How a Mass Spectrometer Works – Structure of an Atom and Mass Spectrum (Senior 4 Chemistry) | Ganzaa

Structure of an Atom and Mass Spectrum

Lessons

Senior 4 · Chemistry

Structure of an Atom and Mass Spectrum

4 lessons

Lesson 3 of 4

How a Mass Spectrometer Works

25 min

Weighing atoms one kind at a time

The last lesson used numbers such as "75.76% chlorine-35". Nobody can pick chlorine atoms out one by one and put them on a balance. Those numbers come from a mass spectrometer, an instrument that turns atoms or molecules into ions, sorts the ions by mass, and counts how many there are of each. Today mass spectrometers measure isotope ratios, identify unknown compounds, test athletes' urine for banned drugs and analyse the soil of Mars. This lesson follows a sample through a classic magnetic-sector instrument, stage by stage.

Definition

Mass spectrometer: an instrument that separates gaseous ions according to their mass-to-charge ratio and records how many ions of each ratio there are.

Mass-to-charge ratio, m/z: the mass of an ion (in u) divided by the number of charges on it. For a 1+ ion, m/z is simply its relative mass: ${}^{35}\mathrm{Cl^{+}}$ has m/z = 35, while ${}^{40}\mathrm{Ca^{2+}}$ has m/z = $\frac{40}{2} = 20$ .

The five stages

Vaporisation. The sample is injected and, if it is a solid or liquid, heated so that it becomes a gas. Its particles are then separate and can be ionised one by one.
Ionisation. Electrons from a heated metal filament (an "electron gun") are fired at the gaseous particles. A fast electron knocks an electron off a particle and leaves a positive ion: $\mathrm{X(g)} + e^- \longrightarrow \mathrm{X^{+}(g)} + 2e^-$ Most ions formed are 1+; a few lose two electrons and become 2+.
Acceleration. The positive ions are attracted towards negatively charged plates with slits in them. They speed up and pass through the slits as a fine, fast beam. Every ion with the same charge gains the same kinetic energy.
Deflection. The beam enters a curved tube between the poles of an electromagnet. The magnetic field bends each ion's path into an arc. Ions with a small m/z are bent more; ions with a large m/z are bent less.
Detection. Only ions of one particular m/z follow the curve exactly and reach the detector, where they pick up electrons and produce a tiny electric current. The current, which is proportional to the number of ions arriving, is amplified and recorded. By slowly changing the strength of the magnetic field, ions of each m/z are brought onto the detector in turn.

The whole instrument is kept at a high vacuum. Otherwise the ions would collide with air molecules, which would knock them off course, slow them down or neutralise them.

Why the deflection depends on m/z

An ion of mass $m$ and charge $z e$ is accelerated through a potential difference $V$ , so its kinetic energy is

zeV = \tfrac{1}{2}mv^2 \qquad (1)

In a magnetic field $B$ at right angles to its motion, the magnetic force $B z e v$ supplies the centripetal force for a circular path of radius $r$ :

Bzev = \frac{mv^2}{r} \quad\Rightarrow\quad r = \frac{mv}{Bze} \qquad (2)

Eliminating $v$ between (1) and (2):

r = \frac{1}{B}\sqrt{\frac{2Vm}{ze}}

For fixed $B$ and $V$ , the radius depends only on $\frac{m}{z}$ : $r \propto \sqrt{\frac{m}{z}}$ . A heavier ion follows a wider curve (it is deflected less); a more highly charged ion follows a tighter curve (it is deflected more). Two different ions with the same m/z, such as ${}^{16}\mathrm{O^{+}}$ and ${}^{32}\mathrm{S^{2+}}$ , follow exactly the same path, so the instrument measures m/z, not mass alone.

Worked example 1: which ion is deflected most?

The ions ${}^{1}\mathrm{H^{+}}$ , ${}^{4}\mathrm{He^{+}}$ , ${}^{4}\mathrm{He^{2+}}$ , ${}^{12}\mathrm{C^{+}}$ and ${}^{20}\mathrm{Ne^{2+}}$ pass through the same instrument. List them from most deflected to least deflected.

Solution. Work out m/z for each: $\mathrm{H^{+}}$ $\frac{1}{1} = 1$ ; $\mathrm{He^{+}}$ $\frac{4}{1} = 4$ ; $\mathrm{He^{2+}}$ $\frac{4}{2} = 2$ ; $\mathrm{C^{+}}$ $\frac{12}{1} = 12$ ; $\mathrm{Ne^{2+}}$ $\frac{20}{2} = 10$ . The smaller m/z, the greater the deflection.

Answer: $\mathrm{H^{+}}$ (1) > $\mathrm{He^{2+}}$ (2) > $\mathrm{He^{+}}$ (4) > $\mathrm{Ne^{2+}}$ (10) > $\mathrm{C^{+}}$ (12).

Worked example 2: radius of the path

With a certain magnetic field and accelerating voltage, ${}^{20}\mathrm{Ne^{+}}$ ions follow a path of radius 10.0 cm. Without changing the settings, what is the radius of the path of ${}^{22}\mathrm{Ne^{+}}$ ions? What must be done to bring the ${}^{22}\mathrm{Ne^{+}}$ ions onto the detector instead?

