The difference(s) between stable and unstable isotopes

Most chemical elements in the natural world consist of a mixture of isotopes.

By definition, an isotope is one two or more types of a specific chemical element having different numbers of neutrons in the nucleus, i.e. different relative atomic masses and different nuclear properties, but the same chemical properties.

From a historical perspective, the possibility of isotopes was first suggested in 1913 by Frederick Soddy, after studying radioactive decay chains that indicated about 40 different species referred to as radioelements (or radioactive elements) between uranium and lead. Soddy proposed that several types of atoms, differing in radioactive properties, could occupy the same place in the periodic table. In 1922, Frederick Soddy and Francis William Aston were awarded the Nobel Prize in chemistry for their work in discovering isotopes.

Stable isotopes are atoms with stable nuclei that do not emit radiation. They do not go through radioactive decay.

Unstable isotopes are essentially atoms having unstable nuclei that emit radiation. They are radioactive isotopes.

The first evidence for the existence of multiple isotopes of a stable, non-radioactive, element was found by J. J. Thomson in 1912 as part of his exploration into the composition of canal rays (or positive ions).

The sum of protons and neutrons and the ratio of protons to neutrons represent the two main influences on the stability of nuclei.

The unstable isotope of an element undergoing radioactive decay is called a radioisotope.

Stable as well as unstable isotopes have various applications in science, medicine, agriculture, …

The hydrogen element has three isotopes: protium ¹H with zero neutrons, deuterium ²H with one neutron, and tritium ³H with two neutrons. Protium is the most stable and abundant isotope, tritium the most unstable. Deuterium is stable but not too abundant, and is used as heavy water in laboratory applications.

The following image shows the three isotopes of hydrogen:

Image source: https://en.m.wikipedia.org/wiki/File:Hydrogen_Deuterium_Tritium_Nuclei_Schmatic-en.svg

A known example of application is isotopic labeling, the use of unusual isotopes as tracers or markers in chemical reactions. Normally, atoms of a given element are indistinguishable from each other. By using isotopes of different masses, even different nonradioactive stable isotopes can be distinguished by mass spectrometry or infrared spectroscopy. For example, in ‘stable isotope labeling with amino acids in cell culture (SILAC)’ stable isotopes are used to quantify proteins. If radioactive isotopes are used, they can be detected by the radiation they emit (this is called radioisotopic labeling).

A technique similar to radioisotopic labeling is radiometric dating: using the known half-life of an unstable element, one can calculate the amount of time that has elapsed since a known concentration of isotope existed. The most widely known example is radiocarbon dating, used to determine the age of carbonaceous materials.

Isotope geochemistry is an aspect of geology based upon the study of natural variations in the relative abundances of isotopes of various elements. Variations in isotopic abundance are measured by isotope ratio mass spectrometry, and can reveal information about the ages and origins of rock, air or water bodies, or processes of mixing between them.

Stable isotope geochemistry is largely concerned with isotopic variations arising from mass-dependent isotope fractionation, whereas radiogenic isotope geochemistry is concerned with the products of natural radioactivity.

As an application in medicine, it is possible to use or apply radioactive isotopes on diseased tissue. Some gamma ray emissions coming from isotopes can be pointed in the direction of the tissue to be destroyed. Cobalt-60 is an exampke of a very convenient isotope used for this kind of procedure.

Anemia is a condition where there is deficiency in, a low number of or not enough healthy red blood cells or hemoglobin to carry oxygen to the body’s tissues, resulting in shortness of breath and lack of energy. The radioisotope Cobalt-57 can be used as a tracer and as an agent for the diagnosis of pernicious anemia, and other conditions related to the imperfect or bad absorption of vitamin B-12. It is also useful for the calibration of radiometric equipment and medical gamma-cameras.

Radioactive iodine may be used to image the thyroid gland for medical and diagnostic applications and purposes.

Several forms of spectroscopy rely on the unique nuclear properties of specific isotopes, both radioactive and stable. For example, nuclear magnetic resonance (NMR) spectroscopy can be used only for isotopes with a nonzero nuclear spin.

