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### Course: Chemistry library>Unit 2

Lesson 1: Mass spectrometry

# Isotopes and mass spectrometry

## Key points:

• Atoms that have the same number of protons but different numbers of neutrons are known as isotopes.
• Isotopes have different atomic masses.
• The relative abundance of an isotope is the percentage of atoms with a specific atomic mass found in a naturally occurring sample of an element.
• The average atomic mass of an element is a weighted average calculated by multiplying the relative abundances of the element's isotopes by their atomic masses and then summing the products.
• The relative abundance of each isotope can be determined using mass spectrometry.
• A mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on their mass-to-charge ratios ($m/z$).
• The mass spectrum of a sample shows the relative abundances of the ions on the y-axis and their $m/z$ ratios on the x-axis. If $z=1$ for all ions, then the x-axis can instead be expressed in units of atomic mass ($\text{u}$).

## Introduction: Dissecting an atom

Everything is composed of atoms. These tiny building blocks of matter make up your computer or phone screen, the chair you're sitting on, even your own body. If we could zoom in far enough, we'd see that atoms themselves are made up of even tinier components, which we call subatomic particles.
There are three main types of subatomic particles in an atom: protons, neutrons, and electrons. A proton carries a $1+$ charge, an electron carries a $1-$ charge, and a neutron carries $0$ charge. Protons and neutrons are found in the nucleus at the center of an atom, whereas electrons are found in orbitals that surround the nucleus. Since electrons are negatively charged, they are strongly attracted to the positively charged protons in the nucleus.
We can represent the particles that make up an atom (in this case, a neutral helium atom) using a simplified diagram like this:
According to the diagram, this helium atom contains two protons, two neutrons, and two electrons. The numbers of protons and electrons make sense: the atomic number of helium is $2$, so any helium atom must have two protons in its nucleus (otherwise, it would be an atom of a different element!). And, because this is a neutral atom, it must contain two electrons to balance out the positive charge from the nucleus. But what about the number of neutrons? Do all helium atoms have two neutrons in their nuclei?
As it turns out, they don't! We know that atoms with different numbers of protons in their nuclei are different elements. The same is not true when it comes to neutrons, though: atoms of the same element can contain different numbers of neutrons in their nuclei and still retain their identity. Such atoms are known as isotopes, and a single element can have many different isotopes.
The word isotope is derived from Ancient Greek: the prefix iso- means "same," while -tope (from the Greek word topos) means "place." The isotopes of a given element always contain the same number of protons and therefore occupy the same place on the periodic table. However, because isotopes contain different numbers of neutrons, each isotope has a unique atomic mass.

## Particle masses and unified atomic mass units

How do we express the mass of a single atom? Because atoms are so small (and subatomic particles are even smaller!), we can't easily use everyday units such as grams or kilograms to quantify the masses of these particles. This is why scientists developed the unified atomic mass unit, or $\text{u}$, which allows us to think about mass on the atomic or molecular scale.
By definition, is equal to exactly one twelfth the mass of a single neutral atom of carbon-$12$, which is the most common isotope of carbon. The number after the hyphen, $12$, is the sum of the protons and neutrons found in this particular isotope of carbon.
Concept check: How many protons are in the nucleus of an atom of carbon-$12$?
To see how useful the unified atomic mass unit can be, let's look at the masses of protons, neutrons, and electrons in both $\text{kg}$ and $\text{u}$:
NameChargeMass $\left(\text{kg}\right)$Mass $\left(\text{u}\right)$Location
proton$1+$$1.673×{10}^{-27}$$1.007$inside nucleus
neutron$0$$1.675×{10}^{-27}$$1.009$inside nucleus
electron$1-$$9.109×{10}^{-31}$$5.486×{10}^{-4}$outside nucleus
Using unified atomic mass units makes the masses of these particles much easier to understand and compare. For example, we can see from the numbers above that protons and neutrons are much more massive than electrons (nearly 2000 times more, to be precise!). This tells us that the bulk of an atom's mass is located in its nucleus.
In fact, it turns out that the mass of an electron is so small relative to the masses of protons and neutrons that electrons are considered to have a negligible effect on the overall mass of an atom. This is a fancy way of saying that when we calculate the mass of an atom or molecule, we can safely ignore the masses of the electrons. Sometimes, we might further simplify these calculations by assuming that protons and neutrons both have a mass of exactly $1\phantom{\rule{0.167em}{0ex}}\text{u}$. In this article, however, we'll generally be working with atomic masses that were calculated more precisely.

