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 importance of using mathematics in the sciences, and some cases where math is not needed in physics

Simply put, without mathematics there is no exact science: no physics, no chemistry, no (scientific and accurate ) biology or medicine …
Mathematics is an essential component of the scientific method; data collection and observation and hypotheses are sustained by relevant mathematical models, and mathematics is the language in which the Natural or Physical World is written, as Galileo once said.
Can anyone imagine physics without numbers , or without derivatives, integrals, equations , tensors, geometrical figures, etc ? Physics would be a barren field of study based on verbal statements with no precision.
The xkcd image below expresses or conveys the importance of mathematics:

Math & the sciences

All the exact sciences are useful and important, but they all need and use mathematics.
That being said, there are a few cases or circumstances where (as an exception) mathematics may temporarily not be needed in theoretical physics.
When a teacher is explaining general concepts in (theoretical) physics to students who are beginning to learn physics, he may not use mathematics.
When a scientist or physicist is giving a lecture to a general audience, he may qualitatively describe physical theories and phenomena without using mathematics.
Similarly, when a scientist writes a popularization book about physics, he/she may use words (and some images) to present or explain concepts and topics in physics, without mathematics.
When one is imagining or mentally elaborating a thought experiment, considering some hypothesis, theory, or principle for the purpose of thinking through its consequences and repercussions, mathematics is generally not used.
When observing a physical phenomenon (with the naked eye or without instruments) for the first time, or when conducting general qualitative observations, mathematics may not be used, but math will be used afterwards to collect, interpret and classify data and to formulate or build a coherent theory.
The above were particular instances of mathematical equations, formulas and tools temporarily not being used or needed in (theoretical) physics.

---

Here are some additional thoughts or remarks about math, physics, and the people who work or “dabble” with these topics or disciplines.

A mathematical theory that is coherent, logical and self-consistent can be regarded as beautiful. Mathematical shapes, curves, solids and surfaces can also be described as “beautiful”. However consistency, coherence and beauty (or elegance) are not enough in relation to physics.

Physical theories must be coherent and follow the rules of the scientific method, which means they use correct and adequate mathematical tools and models, but they also rely on observations, on scientific data, and they must be testable and experimentally verified.

Conceptions, criteria and/or perceptions of beauty or of what is considered beautiful may change with time with regard to science. Some perceptions might be personal, subjective or philosophical.

The tendency in physics during recent years or during the last few decades to formulate sophisticated theories that are regarded as “beautiful” but are difficult to test or verify has sometimes lead to stagnation and to a counterproductive lack of progress.

Interdisciplinary or multidisciplinary knowledge is always possible and helpful. A physicist could find or elaborate the necessary or appropriate math to be used in a physical theory or in theoretical physics, but this depends on the prior knowledge and skills the physicist has in relation to both math and physics.
Moreover, it would be beneficial if people who are known as mathematicians do not get haughty or boastful with others, and the educational methods, frameworks and systems within which mathematics and the sciences are taught ought to be reassessed regularly and reformed when or if necessary.