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Atomic nuclei: elements, isotopes, isomers

An atom consists of a nucleus and electrons moving around it (they are often called orbital electrons). Atomic nucleus consists of protons and neutrons. The number of protons in an atomic nucleus determines the chemical element, and the number of neutrons in the nucleus determines the element’s isotope.

For example, the nucleus of the element Helium has 2 protons (therefore, Helium’s atomic number in the periodic table is 2), and its most common isotope has 2 neutrons, i.e. 4 nucleon total (collective name for protons and neutrons) and its symbol is  , or He-4, i.e. Helium-4 (4 is the nucleus mass number).

In addition, an isotope’s atomic nucleus may have greater energy in relation to its so-called ground state, the lowest-energy state of that nucleus. Different energy states of an isotope’s atomic nucleus are called isomers of that isotope.

Nuclides and radionuclides; radioisotopes

To give a description of an atomic nucleus which includes the number of protons, the number of neutrons and the energy state of the nucleus – we use the term nuclide. For example, the nuclei of different elements are different nuclides, the nuclei of different isotopes of an element are different nuclides, and the nuclei of different energy states (i.e. different isomers) of an isotope are different nuclides.

When a nuclide is unstable, i.e. if it has radioactive properties (to spontaneously change into a different nuclide, or split into different nuclides), it is called a radionuclide.

The term radioisotope is frequently used for unstable isotopes without metastable isomers.

Alpha radiation, alpha emitters

Alpha radiation consists of alpha particles emitted from radioactive atomic nuclei during alpha decay. An alpha particle is identical, composition-wise, to the atomic nucleus of Helium-4. Radioactive nuclei emitted by alpha particles are called alpha emitters. They were named before the structure of alpha particles was known.

Alpha radiation is the least penetrating type of radiation: in air, it penetrates only several centimeters, and is stopped by a sheet of paper. This means that alpha particles give all their energy in a very short path through matter, which makes them especially dangerous in living tissue (see equivalent dose). However, real damage is caused only if the alpha emitters are introduced into the organism (through food, drink or breathing), because the dead surface layer of the skin prevents it from entering through skin.

Beta radiation, beta emitters

Beta radiation consists of beta particles emitted from radioactive atomic nuclei during beta minus decay. A beta particle is an electron created during beta minus decay in the nucleus and ejected from it at great speed. It was named before it was established that a beta particle is actually an electron. Also, beta plus decay still hadn’t been discovered so the name “beta decay” was used.

During beta plus decay a positron is created in the nucleus instead of an electron. However, after exiting the nucleus, the positron reacts with one of the orbital electrons, turning both of them into gamma radiation. That is why radioactive materials don’t emit “beta plus” radiation (which would consist of positrons).

Radioactive nuclei that emit beta radiation are called beta emitters.

Beta radiation is more penetrating than alpha radiation, but not dramatically more so. In air, it penetrates several meters, and is stopped by aluminum foil or thin plastic. However, it can penetrate the dead surface layer of the skin and damage deeper live skin layers. Beta emitters are the most harmful if introduced into the organism (through food, drink or breathing), but much less than alpha radiation (see equivalent dose).

Gamma radiation, gamma photons

Gamma radiation consists of electromagnetic waves of shortest wavelengths, i.e. high-frequency and high-energy photons. Photons are non-material particles that make up electromagnetic waves, which is why we say colloquially that photons are pieces (quanta) of energy of electromagnetic waves. Energy of an individual photon is equal to the wave frequency.

Gamma radiation from radioactive decays typically has wavelengths approximately a million times shorter than visible light, therefore these gamma photons have an energy approximately a million times greater than the visible light photons. Atomic nucleus emits one gamma photon during each transition from higher-energy state to lower-energy state (unless it doesn’t get rid of excess energy in some other way, see for example internal conversion).

Gamma radiation is a term generally used for electromagnetic radiation from nuclear reactions (and radioactive decay) and for electromagnetic radiation resulting from annihilation, as well as for electromagnetic radiation of similar or higher frequencies coming to Earth from space (part of cosmic radiation) whose mechanism of origin is often unknown. The name was introduced at the time of discovery of radioactivity, when the nature of radiation was still unknown.

Gamma radiation range isn’t strictly delimited from X-radiation range, which generally extends towards lower frequencies. Traditionally, the distinction is made based on the origin of radiation: usually the term X-radiation is used for electromagnetic radiation from processes of electrons changing their energy, and gamma radiation for nuclear processes. For example, gamma radiation of Technecium-99m is identical to same-frequency X-radiation generated in a diagnostic X-ray machine.