## Mass number and isotope notation

Now that we have an understanding of the different charges and masses of protons, neutrons, and electrons, we can discuss the concept of mass number. By definition, the mass number of an atom is simply equal to the number of protons plus the number of neutrons in its nucleus.
$\text{Mass number}=\left(\mathrm{#}\phantom{\rule{0.278em}{0ex}}\text{protons}\right)+\left(\mathrm{#}\phantom{\rule{0.278em}{0ex}}\text{neutrons}\right)$
Just as the atomic number defines an element, we can think of the mass number as defining a specific isotope of an element. In fact, a common way of specifying an isotope is to use the notation "element name-mass number," as we've already seen with carbon-$12$.
Importantly, we can use an isotope's mass number to calculate the number of neutrons in its nucleus. For example, let's use the mass number of carbon-$12$ and the equation above to calculate how many neutrons are in a single atom of carbon-$12$. After rearranging the equation to solve for number of neutrons, we get:
$\begin{array}{rl}\mathrm{#}\phantom{\rule{0.278em}{0ex}}\text{neutrons}& =\text{mass number}-\left(\mathrm{#}\phantom{\rule{0.278em}{0ex}}\text{protons}\right)\\ \\ & =12-6\\ \\ & =6\phantom{\rule{0.167em}{0ex}}\text{neutrons in carbon-}12\end{array}$
So, an atom of carbon-$12$ has $6$ neutrons in its nucleus. Let's try another example.
Concept check: Chromium-$52$ is the most stable isotope of chromium. How many neutrons are found in a single atom of chromium-$52$?
Another way that chemists commonly represent isotopes is through the use of isotopic notation, also known as nuclear notation. Isotopic notation shows the atomic number, mass number and charge of an isotope in a single symbol. For example, consider the isotopic notation for neutral hydrogen-$3$ and the magnesium-$24$ cation:
As we can see, the chemical symbols for hydrogen and magnesium are written in the center of the notation for each isotope. To the left of these symbols are each isotope's atomic number and mass number, and to the right is the net charge on the isotope. The net charge is not included for neutral atoms, as in the notation for hydrogen-$3$ above.

## Atomic mass vs. mass number

An isotope's mass number is closely related to its atomic mass, which is the mass of the isotope expressed in units of $\text{u}$. Since the mass of a neutron and the mass of a proton are both very close to $1\phantom{\rule{0.167em}{0ex}}\text{u}$, the atomic mass of an isotope is often nearly the same as its mass number. However, don't confuse the two numbers! Mass numbers are always integers (since nuclei contain only whole numbers of protons and neutrons) and are usually written without units. In contrast, atomic masses are essentially never integers (unless they've been rounded), and they are always shown with units of mass ($\text{u}$).
Another term that students often might find confusingly similar to atomic mass and mass number is average atomic mass (sometimes referred to as atomic weight), which is a related concept. Don't worry, though, we will discuss average atomic mass in the following section!

