Mass Spectrometry

What is "mean free path" in mass spectrometry?

The average distance a molecule/ion travels before it collides with another molecule.

Why does a mass spectrometer need a long mean free path (low pressure)?

If the mean free path is short, ions collide constantly, pick up random energy, and fragment/fall apart before reaching the detector — vacuum is needed so ions travel a clean, predictable path + mean free path stretches out into metres.

What is the formula for mean free path (kinetic theory)?

λ = kT / (√2 · π · d² · P), where k = Boltzmann constant, T = temperature, d = molecular diameter, P = pressure.

Worked example: mean free path at 10⁻⁵ mbar (10⁻³ Pa), room temperature (298 K), air molecule diameter ≈3.7×10⁻¹⁰ m — what is λ?

λ = (1.38×10⁻²³ × 298) / (√2·π·(3.7×10⁻¹⁰)²·10⁻³) ≈ 6.8 m — far longer than the instrument, so essentially no collisions.

Sanity check: what is the mean free path at atmospheric pressure (≈101,325 Pa), same T and d?

≈67 nm (using the same formula) — matches the known literature value of ~68 nm, confirming the formula.

What is 1 dalton (Da) defined as?

1/12 of the mass of one unbound, neutral carbon-12 atom.

What is "nominal mass" vs "exact mass"?

Nominal mass = mass using rounded integer atomic masses (C=12, H=1, O=16…). Exact mass = precise mass accounting for the true mass of each isotope (e.g. ¹³C is not exactly 13).

What is "average (molar) mass" vs "monoisotopic mass"?

Average/molar mass = weighted average across all naturally occurring isotopes (what's on the periodic table). Monoisotopic mass = mass calculated using only the single most abundant isotope of each element (usually ¹²C).

Worked example: molar mass of water (H₂O)?

2 × 1.008 (H) + 16.00 (O) = 18.02 Da.

What is "mass defect"?

The difference between an isotope's exact mass and its nominal (integer) mass — arises because protons/neutrons don't weigh exactly 1 Da each once bound in a nucleus.

What are the natural abundances of carbon-12 and carbon-13?

¹²C ≈ 98.9% (98.93%), ¹³C ≈ 1.1% (1.07%).

What formula predicts isotope pattern peak intensities?

Binomial distribution: P(k) = C(n,k) · p^(n−k) · q^k, where n = number of that atom in the molecule, p = abundance of the light isotope, q = abundance of the heavy isotope, k = number of heavy isotopes.

Worked example: for a molecule with 5 carbons, what % intensity is the M+1 peak (relative to M+0, the base peak)?

P(k=1) = C(5,1)(0.9893)⁴(0.0107)¹ ≈ 5.12%; relative to base peak (94.76%) that's ≈5.4%.

Quick shortcut for estimating M+1 peak height from carbon count?

M+1 intensity (%) ≈ number of carbons × 1.1%.

Why do very large molecules (proteins, polymers) show a smooth bell-curve isotope envelope instead of a clean monoisotopic peak?

So many possible combinations of heavy isotopes become likely that the binomial distribution approximates a Gaussian — no single k value dominates, so no distinguishable monoisotopic peak.

What is the "base peak"?

The tallest (most intense) peak in the spectrum representing highest abundance / stability; other peaks are often reported as % relative to it.

What SNR (signal-to-noise ratio) is the rule of thumb for a real signal?

SNR > 3.

What is "resolving power" and its formula?

The ability to distinguish two adjacent peaks; R = m/Δm, where m is the (average) mass of the two peaks and Δm is their mass difference.

What is "resolution" (as opposed to resolving power)?

The width of a single peak measured at 50% of its height, referenced to that peak's mass — narrower peak = better resolution.

Worked example: two peaks at m=500.00 and m=500.05 — what is the resolving power?

RP = 500 / 0.05 = 10,000. RP = mass / change in mass

How do you determine a molecule's mass from a singly-charged [M+H]⁺ peak?

Subtract the mass of one proton (≈1.007 Da) from the observed m/z: M = (m/z) − 1.007.

