Mass Spectrometry & Isotopes

Atoms of the same element can exist in different forms called isotopes, which have the same number of protons but different numbers of neutrons. For example, carbon exists naturally as carbon-12 (⁶¹²C, 6 protons + 6 neutrons), carbon-13 (⁶¹³C, 6 protons + 7 neutrons), and the radioactive carbon-14 (⁶¹⁴C, 6 protons + 8 neutrons). Because isotopes differ in mass but are chemically almost identical, separating and measuring them requires a physical technique based on mass rather than chemical behaviour. Mass spectrometry is an analytical technique that ionises a sample, accelerates the resulting ions through a magnetic or electric field, and separates them according to their mass-to-charge ratio (m/z). The instrument produces a mass spectrum — a bar chart showing relative abundance on the y-axis versus m/z on the x-axis. Each peak corresponds to a different isotope (or fragment) of the element being studied. From the positions and heights of these peaks, chemists can identify which isotopes are present and calculate their relative abundances with extreme precision. The weighted average of all naturally occurring isotope masses, calculated using their percentage abundances, gives the relative atomic mass (Ar) of the element. This is why the periodic table lists chlorine as approximately 35.5 rather than a whole number — it is a weighted average of ³⁵Cl (about 75%) and ³⁷Cl (about 25%). Understanding mass spectrometry and isotopic abundance is therefore essential not only for understanding atomic structure but also for fields ranging from carbon dating to pharmaceutical quality control and forensic science.

Key takeaways
  • Vaporisation
  • Ionisation
  • Acceleration
  • Deflection (Ion Separation)
  • Detection and the Mass Spectrum

Vaporisation

The sample (solid, liquid, or gas) is introduced into a vacuum chamber and vaporised so that individual atoms or molecules are in the gas phase. The vacuum prevents collisions with air molecules that would scatter the ions and ruin the measurement. For metals like iron or lead, this may require heating to very high temperatures.

Ionisation

Gas-phase atoms are bombarded with a beam of high-energy electrons (electron impact ionisation). A collision knocks one electron from the atom, producing a positive ion with a 1+ charge: X(g) + e⁻ → X⁺(g) + 2e⁻. Because most ions formed this way carry a single positive charge, the m/z ratio equals the mass number of the isotope. Modern instruments may also use electrospray ionisation (ESI) for molecules, but for atomic mass spectrometry, electron impact is standard.

Acceleration

The positive ions are accelerated through an electric field created by negatively charged plates. All ions of charge +1 gain the same kinetic energy: kinetic energy = qV, where q is the ionic charge and V is the accelerating voltage. Heavier ions therefore move more slowly than lighter ones after acceleration, since KE = ½mv². This velocity difference is what allows separation by mass.

Deflection (Ion Separation)

The accelerated ion beam passes through a magnetic field oriented perpendicular to the beam. The magnetic force causes ions to travel in a curved path. The radius of curvature r is given by r = mv/(qB), where m is mass, v is velocity, q is charge, and B is magnetic field strength. Lighter ions are deflected more (smaller radius) than heavier ones. By varying B, ions of different m/z values are brought successively onto the detector. Only ions with the correct radius reach the detector at any given field setting.

Detection and the Mass Spectrum

Ions that complete the correct curved path strike a detector (e.g., a Faraday cup or electron multiplier), generating an electric current proportional to the number of ions arriving per second. A computer plots current versus m/z to produce the mass spectrum. The height (relative abundance) of each peak reflects how common that isotope is in the natural sample. The most abundant peak is called the base peak and is set to 100% relative abundance; all others are expressed relative to it.

The Key Equation

Ar=∑i(isotope massi×%abundancei)100A_r = \sum_{i} \frac{(\text{isotope mass}_i \times \% \text{abundance}_i)}{100}
  • A_r — Relative atomic mass (dimensionless (unified atomic mass units, u)): The weighted average mass of all naturally occurring isotopes of an element, relative to 1/12 the mass of carbon-12.
  • \text{isotope mass}_i — Mass of isotope i (u (atomic mass units)): The mass number (or precise mass) of a particular isotope. For exam-level calculations, the integer mass number is used.
  • \% \text{abundance}_i — Percentage abundance of isotope i (%): The percentage of atoms of that isotope in a naturally occurring sample of the element, read directly from the height of the peak in the mass spectrum.

Worked Example

Problem. A mass spectrum of naturally occurring boron shows two peaks: m/z = 10 with relative abundance 19.9%, and m/z = 11 with relative abundance 80.1%. Calculate the relative atomic mass of boron to two decimal places.

Ar(B)=(10×19.9)+(11×80.1)100=199+881.1100=10.80A_r(\text{B}) = \frac{(10 \times 19.9) + (11 \times 80.1)}{100} = \frac{199 + 881.1}{100} = 10.80

Answer. The relative atomic mass of boron is 10.80 (to 2 d.p.).

Figure
Diagram
Mass Spectrum of Chlorine (Atomic Ions)m/z (mass-to-charge ratio)Relative Abundance (%)020406080100100%35³⁵Cl62.8%37³⁷Clbase peak = 100%75.0% ³⁵Cl25.0% ³⁷ClAr = (35×75 + 37×25)/100Ar = 35.50
Origins · 1 minFrancis William Aston and how this was discovered
FW
Francis William Aston
1877–1945 · British

Francis Aston invented the mass spectrograph in 1919 at Cambridge University, an improved version of J.J. Thomson's earlier parabola spectrograph. His instrument could focus ion beams of the same m/z onto a single point, vastly improving resolution. Using it, Aston discovered 212 of the 287 naturally occurring isotopes, demonstrating that nearly every element exists as a mixture of isotopes. His precise measurements confirmed Einstein's mass–energy equivalence through the 'packing fraction' of nuclear masses. He was awarded the Nobel Prize in Chemistry in 1922 for these discoveries. Aston was an enthusiastic amateur sportsman and mountaineer. He was also an accomplished photographer and glassblower, skills that proved invaluable when constructing the delicate vacuum tubes required for his mass spectrograph experiments.

  • Protons, Neutrons, and Electrons — Isotopes are defined by their differing neutron numbers while proton number remains fixed; understanding subatomic particles is a prerequisite for understanding isotopic identity.
  • Relative Atomic Mass and the Mole — Relative atomic mass (Ar) is calculated directly from mass spectrometry data and is the foundation for molar mass calculations used throughout quantitative chemistry.
  • Nuclear Stability and Radioactivity — Some isotopes detected by mass spectrometry are radioactive; understanding nuclear stability explains why certain isotope ratios exist in nature and underpins applications like carbon-14 dating.
  • Molecular Mass Spectrometry and Fragmentation Patterns — The same mass spectrometer principles applied to isotope analysis extend to organic molecules, where fragmentation patterns are used to determine molecular structure.