## Relative abundance and average atomic mass

There are two stable isotopes of chlorine: chlorine-$35$ and chlorine-$37$.
The atomic mass of chlorine-$35$ is $34.97\phantom{\rule{0.167em}{0ex}}\text{u}$, and the atomic mass of chlorine-$37$ is $36.97\phantom{\rule{0.167em}{0ex}}\text{u}$. And yet, if you look on the periodic table, you'll find that the mass of chlorine is given as $35.45\phantom{\rule{0.167em}{0ex}}\text{u}$. Where does this number come from?
If you guessed that it is the average mass of chlorine atoms, you would be correct. In fact, all of the masses that you see on the periodic table are averages, each based on the atomic masses and natural abundances of an element's stable isotopes. These average masses are referred to as average atomic masses or, in some textbooks, as atomic weights.
Let's think more about the average atomic mass of chlorine. If the atomic masses of chlorine-$35$ and chlorine-$37$ are $34.97$ and $36.97\phantom{\rule{0.167em}{0ex}}\text{u}$, respectively, why isn't the average atomic mass of chlorine simply the average of these two values?
The answer has to do with the fact that different isotopes have different relative abundances, which means that some isotopes are more naturally abundant on Earth than others. In the case of chlorine, chlorine-$35$ has a relative abundance of $75.76\mathrm{%}$, whereas chlorine-$37$ has a relative abundance of $24.24\mathrm{%}$. Relative abundances are typically reported as percentages, which means that the relative abundances of all of the different stable isotopes of an element always add up to $100\mathrm{%}$. An element's average atomic mass is actually a weighted average calculated from these values. To better illustrate this, let's calculate the average atomic mass of chlorine.

## Example: Calculating the average atomic mass of chlorine

Remember that the average atomic mass of an element is a weighted average. When we want to calculate a weighted average, we multiply the value of every item in our set—in this case, the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction, and then we sum up all of the products. This can be written as follows:
$\text{average atomic mass}=\sum _{i=1}^{n}\left(\text{relative abundance}×\text{atomic mass}{\right)}_{i}$
Plugging in the values for chlorine, we get:
$\begin{array}{rl}\text{average atomic mass of chlorine}& =\left(0.7576×34.97\phantom{\rule{0.278em}{0ex}}\text{u}\right)+\left(0.2424×36.97\phantom{\rule{0.278em}{0ex}}\text{u}\right)\\ \\ & =26.49\phantom{\rule{0.278em}{0ex}}\text{u}+8.96\phantom{\rule{0.278em}{0ex}}\text{u}\\ \\ & =35.45\phantom{\rule{0.278em}{0ex}}\text{u}\end{array}$
Because chlorine-$35$ is about three times more abundant than chlorine-$37$, the weighted average is closer to $35\phantom{\rule{0.167em}{0ex}}\text{u}$ than it is to $37\phantom{\rule{0.167em}{0ex}}\text{u}$.
Concept check: Bromine has two stable isotopes—bromine-$79$ and bromine-$81$. The relative abundance of the isotopes are $50.70\mathrm{%}$ and $49.30\mathrm{%}$, respectively. Is the atomic weight of bromine closest to $79$, $80$, or $81\phantom{\rule{0.167em}{0ex}}\text{u}$?