How do you determine molecular mass from a multiply-charged ESI spectrum?

For a peak at m/z carrying charge z: M = z×(m/z) − z×1.007. Using two adjacent charge states (differing by 1) and their m/z values lets you solve for z and then M algebraically.

What is a radical cation, and how is it written?

M⁺• — formed by knocking an electron out of a neutral molecule; the dot shows an unpaired electron; mass is essentially unchanged (minus one electron's negligible mass).

What is a radical anion, and how is it written?

M⁻• — formed by adding an electron to a neutral molecule (still has one unpaired electron).

What is [M+H]⁺ and [M−H]⁻?

Pseudo-molecular ions formed by adding or removing a proton; mass changes by ±1.007 Da relative to M.

What are [M+Na]⁺ and [M+K]⁺?

Adduct ions formed when the analyte picks up a sodium or potassium cation instead of a proton — common in MALDI when the matrix isn't perfectly pure.

In tandem MS, what is a "precursor ion" vs a "product/fragment ion"?

Precursor ion = the intact ion selected in the first analyser; product/fragment ion = the smaller pieces it breaks into after collision-induced fragmentation, measured by the second analyser.

What is the formula relating photon frequency to energy?

E = hν, where h = Planck's constant (6.626×10⁻³⁴ J·s) and ν = frequency (Hz).

How do you convert photon wavelength directly to energy in eV?

E (eV) = 1240 / λ (nm) — a convenient shortcut form of E = hc/λ.

Worked example: energy of a 337 nm laser photon (common MALDI N₂ laser)?

E = 1240/337 ≈ 3.68 eV (equivalently E=hc/λ ≈5.90×10⁻¹⁹ J, which converts to the same 3.68 eV).

What's the difference between a "hard" and a "soft" ionisation method?

Hard methods deposit a lot of excess energy into the molecule, causing vibration + fragmentation; soft methods (ESI, MALDI) minimise excess energy so intact molecular ion survives.

What is SIMS and its key feature?

Secondary Ion Mass Spectrometry — a primary ion beam hits a surface and knocks off secondary ions; extremely fine spatial resolution (10–15 nm spot size), good for surface/material mapping.

How does MALDI ionize a sample?

Analyte is mixed with a matrix that strongly absorbs the laser wavelength; the matrix absorbs the laser energy, vaporizes explosively, and protonates/carries the analyte into the gas phase without directly blasting it with laser energy — a soft technique.

Why might MALDI spectra show [M+Na]⁺ or [M+K]⁺ instead of just [M+H]⁺?

Trace sodium/potassium impurities in the matrix get picked up by the analyte instead of a proton.

What does MALDI-2 add?

A second laser pulse that generates an excess of protons in the plume, enhancing ionization efficiency.

For a polymer's MALDI spectrum (series of evenly spaced peaks), how do you find the monomer mass?

Peak mass = n (# of repeating monomer units) × (monomer mass) + residual mass (end groups + cation mass). Plotting peak mass vs n, the slope of the line = the monomer's mass.

What is the Taylor cone in ESI?

The cone-shaped liquid meniscus formed at the capillary tip under high voltage, just before it emits a jet of highly charged droplets.

What is "Coulombic explosion" in ESI?

As solvent evaporates from a charged droplet, charge density rises until electrostatic repulsion overcomes surface tension, splitting the droplet into smaller ones — repeats until bare ions remain.

Describe the Charge Residue Model (CRM) of ESI ion formation.

Repeated evaporation and Coulombic explosions shrink a droplet down until essentially only ONE analyte molecule remains inside a tiny droplet; as the last solvent evaporates, the droplet's charges transfer directly onto the analyte, leaving a "residue" of charge on the molecule itself.

How does the Ion Evaporation Model (IEM) differ from CRM?

In IEM, small ions/charges are ejected directly off the surface of a still-shrinking droplet (before it's fully evaporated), rather than waiting for the droplet to disappear entirely as in CRM.

How does the Chain/Charge Ejection Model (CEM) differ from CRM and IEM?

