Mass Spectrometer

The intuition — a coin sorter for atoms

Roll a marble and a bowling ball across a tilted floor with the same sideways push. The marble whips into a tight arc; the bowling ball barely bends. A mass spectrometer does exactly this to atoms and molecules, except the "push" is a magnetic field and the "marbles" are electrically charged ions.

The trick is that you cannot grab a single atom and put it on a scale — an atom weighs around 10⁻²⁵ kg. So instead you give every particle the same energetic kick and watch how much it bends. Heavier ions resist being turned (more inertia), so they trace a wider curve and land farther out. Read off where each one lands, and you have weighed individual atoms.

Every mass spectrometer, no matter the design, runs the same three-stage assembly line:

• Ionize. Knock electrons off (or stick charges onto) the sample so the particles carry a net charge q. Neutral atoms ignore electric and magnetic fields; charged ones obey them.
• Accelerate. Pull the ions through a known voltage V. Every ion of charge q gains the same kinetic energy, qV.
• Separate & detect. Use a field (magnetic, electric, or just a drift tube) to spread the ions by mass-to-charge ratio, then count where and when each one arrives.

The governing physics

Start at the accelerator. An ion of charge q dropped through a potential difference V converts all that electrical energy into kinetic energy:

qV = ½·m·v²   →   v = √(2qV/m)

So lighter ions come out faster — a fact the time-of-flight design exploits directly.

Now send the moving ion into a uniform magnetic field B pointing out of the plane. The magnetic part of the Lorentz force is

F = q·v × B

This force is always perpendicular to the velocity, so it does no work (speed stays constant) — it only turns the ion. A constant-magnitude perpendicular force is the definition of circular motion. Set the magnetic force equal to the required centripetal force:

q·v·B = m·v²/r   →   r = m·v/(q·B)

Substitute the accelerated speed v = √(2qV/m) and simplify:

r = (1/B)·√(2·m·V/q)

This is the master equation. With B and V fixed by the instrument, the landing radius depends only on the ratio m/q, and it scales with its square root. Double the mass and the radius grows by a factor of √2 ≈ 1.41, not 2 — the spread is gentle, which is why high-resolution machines use long flight paths and strong fields.

Equivalently, the time it takes to complete a full circle (the cyclotron period) is independent of speed:

T = 2π·m/(q·B)

The four common analyzers

"Mass spectrometer" describes the function, not one machine. The separation stage comes in several flavors, each with a different physical principle:

Analyzer	Separating principle	Sorted by	Strength
Magnetic sector	Bending radius r = (1/B)·√(2mV/q)	Position in space	High accuracy, classic design
Time-of-flight (TOF)	Drift time t = L·√(m/2qV)	Arrival time	Unlimited mass range, very fast
Quadrupole	Stable trajectory in an RF field	Filter (scans m/z)	Compact, cheap, robust
Orbitrap / FT-ICR	Oscillation/cyclotron frequency	Frequency	Extreme resolution (>10⁶)

Sectors and TOF instruments are the most intuitive — they directly realize the "heavier ions bend/lag" picture. Quadrupoles act as a tunable mass filter: oscillating voltages on four rods let only one m/z through at a time, and the machine scans across the range. Orbitraps and Fourier-transform ion cyclotron resonance (FT-ICR) cells measure the frequency at which trapped ions orbit, which is the most precise quantity physics lets us measure.

Worked numbers — where do the isotopes land?

Take a magnetic-sector instrument with B = 0.50 T and an accelerating voltage V = 2,000 V, ionizing neon. Neon has two main isotopes, ²⁰Ne and ²²Ne, both singly charged (q = e = 1.6 × 10⁻¹⁹ C). Using r = (1/B)·√(2mV/q) with masses in kilograms (1 u = 1.66 × 10⁻²⁷ kg):

Ion	Mass (u)	Speed v (m/s)	Radius r (cm)	Where it lands
²⁰Ne⁺	19.99	1.39 × 10⁵	5.76	Inner arc
²²Ne⁺	21.99	1.32 × 10⁵	6.04	Outer arc (+2.8 mm)
Na⁺ (²³)	22.99	1.29 × 10⁵	6.18	Just beyond ²²Ne

A 10% mass difference produces only a ~5% radius difference (the square-root law), yet ~2.8 mm of separation at the detector is easily resolved. This is essentially Aston's 1919 experiment, which first proved neon is a mix of isotopes and won him the 1922 Nobel Prize in Chemistry.

Real-world figures and costs

• Resolving power. Routine instruments resolve R = m/Δm of a few thousand; an Orbitrap reaches 10⁶, enough to distinguish N₂ (28.0062 u) from CO (27.9949 u) — a difference in the third decimal place.
• Sensitivity. Detectors count single ions through electron multipliers (gain ~10⁶). Trace methods detect parts-per-trillion — about one drop of contaminant in 20 Olympic pools.
• Speed. A TOF analyzer records a complete spectrum in tens of microseconds, so it can fire tens of thousands of times per second — fast enough to ride the back of a gas chromatograph.
• Vacuum. Analyzers run at 10⁻⁶–10⁻⁹ torr so ions fly meters without colliding; turbomolecular pumps spinning at ~90,000 rpm maintain it.
• Cost. A benchtop quadrupole GC-MS starts around US$50,000; a high-resolution Orbitrap or FT-ICR system runs US$500,000 to over US$1,000,000. NASA flew miniature mass spectrometers on the Curiosity and Cassini missions to sniff alien atmospheres.

Where it shows up

• Drug and doping testing. GC-MS and LC-MS are the legal gold standard — the World Anti-Doping Agency confirms positives by matching exact mass and fragmentation patterns.
• Proteomics and medicine. Sequencing proteins, identifying disease biomarkers, and newborn screening for metabolic disorders from a single dried blood spot.
• Geology and archaeology. Radiocarbon dating, potassium-argon dating of rocks, and isotope ratios that reveal where a material — or a person — came from.
• Environmental monitoring. Detecting pesticides, dioxins, and PFAS "forever chemicals" at parts-per-trillion in water and soil.
• Space exploration. Onboard mass spectrometers measured the composition of Titan's atmosphere (Cassini) and detected organic molecules in Martian soil (Curiosity's SAM instrument).
• Semiconductors and forensics. Tracing ppb-level impurities in silicon, and matching trace evidence such as accelerants or gunshot residue.

Common misconceptions & edge cases

• It measures mass, not mass-to-charge. No — it measures m/z. A doubly charged ion lands where a singly charged ion of half the mass would. Multiply-charged spectra (common for big biomolecules) must be deconvolved to recover the real mass.
• The magnetic field changes the ion's speed. It cannot. The magnetic force is always perpendicular to velocity, so it does zero work — it only curves the path. All the energy was set by the accelerating voltage.
• Heavier ions move faster. The opposite. After the same accelerating voltage, all ions share kinetic energy qV, so heavier ions move slower (v = √(2qV/m)) — which is exactly why they arrive last in a time-of-flight tube.
• You can skip ionization for neutral atoms. Neutral particles feel no electric or magnetic force and fly straight through. Ionization is non-negotiable; the choice of ionization method (electron impact, electrospray, MALDI) strongly shapes the spectrum.
• Bigger mass difference always means easier separation. Because radius and flight time scale with √m, the separation between adjacent masses shrinks at high mass. Distinguishing mass 1000 from 1001 is far harder than 20 from 21 — high-mass work demands high-resolution analyzers.
• It works in open air. Without high vacuum, collisions with air molecules scatter and neutralize the ions, destroying the spectrum before it forms.