Gamma radiation is much more penetrating than alpha or beta radiation, especially if it consists of high-energy photons. Moreover, it is not stopped completely in a material, instead it gradually weakens. For example, it takes a layer of lead approximately 0.7 cm thick to reduce the intensity of gamma radiation of Caesium-137 in half, and a layer approximately 5 cm thick to reduce the intensity of radiation to below 1%.

Alpha decay

During alpha decay, the radioactive nucleus emits a particle traditionally called an alpha particle, i.e. the atomic nucleus of Helium-4 (consisting of 2 protons and 2 neutrons). That is why the new nucleus, created in the transformation of the previous radioactive nucleus, has 2 protons and 2 neutrons less.

In most types of radioactive nuclei decaying in alpha decay, the newly created nucleus has an excess of energy that it gets rid of by emitting one or more gamma photons. This is why gamma radiation frequently occurs contemporaneously with alpha radiation (see metastable isomers).

Depending on the type of the preceding nucleus (ancestor), the newly formed nuclei (descendants) may themselves be radioactive and decay in the same or a different type of decay.

Beta decay

There are two types of beta decay, beta minus and beta plus, and the term “beta decay” was originally used to describe beta minus decay, which was the first to be discovered.

In beta minus decay, the radioactive nucleus emits one electron, which was named beta-particle at a time before it was discovered that it was an electron and that there was another type of beta decay. There are no electrons in the atomic nucleus; during decay, one of its neutrons turns into a proton and an electron (keeping the overall charge). The electron gets released from the nucleus while the proton stays in it, so the nucleus doesn’t change its mass number but its charge increases by one, i.e. the nucleus crosses into the next element of the periodic table.

It was later discovered that one neutrino (an electron antineutrino, to be precise) is also created in beta minus decay, a neutral particle of insignificant rest mass (if any at all) which easily passes through matter with no effect, therefore it is insignificant when describing radiation.

In most types of radioactive nuclei decaying in beta minus decay, the newly formed nucleus has an excess of energy that it gets rid of by emitting one or more gamma photons. This is why gamma radiation frequently occurs contemporaneously with alpha radiation (see metastable isomers).

During beta plus decay, the radioactive nucleus emits one positron, which is the antiparticle of the electron (positron is the traditional name for an antielectron). Antielectron has the same mass (and some other properties) as an electron, but opposite charge. The key property of the matter - anti-matter pair is that when they collide they turn into gamma radiation (this is called annihilation). This is why the emitted positron, together with some of the neighboring orbital electrons it will come in contact with after it gets released from the nucleus, turns into two gamma photons, therefore the beta plus radioactive material emits gamma radiation.

Since there are no protons in an atomic nucleus, during beta plus decay one of its protons turns into a neutron and a positron (keeping the overall charge). The positron gets expelled from the nucleus and the neutron stays in it, therefore the nucleus doesn’t change its mass number but its charge decreases by one, i.e. the nucleus crosses into the previous element of the periodic table.

One neutrino (an electron neutrino, to be precise) is also created in beta plus decay, a neutral particle of insignificant rest mass (if any at all) which easily passes through matter with no effect, therefore it is insignificant when describing radiation.

In most types of radioactive nuclei decaying in beta plus decay, the newly formed nucleus has an excess of energy that it gets rid of by emitting one or more gamma photons. This is why this emission frequently occurs almost contemporaneously with positron emission, i.e. gamma radiation created during its annihilation (see metastable isomers).

Depending on the type of the beta plus radioactive nucleus, a percentage of beta plus decay happens as a so-called electron capture. In that case, the nucleus, instead of emitting a positron, absorbs (“captures”) the closest orbital electron.

Depending on the type of the preceding nucleus (ancestor), the nuclei formed during beta decay (descendants) may themselves be radioactive and decay in the same or a different type of decay.

Gamma decay, isomeric transition, metastable isomers

Gamma decay is a process in which the atomic nucleus goes from excess-energy state to a lower-energy state by emitting a gamma photon. The nucleus remains the same isotope, but it is no longer the same isomer.

During alpha decay, and especially beta decay, the newly formed nuclei often have an excess of energy (they are created as isomers in excited state). They usually get rid of this excess by gamma emission which is practically contemporaneous with alpha or beta emission (e.g. within one millionth of a billionth of a second). Some types of newly formed nuclei, however, keep that excess of energy for longer, and cross into lower state later: an atomic nucleus in this excited state is called a metastable isomer.