The difference between quantum mechanics and quantum field theory, some basic explanations

Let’s start with some historical notes and considerations.

Quantum mechanics as a theory was gradually created and formulated during the first two decades of the 20th century. Important milestones include the 1900 quantum hypothesis by Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete “energy elements” such that each of these elements is proportional to the frequency ν with which each of them individually radiate energy, and then the interpretation of the photoelectric effect.

The origins of quantum field theory date to the 1920s and to the problem of creating a quantum theory of the electromagnetic field.
The first coherent and acceptable theory of quantum electrodynamics, which included the electromagnetic field and electrically charged matter as quantum mechanical objects, was created by Paul Dirac in 1927.

A further development for quantum field theory (or QFT) came with the discovery of the Dirac equation, which was originally formulated and interpreted as a single-particle equation similar to the Schrodinger equation, but the Dirac equation additionally satisfies both the Lorentz invariance, i.e. the requirements of special relativity, and the rules of quantum mechanics.

Theoretical formulations and advances took place during the 1940s and 1950s, resulting the introduction of renormalized quantum electrodynamics (or QED).

Quantum chromodynamics (QCD), the theory of the strong interaction between quarks mediated by gluons, was formulated diring the 1960s.

In the 1960s and 1970s it was shown that the weak nuclear force and quantum electrodynamics could be merged into a single electroweak interaction.

The Standard Model of particle physics, the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles, is a paradigm of a quantum field theory for theorists, exhibiting a wide range of physical phenomena.

Quantum field theory is a quantum mechanical theory. In this theory, fields with quantized normal modes of oscillation represent particles. So particles are regarded as excitations of quantum fields filling all of space. Relativistic theories of quantized fields depict the interactions between elementary particles.

In general, quantum field theory is a theoretical framework combining classical field theory, special relativity, and quantum mechanics. It is used to build physical models of subatomic particles (in relation to particle physics) and quasi-particles (in relation to condensed matter physics).

Below is a helpful description and explanation of quantum field theory, taken from the book A Modern Introduction to Quantum Field Theory, by Michele Maggiore:

“Quantum field theory is a synthesis of quantum mechanics and special relativity, and it is one of the great achievements of modern physics. Quantum mechanics, as formulated by Bohr, Heisenberg, Schrodinger, Pauli, Dirac, and many others, is an intrinsically non-relativistic theory. To make it consistent with special relativity, the real problem is not to find a relativistic generalization of the Schrodinger equation. Actually, Schrodinger first found a relativistic equation, that today we call the Klein–Gordon equation. He then discarded it because it gave the wrong fine structure for the hydrogen atom, and he retained only the non-relativistic limit. Wave equations, relativistic or not, cannot account for processes in which the number and the type of particles changes, as in almost all reactions of nuclear and particle physics.[…] Furthermore, relativistic wave equations suffer from a number of pathologies, like negative-energy solutions.

A proper resolution of these difficulties implies a change of viewpoint, from wave equations, where one quantizes a single particle in an external classical potential, to quantum field theory, where one identifies the particles with the modes of a field, and quantizes the field itself. The procedure also goes under the name of second quantization.

The methods of quantum field theory (QFT) have great generality and flexibility and are not restricted to the domain of particle physics. In a sense, field theory is a universal language, and it permeates many branches of modern research. In general, field theory is the correct language whenever we face collective phenomena, involving a large number of degrees of freedom, and this is the underlying reason for its unifying power. For example, in condensed matter the excitations in a solid are quanta of fields, and can be studied with field theoretical methods. An especially interesting example of the unifying power of QFT is given by the phenomenon of superconductivity which, expressed in the field theory language, turns out to be conceptually the same as the Higgs mechanism in particle physics. As another example we can mention that the Feynman path integral, which is a basic tool of modern quantum field theory, provides a formal analogy between field theory and statistical mechanics, which has stimulated very important exchanges between these two areas.”

For additional info and details about these topics, the following links can be viewed or consulted:

Differences between principles of QM and QFT

What is the difference between QM and non-relativistic QFT

Formalism of Quantum Field Theory vs Quantum Mechanics