the nuclear model of the atom (protons, neutrons, electrons), the use of nuclear notation, isotopes, and the calculation of relative atomic mass from isotopic composition determined by mass spectrometry

What this dot point is asking

VCAA wants you to know the nuclear model of the atom (a dense positive nucleus of protons and neutrons surrounded by electrons), to read nuclear notation (mass number, atomic number), to distinguish isotopes of an element, and to use a mass spectrum to calculate a relative atomic mass from isotopic composition.

The answer

The nuclear model

An atom has a tiny, dense nucleus containing protons (positive) and neutrons (neutral), surrounded by electrons (negative) in shells. The nucleus holds almost all the mass; the electrons occupy almost all the volume.

The atomic number Z is the number of protons (and defines the element). The mass number A is protons + neutrons. The number of neutrons is A - Z. In a neutral atom, electrons = protons.

Nuclear notation

An atom is written as ^A_Z X, for example ^12_6 C for carbon-12. Reading it: Z = 6 protons, A = 12 nucleons, so 6 neutrons and (in a neutral atom) 6 electrons.

For an ion, the charge is added: ^23_11 Na^+ has 11 protons, 12 neutrons and 10 electrons.

Isotopes

Isotopes are atoms of the same element (same Z) with different mass numbers (different numbers of neutrons). Examples:

• Carbon: ^12_6 C, ^13_6 C, ^14_6 C
• Chlorine: ^35_17 Cl, ^37_17 Cl
• Hydrogen: ^1_1 H (protium), ^2_1 H (deuterium), ^3_1 H (tritium)

Isotopes of an element have identical chemistry (same electron configuration) but slightly different physical properties (mass, density, rate of diffusion).

Relative isotopic mass and relative atomic mass

The relative isotopic mass of an isotope is its mass relative to one-twelfth the mass of a ^12_6 C atom. By definition, ^12_6 C has a relative isotopic mass of exactly 12.

The relative atomic mass Ar of an element is the weighted mean of the relative isotopic masses of its naturally occurring isotopes:

Ar = sum over isotopes of (relative isotopic mass x fractional abundance)

If abundances are given as percentages, divide each by 100 before multiplying. The result is dimensionless.

Mass spectrometry

A mass spectrometer separates ions by mass-to-charge ratio (m/z). The simplified workflow:

1. Vaporisation: the sample is heated to a gas.
2. Ionisation: high-energy electrons knock an electron off each atom or molecule, producing positive ions (usually +1).
3. Acceleration: an electric field accelerates the ions.
4. Deflection: a magnetic field deflects the ions; lighter ions and more highly charged ions deflect more.
5. Detection: ions hit a detector and the relative numbers at each m/z are recorded.

The output is a mass spectrum: a bar chart of relative abundance (y) against m/z (x). For singly charged atomic ions (the usual case for elements), m/z equals the relative isotopic mass, and the bar heights are proportional to the natural abundance of each isotope. Plug those into the weighted-mean formula and you have Ar.

Examples in context

Example 1. Lead isotope fingerprinting of Broken Hill ore at the Australian Synchrotron. Geochemists at the Australian Synchrotron in Clayton use mass spectrometry on lead-bearing minerals from Broken Hill to date ore bodies. Natural lead has four stable isotopes: $^{204}\text{Pb}$, $^{206}\text{Pb}$, $^{207}\text{Pb}$ and $^{208}\text{Pb}$. The relative abundance of $^{206}\text{Pb}$ (formed by uranium-238 decay) compared to $^{204}\text{Pb}$ (primordial) gives an age. A typical Broken Hill sample reads as $^{206}\text{Pb}$ to $^{204}\text{Pb}$ of about $16.0$, much lower than ratios in younger Australian deposits, consistent with an age near 1.7 billion years. The weighted-mean Ar still falls near $207.2$.

Example 2. Carbon-14 dating of Lake Mungo human remains. ANSTO at Lucas Heights uses accelerator mass spectrometry to count $^{14}\text{C}$ atoms in charcoal and bone from the Willandra Lakes Region. Carbon has three isotopes: $^{12}\text{C}$ (about $98.93\%$), $^{13}\text{C}$ (about $1.07\%$) and trace $^{14}\text{C}$ (about $1 \times 10^{-12}$). The weighted mean gives Ar(C) of $12.01$. AMS ionises carbon, accelerates it, deflects it through a magnetic field, then counts $^{14}\text{C}$ ions directly rather than waiting for them to decay. A Mungo Man sample showed a $^{14}\text{C}$ to $^{12}\text{C}$ ratio about $1.6\%$ of the modern atmospheric value, corresponding to roughly 42,000 years.

Try this

Q1. State the difference between mass number and relative atomic mass, and explain why the relative atomic mass of chlorine is reported as $35.45$ rather than $35$ or $36$. [2 marks]

• Cue. Mass number is integer protons plus neutrons for one isotope. Ar is a weighted mean. Chlorine-35 (about $75.78\%$) dominates so the average sits closer to 35.

Q2. Bromine gives two peaks in its mass spectrum at m/z $= 79$ (relative height $50.7$) and m/z $= 81$ (relative height $49.3$). Calculate the relative atomic mass of bromine to two decimal places. [3 marks]

• Cue. Fractional abundances $0.507$ and $0.493$. Ar(Br) $= (79 \times 0.507) + (81 \times 0.493) = 40.05 + 39.93 = 79.99$.

Q3. A mass spectrum of magnesium shows peaks at m/z $= 24, 25, 26$ with relative heights $79, 10, 11$. (a) Identify the species responsible for each peak. (b) Calculate Ar(Mg). (c) State why these isotopes have identical chemistry. [2+2+2 marks]

• Cue. (a) Singly charged $\text{Mg}^{+}$ cations of $^{24}\text{Mg}$, $^{25}\text{Mg}$, $^{26}\text{Mg}$. (b) $(24 \times 0.79) + (25 \times 0.10) + (26 \times 0.11) = 24.32$. (c) Same number of protons and electrons, so same electron configuration.