With these metastable isomers, gamma emission is timewise clearly separated from alpha or beta emission preceding it, and the name “gamma decay” clearly makes sense because the transition to a lower-energy state happens in accordance with the law of radioactive decay.

Gamma decay is one of two forms of isomeric transition. Other than with gamma decay, a metastable isomer can also get rid of excess energy by giving it to an orbital electron. This form of isomeric transition is called internal conversion. The orbital electron thusly emitted from an atom does not count as beta radiation (nor is it accompanied by neutrino emission).

For example, the metastable Technetium-99m is widely used in medical diagnostic procedures. The isomeric transition of Technetium-99m into the basic isomer Technetium-99 happens with a 6 hour half-life, as gamma decay in 88% of the cases, and in 12% as internal conversion.

Fission and fission products; chain fission

Fission is when a heavy atomic nucleus splits into two equal parts, producing emission of several neutrons, called fission neutrons (usually two to three neutrons), and gamma radiation. The newly formed atomic nuclei, called fission products, move at very high speeds after fission (they have a large amount of energy). One fission releases approximately a hundred million times more energy than one chemical reaction occurring during coal combustion.

Fission as a form of radioactive decay of some types of naturally unstable atomic nuclei is also called spontaneous fission. This type of spontaneous change of the nucleus, which is most deserving of the term “decay”, was detected several decades after radioactivity was discovered. Spontaneous fission, as well as other types of spontaneous decay, happens in accordance with the law of radioactive decay. For example, in Uranium-238 alpha decay dominates with a half-life of approximately 4.5 billion years, and simultaneously spontaneous fission is happening with an approximately two million times longer half-life (per 1 gram of Uranium-238, 1 fission occurs per 2.5 minutes, and 750,000 alpha decays per 1 minute).

In some types of atomic nuclei an instantaneous fission may be caused by a neutron striking the nucleus; this type of fission is called induced fission. If the newly formed fission neutrons cause further induced fissions in the same manner, and their fission neutrons as well, and so on, a chain reaction called chain fission happens.

In a nuclear bomb explosion, chain fission catches a very large number of atomic nuclei in a very short period of time. In a nuclear reactor, chain fission is controlled, usually by controlling fission neutrons. This type of fission is called controlled fission.

Radioactivity or activity; the Becquerel; specific activity

The term radioactivity in qualitative terms applies to the phenomenon, i.e. property of spontaneous change (decay) of unstable atomic nuclei. Natural materials on Earth contain more or less of these unstable nuclei that decay more or less fast. The same term is used for the quantitative description of the phenomenon: radioactivity (or activity for short, if it is clear from the context what type of activity it is) of a body or an amount of a substance (some sample) is equal to the number of radioactive decays in that sample per unit of time. The measuring unit of activity, the becquerel (Bq), equals one decay per second.

For example, natural radioactivity of an average person is over 4,000 Bq, meaning there are over 4,000 radioactive decays occurring in the human body each second. Radioactivity of all the oceans on Earth is estimated to approximately ten thousand billion Bq, and the entire Earth’s core to approximately a thousand times that.

The old unit of activity, the curie (Ci), which equaled 37 billion Bq, was defined as the activity of 1 gram of Radium-226.

The activity of a sample of N radionuclides with the decay constant λ is  A = λN .

When describing the radioactivity of a relatively homogenous material, activity per unit of mass (e.g. Bq/kg) or activity per unit of volume (e.g. Bq/m3) is usually stated. The terms specific activity or activity concentration are used for both.

Law of radioactive decay, decay constant, half-life

Law of radioactive decay describes how radioactive decay happens over time: the number of unstable nuclei in a sample, that haven’t decayed yet, exponentially decreases over time.

The same can be reformulated as follows: after a certain time interval, which is called half-life, the number of undecayed nuclei from the beginning of the interval is reduced in half, and after another such interval the number of remaining undecayed nuclei is reduced in half, etc.

This means that – starting from some initially determined number of undecayed nuclei – a half remains after one half-life, a quarter remains after two half-lives, an eighth remains after three half-lives etc. Half-life is determined (through measuring) for a certain type of radionuclides, but also for a certain manner of decay, if that type decays in more manners.

Additional explanations of the law, as well as mathematical descriptions, are set out below.

Radioactive or spontaneous decay of unstable atomic nuclei and other unstable particles is an accidental process, meaning that the timing of the event cannot be predicted for an individual particle, only for a number of homogeneous particles can it be statistically predicted how many of them will decay at a certain time. If the moment of decay of individual homogeneous particles were determined in advance they wouldn’t be homogeneous, they would have different half-lives. Instead, only the expected or mean lifetime can be determined for a certain particle (calculated by dividing the half-life of the type by ln2).

