The nuclear model of the atom

An atom is a particle of an element that keeps the chemical identity of that element and has a central nucleus with electrons outside it. A nucleus is a tiny, dense, positively charged region at the centre of an atom that contains protons and neutrons. “Tiny” is doing real work here: most of the atom is space, while almost all of its mass sits in the nucleus.

A subatomic particle is a particle smaller than an atom that forms part of atomic structure. In this topic, the three subatomic particles are protons, neutrons and electrons. A proton is a positively charged subatomic particle found in the nucleus. A neutron is an uncharged subatomic particle found in the nucleus. An electron is a negatively charged subatomic particle occupying the space outside the nucleus. A nucleon is a proton or neutron in the nucleus.

Rutherford’s gold foil experiment gives the classic evidence for the nuclear model. Most alpha particles went straight through the foil, so atoms must be mostly empty space. Some alpha particles were deflected, which showed that the positive charge is concentrated rather than spread out. A very small number bounced back. That only fits if the positive region is also very dense and massive compared with the alpha particle’s path.

Scientific models simplify reality in a useful way. When you draw an atom with a visible nucleus, the drawing is not to scale: a typical atom has a diameter of about 1 × 10⁻¹⁰ m, while the nucleus is roughly 100 000 times smaller in diameter. So a nuclear model diagram helps us think, but it should not be treated like a photograph of the atom.

Relative charge and relative mass

For IB, you need the relative charges and relative masses of the three subatomic particles:

The elementary charge is the magnitude of the charge on a single proton or electron, equal to about 1.602 × 10⁻¹⁹ C. We usually write relative charges as +1 for a proton and −1 for an electron, rather than using the actual charge in coulombs. Since the electron’s mass is so small compared with a proton or neutron, ordinary mass-number calculations treat it as negligible. Actual masses and charges are in the data booklet.

Atomic number, mass number and nuclear symbols

The atomic number is the number of protons in the nucleus of an atom. The mass number is the total number of protons and neutrons in the nucleus of an atom. Atomic number identifies the element: a nucleus with 6 protons is carbon; one with 79 protons is gold. This gives the first link to the periodic table. Elements are arranged in order of increasing atomic number, so atomic number fixes an element’s position in the table.

A nuclear symbol is a notation that shows the chemical symbol, mass number and atomic number of an atom or ion. It is written as ${}^{A}_{Z}X^{q}$, where A is the mass number, the number of nucleons (SI unit 1), Z is the atomic number, the number of protons (SI unit 1), X is the chemical symbol of the element (no unit), and q is the ionic charge expressed as a charge number in elementary-charge units (SI unit 1; actual charge would be in C).

Use these relationships:

N = A − Z, where N is the number of neutrons in the nucleus (SI unit 1), A is the mass number and Z is the atomic number.

For a neutral atom, the number of electrons equals the number of protons. For an ion, compare the charge with the number of protons carefully: a positive ion has fewer electrons than protons; a negative ion has more electrons than protons. For example, ${}^{24}_{12} ext{Mg}^{2+}$ has 12 protons, 12 neutrons and 10 electrons. The 2+ charge comes from having two more protons than electrons.

Small scales, prefixes and notation

Atomic dimensions are so small that scientific notation and SI prefixes are not decoration; they are the language of the topic. A picometre is a length unit equal to 10⁻¹² m. A femtometre is a length unit equal to 10⁻¹⁵ m. A nanometre is a length unit equal to 10⁻⁹ m. When you compare an atomic radius, a bond length and a nuclear radius, convert them into metres first, then compare powers of ten. A common mistake is to compare only the front numbers and forget the prefixes — that’s how a femtometre accidentally becomes larger than a picometre.

What controls chemical properties?

The nucleus determines the element because the number of protons fixes the atomic number. Chemical properties, though, depend mainly on how the electrons are arranged outside the nucleus, especially the outer electrons. That is why this topic leads naturally into electron configurations: the nucleus tells you which element you have; the electrons explain much of how it reacts.

Same element, different nuclei

An isotope is an atom of the same element as another atom, but it has a different number of neutrons. Isotopes have the same atomic number because they contain the same number of protons. Their mass numbers are different, though, since their nuclei contain different numbers of neutrons.

The chemical symbol already gives the atomic number, so isotope notation is often shortened. For example, an isotope can be written as ${}^{37} ext{Cl}$ or as chlorine-37 instead of writing the atomic number every time. You don't need to memorise specific isotope examples for this topic; the key skill is interpreting the notation and carrying out the calculation.

Isotopes of the same element usually have very similar chemical properties. In neutral atoms, they have the same number of electrons, so they have the same electron arrangement. Their physical properties can differ because mass affects properties such as density, melting point, boiling point and rates of diffusion. For instance, a molecule made with a heavier isotope has a slightly greater mass than the corresponding molecule made with a lighter isotope, so measurable physical differences can appear.

Relative atomic mass as a weighted mean

The relative atomic mass is the weighted mean mass of the atoms of an element compared with one twelfth of the mass of a carbon-12 atom. It is written Aᵣ, where Aᵣ is relative atomic mass (SI unit 1, because it is a ratio). It often isn't a whole number because most elements occur as mixtures of isotopes.

The natural abundance of an isotope is the percentage of atoms of that isotope in a naturally occurring sample of the element. To calculate a relative atomic mass from isotope data, use:

Aᵣ = Σ(mᵢ × pᵢ) / 100, where mᵢ is the relative isotopic mass or mass number of isotope i (SI unit 1), pᵢ is the percentage abundance of isotope i (unit %, dimensionless in SI), and i is an index labelling each isotope (no unit).

For a two-isotope element, if one isotope has percentage abundance p, where p is the percentage abundance of the first isotope (unit %, dimensionless in SI), then the other isotope has abundance 100 − p. Substitute both into the weighted mean equation and solve. “Weighted” is doing the work here: a rare heavy isotope only nudges the average a little, while an abundant isotope pulls the average strongly towards its own mass.

Why calculated values may not exactly match the data booklet

In many school calculations, mass numbers are used instead of precise isotopic masses. A mass number is a whole-number count of nucleons, but the actual isotopic mass is not exactly the same as that count. So a calculated Aᵣ using mass numbers may differ slightly from the more accurate value in the data booklet. The idea is still correct; the small difference comes from using rounded data.

Isotope tracers and evidence for mechanisms

An isotope tracer is an isotope deliberately introduced into a substance so that the path of particular atoms can be followed through a process. Isotopes of the same element behave similarly in many reactions, but they can still be distinguished by mass or radioactivity, which makes them useful evidence for reaction mechanisms. If the labelled atom is found in a particular product or intermediate, it shows where that atom moved during the reaction. This is a neat Nature of Science point: the isotope is not just a label, it is evidence for a proposed sequence of steps.

Isotope separation also has real-world consequences. Differences in physical properties can be used to enrich a sample in one isotope, for example when increasing the proportion of a particular uranium isotope in nuclear fuel. Such applications sit at the awkward but important meeting point of chemistry, technology, ethics, economics and politics.