announced that she was working on her second album, Electra Heart, which was released in April 2012 and went to #1 in the UK and Ireland.

Her stage name, "Marina and the Diamonds", consists of Diamandis' first name and the translation of her surname which means "Diamonds" in Greek. Although "The Diamonds" is often mistakenly believed to refer to her backing band,^[6] it in fact refers to Diamandis' fans: she explains this on her Myspace page by saying "I'm Marina. You are the diamonds."^[7]

Diamandis' musical style ranges from keyboard-based ballads to more up-tempo New Wave-style songs with full band backing.^[4] She has cited a wide-range of influences such as Daniel Johnston, Blondie, The Distillers, Patti Smith, Tom Waits, Nirvana, PJ Harvey, Kate Bush, Britney Spears, Yann Tiersen, Elliott Smith, Dolly Parton and Madonna.^[8][9]

Background[link]

Diamandis was born in Abergavenny, Monmouthshire, Wales. Her father is Greek and her mother is Welsh,^[10] and brought up in the village of Pandy with her parents and her older sister.^[11] She attended Haberdashers' Monmouth School for Girls, of which she said "I sort of found my talent there... I was the one who always skived off choir, but I had an incredible music teacher who managed to convince me I could do anything."^[12] When her parents separated, Diamandis moved to Greece when she was sixteen years old to live with her father but returned to Wales two years later.^[11]

Diamandis moved to London at the age of eighteen where she attended dance school for only two months.^[6] Following this, in 2005 she took a one year singing course at Tech Music Schools.^{[citation needed]} Diamandis enrolled in a music degree at the University of East London, transferring in her second year of studies to Middlesex University, but later dropped out.^[13] She went for many auditions including the West End musical, The Lion King.^[14] Diamandis admitted that she auditioned for a reggae boy band, held by Virgin Records, in 2005 to try to make it into the music business. She said she was "delusional with drive" and ultimately decided to dress up in male attire to try to amuse the record label to sign her, but she was unsuccessful. However, she was called back by the record label a week later.^[15][16]

Diamandis has a synaesthetic condition that involves seeing musical notes and days of the week in different colours.^[17]

Musical career[link]

2005–2008: Early career[link]

Diamandis live at the NME Radar Tour

In 2005, Diamandis created the name "Marina and the Diamonds".^[18] When describing the origin of the name, she said:

I never envisaged a character, pop project, band or solo artist. I saw a simple group made up of many people who had the same hearts. A space for people with similar ideals who could not fit in to life's pre-made mould. I was terribly awkward for a long time! I really craved to be part of one thing because I never felt too connected to anybody and now I feel I have that all around me.^[18]

Early demos of Marina and the Diamonds' songs were self composed and produced on the Apple software application Garageband.^[14] Through Gumtree she found someone to produce a few tracks, for which she paid £500.^[19] These ended up on her debut extended play Mermaid Vs. Sailor EP which was released on 23 November 2007. The record was created on hand-made CD-Rs by Diamandis and sold through her MySpace page. An estimated seventy copies were sold overall.^[20]

In January 2008, Diamandis was first discovered by music scouter Derek Davies of Neon Gold Records. Davies booked Diamandis to open for Belgian-Australian singer Gotye later that year where Warner Music Group first saw her and ended up signing her in October 2008 to 679 Recordings.^[19]

Marina and the Diamonds performing at The Bell House in Brooklyn, New York.

Diamandis' debut single was a double a-side consisting of "Obsessions" and "Mowgli's Road" which was issued on Neon Gold Records in the United States on 19 November 2008, followed by her second extended play The Crown Jewels EP on 1 June 2009 featuring her second single "I Am Not a Robot".^[21] Her first major label single, a re-recording of "Mowgli's Road", was released on 13 November 2009 under 679 Recordings in the UK and through Atlantic Records in the USA. On 7 December 2009 she was listed on the longlist for the BBC Sound of 2010 poll,^[22] and on 7 January 2010 it was announced that she had taken second place.^[23]