## Mass spectrometry

We now know how to find average atomic masses by calculating weighted averages from atomic masses and relative abundances. But where do those relative abundances come from? For example, how do we know that $75.76\mathrm{%}$ of all the chlorine atoms on Earth are chlorine-$35$?
The answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry.
In mass spectrometry, a sample containing the atoms or molecules of interest is injected into an instrument called a mass spectrometer. The sample—typically in an aqueous or organic solution—is immediately vaporized by a heater, and the vaporized sample is then bombarded by high-energy electrons. These electrons have enough energy to knock electrons off the atoms in the sample, a process which creates positively-charged ions. These ions are then accelerated through electric plates and subsequently deflected by a magnetic field (Figure 3).
The amount each ion is deflected depends on its speed and charge. Ions that are moving more slowly (i.e., the heavier ions) are deflected less, while ions that moving more quickly (i.e., the lighter ions) are deflected more. (Think of the force you need to apply to accelerate a bowling ball versus the force needed to accelerate a tennis ball—it takes much less to accelerate the tennis ball!) Additionally, the magnetic field deflects ions with higher charges more than ions with lower charges.
The amount that each ion is deflected is inversely proportional to its mass-to-charge ratio, $m/z$, where $m$ is equal to the mass of the ion and $z$ is equal to its charge. After being deflected, the ions reach a detector in the mass spectrometer, which measures two things: (1) the $m/z$ ratio for each ion and (2) how many ions it sees with a particular $m/z$ ratio. The relative abundance for a specific ion in the sample can be calculated by dividing by the number of ions with a particular $m/z$ ratio by the total number of ions detected. At the end of the experiment, the instrument generates a mass spectrum for the sample, which plots relative abundance vs. $m/z$.
Concept check: A sample of copper is injected into a mass spectrometer. After the sample is vaporized and ionized, the ions ${}^{63}{\text{Cu}}^{2+}$ and ${}^{65}{\text{Cu}}^{2+}$ are detected. Which ion is deflected more inside the spectrometer?
In some experiments, all of the ions generated by the mass spectrometer have a charge of $1+$. In this case, each ion’s $m/z$ ratio is simply equal to $m$, or the ion’s atomic mass. As a result, some simpler mass spectra have atomic mass in $\text{u}$ on the x-axis instead of $m/z$, as in the spectrum for zirconium below (Figure 4).

## Analyzing the mass spectrum of zirconium

Suppose we analyzed an average sample of pure zirconium (atomic number $40$) using mass spectrometry. After putting the sample through the instrument, we would get a mass spectrum that looks like this:
What does this spectrum reveal about zirconium? For one, there are five peaks in the spectrum, which tells us that there are five naturally occurring isotopes of zirconium. Importantly, the height of each peak shows us how abundant each isotope of zirconium is relative to the other isotopes.
Concept check: Based on this spectrum, what is the most common naturally occurring isotope of zirconium?
Finally, notice that the x-axis is labeled with atomic mass ($\text{u}$) and not $m/z$ (which means that all of the ions generated during this experiment had a charge of $1+$). So, we also know the atomic masses of the isotopes, which we can use along with their relative abundances to calculate the average atomic mass of the zirconium in our sample. To try this calculation yourself, see the practice problem at the end of the article!
These days, we already know the average atomic masses of most of the elements on the periodic table, so it's not often necessary to analyze individual elements using mass spectrometry—except to teach students! Most of the time, working chemists use mass spectrometry in the lab to help them determine the chemical formulas or structures of unknown molecules and compounds. Mass spectrometry also finds valuable application in other fields, including medicine, forensics, space exploration and more. Whether it's being used to analyze the atmosphere of an unexplored planet or characterize a newly-created molecule, mass spectrometry is instrumental to the advancement of scientific knowledge and understanding.

## Summary

• Atoms that have the same number of protons but different numbers of neutrons are known as isotopes.
• Isotopes have different atomic masses.
• The relative abundance of an isotope is the percentage of atoms with a specific atomic mass found in a naturally occurring sample of an element.
• The average atomic mass of an element is a weighted average calculated by multiplying the relative abundances of the element's isotopes by their atomic masses and then summing the products.
• The relative abundance of each isotope can be determined using mass spectrometry.
• A mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on their mass-to-charge ratios ($m/z$).
• The mass spectrum of a sample shows the relative abundances of the ions on the y-axis and their $m/z$ ratios on the x-axis. If $z=1$ for all ions, then the x-axis can instead be expressed in units of atomic mass ($\text{u}$).

## Try it!

Based on the mass spectrum of zirconium above, we get the following atomic masses and relative abundances for the isotopes of zirconium:
Isotope$\text{Zr-}90$$\text{Zr-}91$$\text{Zr-}92$$\text{Zr-}94$$\text{Zr-}96$
Atomic mass ($\text{u}$)$89.905$$90.906$$91.905$$93.906$$95.908$
Relative abundance ($\mathrm{%}$)$51.45$$11.22$$17.15$$17.38$$2.80$
Based on the data in the table, what is the average atomic mass of the zirconium in our sample?
$\text{u}$

## Want to join the conversation?

• What is a neutrino? Also, what are quarks, gluons, mesons and bosons? A detailed explanation, please.
• Neutrinos are fundamental particles similar to electrons but without a charge. Electrons and neutrinos are in a class of particles called leptons.

