science

Time-of-flight mass spectrometry

Time-of-flight mass spectrometry is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Time-of-flight mass spectrometry rather than just read about it. In short: Time-of-flight mass spectrometry (TOFMS) is a method of mass spectrometry in which an ion's mass-to-charge ratio is determined by a time of flight measurement. Ions are accelerated by an electric field of known strength.

Key takeaways

Time-of-flight mass spectrometry belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Time-of-flight mass spectrometry to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Time-of-flight mass spectrometry from memory before moving on to harder problems.

Reference excerpt

Time-of-flight mass spectrometry (TOFMS) is a method of mass spectrometry in which an ion's mass-to-charge ratio is determined by a time of flight measurement. Ions are accelerated by an electric field of known strength. This acceleration results in an ion having the same kinetic energy as any other ion that has the same charge. The velocity of the ion depends on the mass-to-charge ratio (heavier ions of the same charge reach lower speeds, although ions with higher charge will also increase in velocity). The time that it subsequently takes for the ion to reach a detector at a known distance is measured. This time will depend on the velocity of the ion, and therefore is a measure of its mass-to-charge ratio. From this ratio and known experimental parameters, one can identify the ion.

Theory

The potential energy of a charged particle in an electric field is related to the charge of the particle and to the strength of the electric field:

where Ep is potential energy, q is the charge of the particle, and U is the electric potential difference (also known as voltage). When the charged particle is accelerated into time-of-flight tube (TOF tube or flight tube) by the voltage U, its potential energy is converted to kinetic energy. The kinetic energy of any mass is:

In effect, the potential energy is converted to kinetic energy, meaning that equations (1) and (2) are equal

The velocity of the charged particle after acceleration will not change since it moves in a field-free time-of-flight tube. The velocity of the particle can be determined in a time-of-flight tube since the length of the path (d) of the flight of the ion is known and the time of the flight of the ion (t) can be measured using a transient digitizer or time to digital converter. Thus,

and we substitute the value of v in (5) into (4).

Rearranging (6) so that the flight time is expressed by everything else:

Taking the square root yields the time,

These factors for the time of flight have been grouped purposely. d 2 U {\displaystyle {\frac {d}{\sqrt {2U}}}} contains constants that in principle do not change when a set of ions are analyzed in a single pulse of acceleration. (8) can thus be given as:

where k is a proportionality constant representing factors related to the instrument settings and characteristics. (9) reveals more clearly that the time of flight of the ion varies with the square root of its mass-to-charge ratio (m/q). Consider a real-world example of a MALDI time-of-flight mass spectrometer instrument which is used to produce a mass spectrum of the tryptic peptides of a protein. Suppose the mass of one tryptic peptide is 1000 daltons (Da). The kind of ionization of peptides produced by MALDI is typically +1 ions, so q = e in both cases. Suppose the instrument is set to accelerate the ions in a U = 15,000 volts (15 kilovolt or 15 kV) potential. And suppose the length of the flight tube is 1.5 meters (typical). All the factors necessary to calculate the time of flight of the ions are now known for (8), which is evaluated first of the ion of mass 1000 Da:

Note that the mass had to be converted from daltons (Da) to kilograms (kg) to make it possible to evaluate the equation in the proper units. The final value should be in seconds:

t = 2.788 × 10 − 5 s {\displaystyle t=2.788\times 10^{-5}\;\mathrm {s} }

which is about 28 microseconds. If there were a singly charged tryptic peptide ion with 4000 Da mass, and it is four times larger than the 1000 Da mass, it would take twice the time, or about 56 microseconds to traverse the flight tube, since time is proportional to the square root of the mass-to-charge ratio.

Delayed extraction

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Time-of-flight mass spectrometry

Start with the simplest possible case. Write down what Time-of-flight mass spectrometry claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Time-of-flight mass spectrometry before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Time-of-flight mass spectrometry ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Time-of-flight mass spectrometry

In research: Time-of-flight mass spectrometry appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Time-of-flight mass spectrometry in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Time-of-flight mass spectrometry is common in secondary-school and first-year university syllabi. It links to neighbouring topics Mass spectrometry, so understanding it makes those chapters shorter.
In everyday life: Look for Time-of-flight mass spectrometry outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Time-of-flight mass spectrometry in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Time-of-flight mass spectrometry means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Time-of-flight mass spectrometry out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Time-of-flight mass spectrometry in simple terms?

Why does Time-of-flight mass spectrometry matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Time-of-flight mass spectrometry?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Time-of-flight mass spectrometry.