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 an atom is space, while almost all its mass sits in the nucleus.

A subatomic particle is a particle smaller than an atom that forms part of atomic structure. For 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 throughout the atom. A very small number bounced back. That only makes sense if the positive region is also very dense and massive compared with the alpha particle’s path.

Scientific models simplify reality in useful ways. When you draw an atom with a visible nucleus, the diagram is not to scale: a typical atom has a diameter of about $1 \times 10^{-10}\,\text{m}$, while the nucleus is roughly 100 000 times smaller in diameter. A nuclear model diagram helps us think, but it is not a photograph of the atom.

Relative charge and relative mass

For IB, learn 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 $1.602 \times 10^{-19}\,\text{C}$. Instead of writing the actual charge in coulombs, relative charges are normally written as +1 for a proton and −1 for an electron. An electron’s mass is tiny compared with a proton or neutron, so in ordinary mass-number calculations we 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. The atomic number identifies the element: a nucleus with 6 protons is carbon; one with 79 protons is gold. Here is 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

Use these relationships:

In 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, ${}^{24}_{12}\text{Mg}^{2+}$ 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 $10^{-12}\,\text{m}$. A femtometre is a length unit equal to $10^{-15}\,\text{m}$. A nanometre is a length unit equal to $10^{-9}\,\text{m}$. 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 is 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 the arrangement of electrons 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 with a different number of neutrons. Isotopes have the same atomic number because they contain the same number of protons. Their mass numbers differ because 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 ${}^{37}\text{Cl}$ or as chlorine-37 rather than writing the atomic number every time. You do not need to learn specific isotope examples for this topic; the useful skill is interpreting the notation and doing the calculation.

Isotopes of the same element usually have very similar chemical properties. In neutral atoms, they have the same number of electrons and therefore the same electron arrangement. Their physical properties can differ, though, because mass affects properties such as density, melting point, boiling point and rates of diffusion. A molecule made with a heavier isotope, for instance, 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 $A_r$, where $A_r$ is relative atomic mass (SI unit 1, because it is a ratio). The value is often not a whole number because most elements exist 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:

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 $100 - p$. Put both values into the weighted mean equation and solve. The “weighted” part matters: 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 $A_r$ using mass numbers may differ slightly from the more accurate value in the data booklet. That difference is not a mistake in the method; it 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 be distinguished by mass or radioactivity, so they can provide 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. That is a useful 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. These applications sit at the awkward but important meeting point of chemistry, technology, ethics, economics and politics.

What a mass spectrum tells you

A mass spectrum is a graph of relative abundance of ions against their mass-to-charge ratio. A mass spectrometer is the instrument that produces this graph by separating ions according to mass-to-charge ratio. You don’t need to explain how the instrument works; IB is assessing whether you can interpret the spectrum.

The horizontal axis is

In many simple elemental isotope spectra, the ions have a single charge, so $z = 1$ and the $m/z$ value is close to the isotope’s mass number. The vertical axis shows relative abundance or relative intensity, so it tells you how much of each isotope is present compared with the others.

In an elemental mass spectrum, each peak usually represents an isotope. Use the peak position to identify the isotope. Use the height or area of the peak to find its relative abundance. In school spectra, peak heights are often used directly. If the intensities are not already percentages, convert them into percentages before calculating the relative atomic mass.

Calculating relative atomic mass from a spectrum

Use the same weighted mean method as you would for isotope tables. Read the $m/z$ values and the relative intensities first. Convert the intensities to percentages if needed, then use the weighted mean equation:

$A_r = \sum(m_i \times p_i) / 100.$

Suppose a spectrum has two peaks, with approximate relative abundances of 20% and 80% at $m/z$ values 10 and 11. The relative atomic mass will be much closer to 11 than to 10, since the isotope at 11 is more abundant. Before you press buttons, check the answer makes sense: it should fall between the isotope masses and sit nearer the taller peak.

Identity and relative abundance of isotopes

Mass spectra can tell apart elements with similar chemical behaviour or similar relative atomic masses when their isotope patterns are different. One element may have a single dominant peak, while another may have several peaks in a recognisable pattern. For this reason, isotope composition can be used to identify elements in geological samples, meteorites and other materials.

You can find authentic spectra in databases. A sensible workflow is to pick out the relevant peak positions and intensities, calculate $A_r$ from the spectrum, and compare your value with the data booklet. Differences can occur if you estimated peak heights from a graph, used mass numbers rather than precise isotopic masses, or used a spectrum from a sample whose isotopic composition is not exactly the standard terrestrial composition.

Link to molecular structure

For elements, the isotope pattern is the focus here. For compounds, a mass spectrum can also show a fragmentation pattern. A fragment ion is a charged piece of a molecule formed when the molecule breaks apart in a mass spectrometer. The $m/z$ values of fragment ions can suggest which groups of atoms were present in the original molecule, so fragmentation patterns help chemists infer structure.