CEM applies mainly to large, unfolded proteins: as the protein unravels, it stretches out of the droplet and drags some of the droplet's charges along with it as it exits — not a simple "last droplet" residue process.

Which ESI ion-formation model is generally accepted for small/medium molecules?

CRM (charge residue model) — small analytes are thought to end up as the sole occupant of a shrinking droplet before the final charges transfer to them.

Why is ESI described as a "game changer"?

because it produces multiply charged ions, reducing m/z of large molecules such as proteins; allows them to be detected by mass analysers with limited m/z ranges; also enables determination of large molecular masses from multiple charge states while preserving intact molecules.

Why is ESI called an "atmospheric ionization technique," and how do ions get into the vacuum system?

It sprays at atmospheric pressure; getting the ions into the ~10⁻⁵ mbar analyser region requires differential pumping — a series of chambers, each pumped to lower pressure, connected by small apertures/skimmers that let ions through while pumping away neutral gas.

What is the basic principle of TOF (time-of-flight) mass analysis?

All ions are accelerated by the same electric field, giving them equal kinetic energy (KE = zeV = ½mv²); lighter ions therefore move faster and reach the detector first; flight time depends on √(m/z); TOF measures the time it takes for the light/heavy ions to get to the detector + calculates their m/z based on that time.

What is the basic principle of a quadrupole mass filter?

Four rods with combined DC + oscillating RF voltage; only ions with a mass in a narrow, stable-trajectory window survive the full length without crashing into a rod; it actively filters, unlike TOF. Has a ceiling cap of the m/z (commonly between 2,000–4,000)

What do the parameters "a" and "q" represent in the Mathieu equation, and how do they depend on mass?

a ∝ DC voltage (U) / mass; q ∝ RF voltage (V) / mass — both are inversely proportional to ion mass, so every mass maps to its own point on the same (q,a) line for fixed U,V.

What does the "apex" of the Mathieu stability region represent?

The narrowest point of the stable (q,a) region — operating near it gives the highest mass resolution but transmits the fewest ions.

What happens in a quadrupole when a = 0 (no DC, RF only)?

Almost the entire mass range stays inside the stability region simultaneously — the quadrupole acts as an ion guide (transmits nearly everything) rather than a mass filter.

How does scan-line steepness (DC/RF ratio) affect resolution vs transmission in a quadrupole?

A steeper scan line crosses each mass's stability region near its narrow apex → high resolution, low transmission. A shallower line crosses near the wide base → low resolution (wide peaks), high transmission.

What is the point of tandem MS (MS/MS)?

Select one precursor ion with the first analyser, fragment it in a collision cell (with an inert gas), then analyse the fragment masses with a second analyser — reveals structural information about that specific ion, not just its total mass.

What is imaging mass spectrometry, in principle?

Acquiring a full mass spectrum at many points across a sample's surface (e.g. via a scanning laser or DESI sprayer) and mapping the intensity of a chosen m/z value by position, producing a label-free chemical image.

Orbitrap

separates ions according to m/z by trapping them in electrostatic field + measuring their oscillation frequencies; ions enter Orbitrap + move around electrode; electrostatic field causes ions to oscillate along central axis; ions with different m/z values oscillate at different frequencies; detects current induced by oscillating ions on outer electrodes; Fourier transform + detected signal → frequency spectrum → mass spectrum

How does FTICR work?

separates ions according to m/z by trapping them in strong magnetic field + move in circular paths; ions excited to larger cyclotron orbits; ions with different m/z values have different cyclotron frequencies: ions w/ lower m/z rotate at higher frequencies; moving ions induce image current in detection plates

How does DESI (Desorption Electrospray Ionisation) work?

sprays charged solvent droplets onto a sample surface; droplets hit the sample, desorbing (molecules released from sample surface) + ionising molecules from its surface; resulting ions carried into the MS, where they are analysed according to m/z; by analysing different positions on sample, DESI-MS → spatial maps of molecules, e.g. to distinguish tumour from healthy tissue.