[edit] 2009–2010: The Family Jewels

Marina and the Diamonds' debut album, The Family Jewels, was released in February 2010. It peaked at number five on the UK Albums Chart and was certified silver in the United Kingdom days before its release.^[24] A re-release of "Mowgli's Road" was released as the album's lead single in November 2009.^[25] However, the song "Hollywood" was released as the first major single from the album in February 2010.^[26] A re-release of "I Am Not a Robot" in April 2010 became the album's third single; Diamandis said she decided to re-release the song because "people seem to empathize and relate with the song, regardless of gender or age."^[27] "Oh No!" became the album's fourth single in August 2010,^[28] and "Shampain" became the fifth single in October 2010.^[29] She embarked on her first headlining tour on 14 February 2010, consisting of seventy dates around the United Kingdom, Ireland, mainland Europe, the United States and Canada.^[30]

Also during 2010, Diamandis collaborated with producer Benny Blanco and guitarist Dave Sitek in Los Angeles on new material which she described as "a really great opportunity for me as a songwriter. [We are] such a weird threesome—a combination of super pop and really indie".^[6]

In March 2010, Atlantic Records signed Marina and the Diamonds to Chop Shop Records in the United States.^[31][32] Before the album's American release in May 2010,^[33] Diamandis released her third extended play, The American Jewels EP, digitally and exclusively for the United States in March 2010.^[31][32] Diamandis made her North American debut on 14 March 2010 through a series of performances.^[34]

Marina and the Diamonds was nominated for Critics' Choice at the 2010 BRIT Awards^[35] and came fifth in SHREDnews' "Ten Artists To Watch in 2010" list in March 2010.^[36] She also won the award for Best UK & Ireland Act at the 2010 MTV Europe Music Awards.^[37]

[edit] 2011–present: Electra Heart

In a January 2011 interview, Diamandis announced that her second album would mainly be about female sexuality and feminism.^{[citation needed]} The same month, Diamandis was announced as a support act for the U.S. leg of Katy Perry's California Dreams Tour.^[38] Three early demos were leaked in early 2011, called "Sex, Yeah", "Living Dead" and "Jealousy", each showing a more pop sound.^[39] Diamandis recorded material with producers Cirkut, Guy Sigsworth, Labrinth, Greg Kurstin, Diplo, Dr. Luke, Stargate and Liam Howe.

In August 2011, Diamandis uploaded a video to her YouTube page titled "Part 1: Fear and Loathing". In an interview with Popjustice, she explained the concept of the album, titled Electra Heart after a character of her creation; she said the guise "epitomises and embodies the lies, illusions and death of American ideologies involved in the corruption of self [...] Electra Heart is the antithesis of everything that I stand for. And the point of introducing her and building a whole concept around her is that she stands for the corrupt side of American ideology, and basically that’s the corruption of yourself. My worst fear—that’s anyone’s worst fear—is losing myself and becoming a vacuous person. And that happens a lot when you’re very ambitious."^[40] The campaign's first single, "Radioactive" produced by Stargate, was released in October 2011 (reaching number twenty-five in the UK),^[41] followed by a demo of the song "Starring Role" in November^[42] and a video titled ♡ PART 3: "THE ARCHETYPES" ♡ in December.^[43] A track titled "Homewrecker" was issued as a free download to her mailing list subscribers.^[44]

Electra Heart was released in April 2012,^[45] preceded by the single "Primadonna" produced by Dr Luke, Diplo and Cirkut.^[46][47] "Primadonna" debuted at number eleven on the UK Singles Chart, becoming Diamandis' highest peaking single to date. "Power and Control" has been announced officially as the next single from the album.^[48]

Artistry[link]

Music style and influences[link]

Marina and the Diamonds performing on The Gem Tour in Birmingham, UK.

Marina and the Diamonds has been influenced by a wide-range of musicians from PJ Harvey to Britney Spears.^[8] Diamandis has also noted Daniel Johnston as one of her major influences saying:

He really opened me up to a whole new world of music and a whole new perception of what an artist is. For me, he really encouraged me because if you think of someone who has been spoon-fed pop, up until twenty-one years old, and you hear someone like Daniel Johnston you're like "God, this is terrible, but I love it." It sounds like a child has made it, like, the production is so all over the place. He's obviously got something very captivating here yet he doesn't fit the normal mould and people still love him. I thought "if he can do it then [so can I]," that's when I started to produce things myself and play live, even though I wasn't even great on the piano. It's all about emotion and if you have heart, people connect to that.^[49]