Quarks are fundamental particles that are the constituent particles of matter. They combined to form a class of composite particles called hadrons. Hadrons include protons and neutrons, as well as mesons, which are quark-antiquark pairs.

Bosons are force carrying particles. They include: photons which mediate the electromagnetic force, gluons which mediate the strong force, W and Z bosons which mediate the weak force, the hypothetical graviton which mediates gravity, and the Higgs boson which mediates the Higgs field. Gluons are the bosons that quarks use to 'stick' together, but they also have the unusual property that they can stick to themselves too.
• At the end of this reading material, when determining the atomic weight of zirconium, why is the answer to the product of (0.0280 x 95.908u) equal 2.68u and not 2.69u? I actually got 2.685424 and rounded up, but in the equation they figured, they did not round up as done normally in math. I'm lost. I actually got 91.24 to this equation. So...can someone please explain the reasons behind not rounding up when appropriate??
• In the 5th paragraph it is said that "1 u is equal to exactly 1/12 of the mass of a single neutral atom of carbon-12". However if you add:
6 protons times |.007 u + 6 neutrons times 1.009 u= 12.096 (mass of carbon-12)
and then we divide by 12 we get something greater than 1 u.
Should n´t the mass of 1 u be between the mass of the proton and the neutrón 1 p < 1 u <1 n? So that the atomic mass for carbón-12 be exactly 12 u?
• The total mass of 6 protons + 6 neutrons is indeed 12.096 u.
But these are isolated protons and neutrons.
Energy is released when you bring them together to form a carbon-12 nucleus.
Energy is equivalent to mass (E =mc²), and the energy released is equal to 0.096 u.
This difference is called the mass defect.
So the mass of a carbon-12 atom is 12.096 u – 0.096 u = 12.000 u
• Hey everyone...i just started learning chemistry (yep i'm a newbie) and i still can't understand the meaning of a charge...could i request a little help please? thankiew:)
• Historically, the units u and amu were defined slightly differently. Can someone please clarify?
• Atomic mass units used to be defined on oxygen and it wasn't consistent in definition between chemistry and physics. It was redefined to Carbon-12 to unify all measurements in physical and chemical sciences and to be consistent. This was officially termed 'unified atomic mass unit' and the symbol set as u.
• What is a subatomic particle?
• "sub-atomic" literally means "below the atom." When we discuss subatomic particles, we talk about any particles smaller than the atom. These could be quarks (up/down quarks, which make up protons and neutrons), leptons (neutrinos but also electrons), as well as bosons. These are typically discussed in particle physics and less often in chemistry.
• Are there any disadvantages of mass spectrometry
• No "disadvantages" but limitations instead: mass spectrometry will not tell you anything about a structure directly. Also, some types of spectrometry will not allow every molecule to be fragmented in every possible way.
• Oh come on, I got 91.31u because I didn't round at each step, only at the end?
(1 vote)
• We really shouldn’t be rounding at intermediate steps, only at the final step. The issue is that when we round too soon it introduces rounding errors which trickle down to the final answer. It is important to keep in mind the amount of significant figures allowed after each operation to know how much you need to round off your final answer.

If you do the full calculation without any premature rounding you should get 91.22377 if you do everything correct. Which would round off to 91.22 using proper significant figures.

Hope that helps.
• why is it that 0.0280×95.908u = 2.68u
I used my calculator got this: 2.685424
if you round it to the hundredths place
you would get 2.69 [5 is a midway number,
so we should round it off to the higher hundredth]
Please explain what is going on.
thanks