Describe the nuclear model of the atom in terms of protons, neutrons and electrons; use nuclear notation and define isotopes; calculate relative atomic mass from isotopic composition determined by mass spectrometry

What this dot point is asking

QCAA wants you to describe the nuclear model of the atom (protons, neutrons, electrons), read and write nuclear notation, define isotopes, and calculate relative atomic mass from a mass spectrum or an abundance table. Unit 1 has no internal assessment, but this dot point underpins every later mole calculation and every periodic-trend argument.

The answer

An atom has a small dense nucleus of protons and neutrons, surrounded by electrons occupying defined energy levels. Atoms of the same element have the same number of protons; isotopes of an element differ in their number of neutrons. The relative atomic mass tabulated on the periodic table is the weighted average of the isotopic masses by their natural abundance.

The nuclear model

The proton number (atomic number, Z) defines the element. The mass number (A) is the total count of protons plus neutrons. A neutral atom has equal numbers of protons and electrons.

Nuclear notation

The standard notation is:

where X is the element symbol, A is the mass number (top), and Z is the atomic number (bottom). Examples:

• Carbon-12: $^{12}_{6}C$ has 6 protons, 6 neutrons, 6 electrons (neutral atom).
• Oxygen-18: $^{18}_{8}O$ has 8 protons, 10 neutrons, 8 electrons.
• Aluminium-27 ion: $^{27}_{13}Al^{3+}$ has 13 protons, 14 neutrons, 10 electrons (3 fewer than the neutral atom).

Number of neutrons is A minus Z. Number of electrons in an ion is Z minus the charge (with sign respected: positive ions have lost electrons).

Isotopes

Isotopes of an element have the same number of protons but different numbers of neutrons, so the same atomic number Z but different mass number A.

• Hydrogen has three isotopes: protium ($^{1}H$, 0 neutrons), deuterium ($^{2}H$, 1 neutron), tritium ($^{3}H$, 1 proton, 2 neutrons; radioactive).
• Carbon has C-12 (98.9 percent), C-13 (1.1 percent), and trace C-14 (radioactive, used in radiocarbon dating).
• Chlorine is essentially a 3:1 mixture of Cl-35 and Cl-37.

Isotopes have identical chemical behaviour (the chemistry is decided by the electrons) but slightly different physical properties (mass-dependent: density, rate of diffusion, vibrational frequencies).

Mass spectrometry

A mass spectrometer ionises a sample (usually by electron impact, knocking out one electron to form a singly charged cation), accelerates the ions through an electric field, separates them by mass-to-charge ratio (m/z) in a magnetic field, and detects each beam. The output is a mass spectrum: a plot of relative abundance against m/z.

For atomic samples, m/z values equal the isotopic mass number (most ions are singly charged). Peak heights give the relative abundance.

Calculating relative atomic mass

The relative atomic mass (Ar) is the weighted mean of the isotopic masses by their natural abundance:

Fractional abundance is the percentage divided by 100. The sum of all abundances must equal 1 (or 100 percent).

Worked example: chlorine. Cl-35 (mass 34.97, abundance 75.78 percent), Cl-37 (mass 36.97, abundance 24.22 percent).

Matches the periodic table value to within rounding.

Worked example: magnesium from a mass spectrum. Peaks at 24, 25, 26 with heights 79, 10, 11.

Convert heights to fractions: 0.79, 0.10, 0.11 (sum 1.00).

If the heights had not summed to 100, divide each by the total first.

Working backwards: from Ar to abundance

If the question gives Ar and the two isotopic masses, solve for the abundances using x for one fraction and (1 - x) for the other:

Example. Boron has Ar = 10.81, with isotopes B-10 (mass 10.01) and B-11 (mass 11.01). Find the abundance of each.

So B-10 is 20 percent abundant, B-11 is 80 percent. A check: (10.01)(0.20) + (11.01)(0.80) = 10.81. Correct.

Connecting to later Unit 1 content

Atomic structure feeds directly into electron configuration (the next dot point) and then into bonding (Topic 2) and the mole concept (Topic 3). The molar mass used in stoichiometry is numerically equal to Ar in g/mol, so accurate weighted-mean reasoning here transfers to mass-to-mole calculations later.

Examples in context

Example 1. Carbon dating Aboriginal rock art near Carnarvon Gorge. Researchers at the Australian Nuclear Science and Technology Organisation use accelerator mass spectrometry to count $^{14}\text{C}$ atoms in charcoal scraped from pigment binders in central Queensland rock-art shelters. Carbon-14 is a radioactive isotope: same six protons as $^{12}\text{C}$, but eight neutrons giving mass number $14$. Once the artist stopped exhaling, the $^{14}\text{C}$ decayed with a half-life of $5{,}730$ years. A measured $^{14}\text{C}\!:\!^{12}\text{C}$ ratio of one quarter the modern value implies two half-lives, or roughly $11{,}500$ years since the pigment was bound, putting the painting near the late Pleistocene.

Example 2. Mass spectrum of magnesium from Mount Isa ore. A QCAA data-test extract gives the relative isotopic abundances of magnesium pulled from dolomite at the Mount Isa lead-zinc operation: $^{24}\text{Mg}$ ($78.99\%$), $^{25}\text{Mg}$ ($10.00\%$) and $^{26}\text{Mg}$ ($11.01\%$). The relative atomic mass is calculated as $A_r = (24 \times 0.7899) + (25 \times 0.1000) + (26 \times 0.1101) = 24.32$. This matches the periodic-table value and confirms the sample is unenriched. The three peaks at $m/z = 24, 25, 26$ all carry charge $+1$ after electron impact, so $m/z$ values double as isotope mass numbers, a key skill in IA1 spectroscopy interpretation.

Try this

Q1. Explain the difference between the mass number and the relative atomic mass of an element. [3 marks]

• Cue. Mass number = protons + neutrons in one isotope (integer). Relative atomic mass = weighted average of all natural isotope masses on the $^{12}\text{C} = 12$ scale (usually non-integer).

Q2. Chlorine from Townsville seawater shows two peaks: $^{35}\text{Cl}$ at $75.77\%$ and $^{37}\text{Cl}$ at $24.23\%$. Calculate $A_r(\text{Cl})$ to two decimal places. [3 marks]

• Cue. $A_r = 35 \times 0.7577 + 37 \times 0.2423 = 35.48$. State weighted-average reasoning.

Q3. A neutral atom $X$ has $11$ protons and a mass number of $23$. (a) Write the standard isotope notation. (b) Give the electron configuration. (c) Identify $X^+$ and state which noble gas it is isoelectronic with. [2+2+2 marks]

• Cue. (a) $^{23}_{11}\text{Na}$. (b) $1s^2 2s^2 2p^6 3s^1$ (knowledge and analysis). (c) $\text{Na}^+$, isoelectronic with neon.