# How to Measure the Extremely Small: Atomic Mass

How does one go about measuring the mass of an object? Mass is defined as the amount of matter an object contains. This is very different from weight, of course, as the mass of our object would remain the same despite the presence or size of a gravitational field. It is safe to say, however,  that most laboratory measurement systems are here on Earth, and we can use the Earth’s gravity to aid in our mass measurement. One way is to use a balance and a known amount of mass. Simply place our object on one side of the balance, and keep adding known amounts of mass to the other side until the balance is balanced.

But what if our object is very small…too small to see and too light to measure with gravity? How does one measure the mass of single atom? Furthermore, how does one determine how much of an object consists of a particular type of atom? There are two commonly used tools just for this purpose. Chances are you’ve heard of one of these but not the other. These tools used to measure substances on the atomic level is the focus of today’s article.

## Qualitative vs Quantitative

If Sir Isaac Newton is knocking on your left cerebral cortex right about now, you’re thinking in the right direction. Force is equal to mass times acceleration. If we apply a known force to our atom and measure its acceleration, we can know its mass. But first, we must define two techniques that often get confused with measurement systems on the atomic scale.

Qualitative:

A qualitative measurement will tell you what is there, but not how much of what is there. It’s subjective in nature, but useful in understanding certain situations. Saying “There are a lot of Arduinos on your workbench” would be a qualitative analysis.

Quantitative:

This is the more intuitive measurement. It’s based on numbers, and is objective. Counting the precise number of Arduinos on your work bench is a quantitative measurement.

These terms are used in other fields and have various definitions that apply to each. But for the purpose of this article, understand that a qualitative measurement will tell you “We have Arduinos here” and a quantitative measurement will tell you “We have X number of Arduinos here.” See the wiki for a more technical explanation of qualitative vs quantitative measurement when applied to chemistry studies.

## Mass Spectrometer

I blew past the diagram above without mentioning it, but glance back for a moment. Let us imagine a small ramp and a handful of small balls that will roll down the ramp. Each ball has a different mass. Now let us imagine that we take a blow dryer and blow the balls sideways as they roll down the ramp. The balls with the most mass will be deflected least, while the balls with the least mass will be deflected most. By looking at where the balls land at the end of the ramp, we can measure the mass of the balls.

A mass spectrometer measures the mass of a single atom or molecule by replacing the ramp with an electric field and the blow dryer with a magnet. First the atoms must be heated to a gas state. Then they are bombarded with high speed electrons to knock electrons free from the sample gas. This turns the sample into positive ions. Note that electrons weigh 1/1836 amu, so missing electrons will not have any measurable effect on the mass of our sample.

Now that the sample has a positive charge, we can use an electric field to accelerate them! Two “plates” at different potentials are used to focus and accelerate the sample ions toward a magnet. The ions are attracted to the magnet, and become deflected by the magnetic field. The amount of this deflection is related to the mass of the sample ion.

Just like how we measured where the balls hit at the bottom of the ramp, we measure where the ions hit at the end of their journey. By measuring where they strike the “detection screen”, we measure the amount the ions were defected by the magnet, and therefore the mass of the ion.

## High Pressure Liquid Chromatography

While a mass spectrometer can give us the mass of atoms and molecules, it cannot quantify how much of an element or molecule is contained within a sample. For this reason, mass spectrometry is generally considered a qualitative measurement.

To know how much of an element or molecule you have, you need to use a technique called Liquid Chromatography. LC instruments that operate under pressure are called HPLCs (High Pressure Liquid Chromatography). Often, mass spectrometers are combined with HPLCs and are called LC-MS machines.

Just how does an HPLC tell us the amount of an element or molecule in a sample? Let us imagine that we have a bucket of nuts and bolts of various sizes. Our goal is to separate and group them according to their individual characteristics. One way of doing this is with a “friction filter.” Imagine we dump the bucket of nuts and bolts into our filter. At the bottom of the filter output is a conveyor belt. The smaller nuts and bolts experience less friction as they fall through the filter and come out first, while the larger ones experience more friction and come out last.

An HPLC does something similar to molecules. A sample is dissolved into a liquid. The liquid sample is then forced through what is known as a column under high pressure. The column is analogous to our friction filter. The size and makeup of HPLC columns vary with the approximate size of the sample that needs analyzing. But they all work the same way. The high pressure forces the sample through the column, and friction causes the smaller molecules to move through the column faster than larger molecules.

With the combination of a mass spectrometer and an HPLC are used to acquire a quantitative measurement of molecules. The mass spectrometer lets scientists know what substances a sample is made of, and the HPLC is then used to measure how much of each particular substance is contained within the sample. The techniques are applied in a wide variety of fields. The accuracy of this method allows for measurements of pesticides (and everything else like vitamins or hormones) in food, and is also invaluable in developing and testing pharmaceuticals.