For homogeneous particles, i.e. nuclei, and for certain type of their decay, the probability of a certain particle decaying in one unit of time (e.g. second) can be determined. This probability is called the decay constant and its symbol is λ. It follows that: the number of particles that will decay in a very short time interval (precisely: in an infinitesimal interval) is equal to the product of the decay constant, that time interval and the number of particles at the beginning of that interval (mathematically: dN = - λNdt).

The aforementioned theorem represents one form of the law of radioactive decay. From that form two other mathematical forms are deduced which are used more often in calculations:


In these formulas, N is the number of particles, i.e. nuclei, that haven’t yet decayed at the t moment, and N0 is the number of particles at the t=0 moment. Half-life T is related to the decay constant λ.

Doses: absorbed, equivalent, effective

Radioactive and other ionizing radiation (such as X-radiation, cosmic radiation etc.) create ion pairs in matter (through different mechanisms, e.g. directly ejecting electrons from atoms or molecules). In live tissue this can cause a disorder in the function of cells or their important components (such as genetic material). Besides direct tissue damage, and even death of the irradiated organism in case of big doses, biological effects can be long-term, such as malign processes and disorders in progeny caused by damage to the reproductive cells.

The radiation dose system (absorbed, equivalent, effective) was conceived to determine health risks based on the energy absorbed.

Absorbed dose equals the ratio of the absorbed radiation energy in a tissue and that tissue’s mass. The gray (Gy) equals absorbed dose of 1 joule per kilogram. (When describing differences in radiation in different parts of the tissue the ratios of absorbed energy and mass need to be calculated for very small tissue volumes, from point to point.)

However, biological effects of radiation do not depend on the absorbed dose alone, they also depend on the type of radiation and the type of irradiated tissue (i.e. organ).

Equivalent dose calculates differences in damaging properties of individual types of radiation. It is calculated by multiplying the mean absorbed dose in a tissue or an organ with the number called the radiation weighting factor. For example, the factor is the smallest in beta i gama radiation and it equals 1, and it is the greatest for alfa radiation and it equals 20, while for neutrons it depends on their speed. The equivalent dose unit is called the sievert (Sv), to stress the difference from the absorbed dose (even though it has the same structure, joule per kilogram).

Effective dose takes into account different sensitivities to radiation of certain tissues. It is calculated for the entire body (organism) by multiplying each equivalent dose for each tissue with its radiation weighting factor and then adding them up. For example, bone marrow has a 0.12 radiation factor, and skin 0.01. The unit for effective dose is the same as for equivalent dose (Sv).

Effective dose represents overall risk that radiation poses on a person’s health. For example, one-time radiation of 5 Sv causes death in approximately 50% of irradiated people within 30 days. A 1 Sv dose may cause temporary symptoms of radiation sickness, and turn into cancer 5% of the time.

Small doses, such as are considered in RW management, are expressed in thousandths of Sv, i.e. millisieverts (mSv), and the risk such doses pose generally comes down to a small probability of cancer. For doses under 10 mSv per year this risk hasn’t been proven but, for radiation protection regulation purposes, a linear extrapolation of risk from larger doses is generally accepted (ICRP and IAEA recommendations, EU and national legislation).

Spent nuclear fuel

Nuclear fuel is a term used for radioactive material in which a controlled chain fission is occurring in a nuclear reactor. Over time this fission process will change the composition and concentrations of radionuclides in fuel in such a way that it will no longer be usable for continuing the process the way it was designed. That is when the fuel gets the name spent nuclear fuel, abbreviation SNF, and is taken out of the reactor and replaced with new fuel. Due to fission products piling up in the fuel, radioactivity of spent fuel at the moment of it being taken out of the reactor is usually approximately a billion times greater than it was when it was first started being used.

At the Krško Nuclear Power Plant, nuclear fuel used is enriched Uranium in the form of Uranium dioxide (which has approximately 5% of Uranium-235, instead of the 0.71% that is usually present in natural Uranium; the rest is Uranium-238). The fuel cycle is 18 months, after which half of the fuel in the reactor gets replaced, meaning that the fuel’s useful life is around 3 years.

Agreement, Convention, Treaty

Agreement is a mutual understanding between two parties. It usually leads to the signing of a contract.

Convention is an agreement between two countries, less formal than a treaty.

Treaty is an official agreement between two or more countries on matters of public benefit.


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