Isotopes
Isotopes are nuclear forms of the same element: the proton number is unchanged while the neutron number differs. The change affects mass and sometimes nuclear stability while leaving electronic chemistry nearly the same.
Notation and identity
Reading A and Z
A nuclear species is written AZX. X is the element symbol, Z is the proton number and A is the mass number. For 3717Cl, the nucleus contains 17 protons and 37 − 17 = 20 neutrons. The 17 already identifies chlorine; the 37 identifies this isotope.
Because the symbol fixes Z, the lower number is often omitted in ordinary writing: chlorine-37 or ³⁷Cl is enough.
Nuclide and isotope
A nuclide is one specific nuclear species. 12C and 13C are two nuclides. Calling them isotopes highlights their relationship: they belong to the same element because they have the same proton number.
Two nuclei can share the same mass number and still belong to different elements. In that case they are not isotopes of each other.
Isotope chemistry
Neutral isotopes of one element have the same number of electrons and essentially the same electronic structure. That is why 12CO₂ and 13CO₂ undergo the same basic reactions and why isotopes occupy one place in the periodic table.
Nearly the same is not exactly the same. Changing nuclear mass changes vibrational frequencies and can slightly alter reaction rates or equilibria. These isotope effects are especially conspicuous for hydrogen because replacing 1H by deuterium almost doubles the nuclear mass.
Mass number and measured mass
The mass number A is an integer count of protons and neutrons. The actual isotopic mass is a measured quantity expressed in unified atomic mass units, u, and is usually not an integer. 13C has mass number 13, but its measured isotopic mass is slightly greater than 13 u.
The mismatch reflects the actual masses of protons, neutrons and electrons and the nuclear binding energy of the assembled atom. Nuclear binding changes mass through E = mc².
Stability and abundance
The nucleus is held together by the strong interaction, while protons also repel one another electrically. Neutrons strengthen nuclear binding without adding Coulomb repulsion. The favourable neutron-to-proton balance therefore shifts as nuclei become heavier.
That balance is not the whole story. Nuclear shell structure, pairing and total binding also matter. Nuclei outside a favourable stability region can lower their energy through radioactive transformations such as beta decay or alpha decay.
Isotopic abundance is the fraction of atoms belonging to a particular isotope. Textbook tables often give one convenient percentage, but real natural materials can have slightly different isotope ratios depending on their origin and history.
Evaporation, condensation, diffusion, mineral formation and biological processes can all fractionate isotopes. For several elements, standard atomic weights are therefore expressed as intervals rather than one exact value valid for every normal terrestrial sample.
Atomic weight and measurement
The atomic weight of an element reflects both isotopic masses and their proportions. In a simple two-isotope system:
average atomic mass = m₁x₁ + m₂x₂, with x₁ + x₂ = 1.
This is a population-weighted average. It does not mean that an individual chlorine atom with a mass of 35.45 u is the typical physical atom. Each atom is one isotope or another.
Chlorine weighted average
Take an illustrative sample containing 75.78% 35Cl with isotopic mass 34.9689 u and 24.22% 37Cl with mass 36.9659 u:
(0.7578 × 34.9689) + (0.2422 × 36.9659) ≈ 35.45 u.
The result lies between the isotope masses and closer to 35Cl because that isotope dominates the sample. Enrich the material in 37Cl and the average mass rises even though every atom remains chlorine.
Mass spectrometry
Mass spectrometry separates ions according to their mass-to-charge ratio m/z. Isotopes of the same element have almost identical chemistry but different masses, so properly resolved isotope peaks can reveal composition.
Molecular mass spectra also carry isotope patterns. Molecules containing chlorine, bromine or several carbon atoms can produce characteristic clusters because different isotope combinations have slightly different masses.
Isotope ratios
Lighter and heavier isotopes do not behave perfectly identically. Evaporation, condensation, diffusion, biochemical reactions and mineral formation can therefore shift isotope ratios slightly. This is isotope fractionation.
The differences may be small, but modern measurements can resolve them. Isotope ratios can therefore preserve information about a process: water-cycle history, biological carbon pathways, mineral formation conditions or the origin of a material.
Small isotope-ratio differences are commonly reported relative to a reference:
δ = [(Rsample/Rreference) − 1] × 1000 ‰
R may be a ratio such as 13C/12C. A positive δ means the sample has a higher heavy-to-light isotope ratio than the reference; a negative value means lower. The reference must always be stated because δ is relative.
Applications
Carbon
12C defines the modern atomic-mass reference. 13C is stable and widely used as a tracer and in structure analysis. 14C is radioactive and can act as a clock for carbon that has exchanged with the atmosphere or biosphere.
These are not different carbon chemistries. They are nuclear variants of the same element whose mass and stability create different experimental opportunities.
Dating
For one radionuclide, individual decays are unpredictable but a large population follows N(t) = N₀e−λt, with T½ = ln 2 / λ. That statistical regularity makes radiometric dating possible.
A measured isotope ratio is not automatically an age. Initial conditions, parent and daughter behaviour, contamination and whether the system remained effectively closed must all be considered.
Tracers
A tracer only needs to be distinguishable. Enriching a compound in 13C, 15N or 18O allows its atoms to be followed through a reaction, an organism or an environmental reservoir while preserving nearly the same chemistry.
Natural isotope ratios can likewise distinguish sources of carbon, trace groundwater, help reconstruct aspects of past climate and reveal food-web relationships.
Medicine
Radioactive decay can be detected from outside the body or can deposit energy in tissue. Selected radionuclides are therefore useful in diagnostic imaging and therapy. A useful isotope must combine the right decay mode, radiation, half-life and chemistry.
A half-life that is too long can give unnecessarily persistent activity; one that is too short may decay before imaging or treatment is complete. Nuclear physics and chemical targeting have to work together.
An enriched material contains a larger fraction of one isotope than a reference or natural material. Enrichment does not change Z, so it does not turn one element into another. It changes the statistical isotopic composition of a collection of atoms.
Exercises
Nuclear composition
For 5826Fe, Z = 26, so there are 26 protons. The neutron number is N = A − Z = 58 − 26 = 32. Another iron atom with 30 neutrons is still iron because Z is still 26; it is 56Fe.
Weighted average
An element has two isotopes: 10.0 u at 20.0% and 11.0 u at 80.0%. Calculate the average atomic mass.
Solution
(0.200 × 10.0) + (0.800 × 11.0) = 10.8 u.