Solution. Since $r \propto \sqrt{\frac{m}{z}}$ and both ions are 1+:

r_{22} = 10.0\,\mathrm{cm} \times \sqrt{\frac{22}{20}} = 10.0 \times 1.049 = 10.5\,\mathrm{cm}

Answer: 10.5 cm (3 s.f.). The heavier ions follow a wider arc. To make them follow the 10.0 cm path to the detector, the magnetic field must be made stronger (by a factor of 1.049), since $r \propto \frac{1}{B}$ .

A modern alternative: time of flight

Many modern instruments have no magnet. In a time-of-flight (TOF) mass spectrometer, every ion is given the same kinetic energy and then drifts down a field-free tube of length $d$ . From equation (1), lighter ions move faster and arrive first. The flight time is

t = \frac{d}{v} = d\sqrt{\frac{m}{2zeV}} \qquad\text{so}\qquad t \propto \sqrt{\frac{m}{z}}

The detector records the arrival times, and a computer converts each time into an m/z value. Whatever the design, the output is the same: a mass spectrum, a graph of ion abundance against m/z, which the next lesson teaches you to read.

Warning

Common mistakes. (1) Heavier ions are deflected less, not more. (2) The spectrometer separates by m/z, not by mass: a 2+ ion appears at half its mass. (3) Ions are positive because electrons are knocked off; do not write $\mathrm{X} + e^- \rightarrow \mathrm{X^{-}}$ for this kind of ionisation. (4) The vacuum is there to prevent collisions, not to "pull the ions along".

Tip

Learn the five stages in order with the first letters V I A D D: Vaporise, Ionise, Accelerate, Deflect, Detect. For each stage in an exam answer, say what happens and how: "Ionise: bombarded with high-energy electrons from an electron gun, which knock out an electron to form $\mathrm{X^{+}}$ ."

Evagating: 2.2 The Mass Spectrometer (3 min). Watch each stage the sample passes through, from vaporisation to detection, and try the short exercises at the end.

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Practice

Name the five stages of a magnetic-sector mass spectrometer in order and state what happens in each.
Write an equation, with state symbols, for the ionisation of a magnesium atom in a mass spectrometer.
Explain why the inside of a mass spectrometer must be kept at a very low pressure.
Calculate m/z for: ${}^{24}\mathrm{Mg^{+}}$ , ${}^{24}\mathrm{Mg^{2+}}$ , ${}^{35}\mathrm{Cl^{+}}$ , $\left({}^{35}\mathrm{Cl}{}^{37}\mathrm{Cl}\right)^{+}$ . Which is deflected most?
Explain why ${}^{14}\mathrm{N^{+}}$ and ${}^{28}\mathrm{Si^{2+}}$ reach the detector at the same magnetic field strength.
In one instrument, ${}^{35}\mathrm{Cl^{+}}$ ions follow a path of radius 12.0 cm. Calculate the radius for ${}^{37}\mathrm{Cl^{+}}$ ions under the same conditions.
In a time-of-flight instrument, ${}^{20}\mathrm{Ne^{+}}$ ions take 25.0 µs to reach the detector. How long do ${}^{22}\mathrm{Ne^{+}}$ ions take?

Show answersHide answers

Vaporisation (sample turned into gas); ionisation (bombarded by high-energy electrons, forming positive ions); acceleration (attracted through slits in negative plates into a fast beam); deflection (bent by a magnetic field by an amount that depends on m/z); detection (ions reaching the detector produce a current proportional to their number).
$\mathrm{Mg(g)} + e^- \rightarrow \mathrm{Mg^{+}(g)} + 2e^-$ .
So that ions do not collide with air molecules, which would deflect them, slow them or neutralise them, and so stop them reaching the detector in proportion to their numbers.
24, 12, 35, 72. ${}^{24}\mathrm{Mg^{2+}}$ (m/z = 12) is deflected most.
Both have m/z = 14 ( $\frac{14}{1}$ and $\frac{28}{2}$ ), and the path depends only on m/z.
$12.0 \times \sqrt{\frac{37}{35}} = 12.0 \times 1.028 = 12.3\,\mathrm{cm}$ .
$t \propto \sqrt{\frac{m}{z}}$ : $25.0 \times \sqrt{\frac{22}{20}} = 26.2\,\mathrm{\mu s}$ .

Quick check

Put the stages of a magnetic-sector mass spectrometer in order.

Tap the cards in the right order.

Key points

Vaporise, ionise ( $\mathrm{X(g)} + e^- \rightarrow \mathrm{X^{+}(g)} + 2e^-$ ), accelerate, deflect, detect; all under high vacuum.
The radius of an ion's path is $r = \frac{1}{B}\sqrt{\frac{2Vm}{ze}}$ , so it depends only on m/z: small m/z, large deflection.
The magnetic field is scanned so that ions of each m/z reach the detector in turn; the current measures how many there are.
A time-of-flight instrument separates ions by arrival time, $t \propto \sqrt{\frac{m}{z}}$ .

Sources and credits

Image: LTQ OrbiTrap XL-Thermo Scientific 1.jpg by Nadine90 (Nadina Wiórkiewicz), via Wikimedia Commons, licensed under CC BY-SA 3.0.
Video: 2.2 The Mass Spectrometer, Evagating, embedded from YouTube.
The text, diagram, derivation, worked examples and Practice items were written and drawn by Ganzaa.
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1Weighing atoms one kind at a time

2The five stages

3Why the deflection depends on m/z

4A modern alternative: time of flight

Weighing atoms one kind at a time

The five stages

Why the deflection depends on m/z

A modern alternative: time of flight