Diamandis calls herself a "DIY musician"^[49] and describes her sound as an alternative to mainstream pop music.^[8] In an interview with ClashMusic Diamandis said that she does not come from a musical background and explained "I probably have a bit of a different sound because I don’t really know what I’m doing".^[50] Lyrically, she says her music analyzes people and that if she wasn't a musician, she would be a psychologist.^[51]

Critics usually catalogue Marina and the Diamonds as a New Wave pop artist. In an interview with The Guardian she said, "I suppose I'm an indie artist with pop goals".^[9] Although Diamandis has asserted that she never tries to sound like any other artist or copy a genre of music, she has been compared to a variety of artists such as Kate Bush^[50] and most commonly Florence and the Machine.^[52] PopMatters commented on her vocal delivery and attitude saying it "has a tendency to overshadow the music, which is often melodically inventive, but we are rarely given the chance to realise this."^[53] The Guardian's Paul Lester wrote that "her songs are hard to fathom. They veer between simple keyboards-based ballads and more upbeat and catchy, quirky new wave-inflected numbers enhanced by percussion, guitar and drums."^[4]

Public image[link]

As well as her music, Marina and the Diamonds is also notable for her unique attire.^[54] When asked in an interview to describe her fashion style in three words, Diamandis said "vintage, cheerleader and cartoon".^[55] You can see an element of this style in the video for 'Oh No!' which was released in June 2010. She has praised model/DJ Leigh Lezark's fashion style and called Gwen Stefani her definitive style icon describing her image as "cartoonized but in a very fresh way".^[55] Diamandis has mentioned that she sometimes makes her own outfits with clothes she buys from charity shops.^[56] She also collects vintage cheer jackets.^[55] She has often been seen wearing clothes by Jean-Charles de Castelbajac,^[57] Laura Mackness,^[58] Beyond Retro,^[59] Motel Rocks,^[60] Jervoise Jackets^[61] amongst others. Diamandis has admitted that she would "like to do something in fashion, not designing, not one of those skanky celebrity lines, but being involved behind the scenes".^[11]

As part of Selfridges' "Sound of Music", Diamandis designed her own window display for the London Oxford Street branch in May 2010.^[62] She also appeared as a "live mannequin" for the display.^[63] Diamandis was featured on Vogue UK's official website throughout November 2010 for a popular sartorial section called "Today I'm Wearing", where she blogged her daily style choices for the fashion website.^[64] In December 2010, Diamandis announced on her Twitter that she would be the new face of the Max Factor make-up range Max Colour Effects.

Discography[link]

• 2010: The Family Jewels
• 2012: Electra Heart

Filmography[link]

• 2013: Homewrecker (Set to be released in Summer 2013)

Touring[link]

Marina and the Diamonds at The Wonder Bar in Asbury Park, NJ

In 2009, Marina and the Diamonds played at BBC Radio 1's Big Weekend in Swindon early in May 2009,^[3] Glastonbury Festival in June 2009,^[65] and the Reading and Leeds Festivals in August 2009.^[66]

In promotion for her album and "Hollywood", Diamandis performed at Brand New: 10 for 10 at London's Dingwalls,^[67] had an eleven minute 4Music special - 4Play: Marina and the Diamonds - on Channel 4,^[68] performed at T4's Outside-In Festival,^[69] New to Q Sessions^[70] in January 2010, was a musical guest on GMTV, Friday Night with Jonathan Ross, The Review Show in February 2010^[71] and Later... with Jools Holland and T4's Frock Me! in April 2010. She performed at the Isle of Wight Festival 2010 and Glastonbury Festival 2010 in June 2010 and is planned to appear at other music festivals across the United Kingdom, mainland Europe and North America.

Diamandis had already sold out the first leg of her first headlining tour, The Family Jewels Tour before the release of her debut album. Her entire tour currently consists of seventy dates across six legs around the United Kingdom, North America, Ireland and mainland Europe.^[30][72][73] Diamandis was accompanied by support acts Clock Opera and Alan Pownall for the first leg of her tour and Spark on The Gem Tour.^[74]

Headlining

• The Family Jewels Tour (2010 - 2011)
• Lonely Hearts Club Tour (2012)

Supporting

• California Dreams Tour (2011)
• Mylo Xyloto Tour (2011 - 2012)

Awards and nominations[link]

References[link]