Mass Spectra of Elements
Look at the periodic table: chlorine's atomic mass is 35.45. But no single chlorine atom has a mass of 35.45 u. So where does that number come from? A mass spectrometer answers the question by sorting atoms by mass and counting how many of each kind there are.
Isotopes and the mass spectrum
Atoms of the same element always have the same number of protons, but they can have different numbers of neutrons. Atoms like these are called isotopes. They have different mass numbers (protons + neutrons), and so slightly different masses.
A mass spectrometer works in four steps. It turns atoms of a sample into positive ions, accelerates them, bends their path with a magnetic field, and counts them at a detector. Lighter ions bend more than heavier ones, so the ions are sorted by mass.
The result is a mass spectrum, a bar graph with two axes:
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The x-axis is the mass-to-charge ratio, $m/z$. For ions with a $1+$ charge, $m/z$ is just the mass of the ion in u.
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The y-axis is the relative abundance: how common that isotope is in the sample.
Each peak is one isotope. The position tells you which isotope it is. The height tells you how much of it there is.
A mass spectrum of a sample of neon shows three peaks, at mass-to-charge ratios of 20, 21, and 22. What does each peak represent, and what does the height of each peak…
A mass spectrum of a sample of neon shows three peaks, at mass-to-charge ratios of 20, 21, and 22. What does each peak represent, and what does the height of each peak tell you?
Why atomic mass is not a whole number
The atomic mass on the periodic table is the average atomic mass. It is a weighted average of the masses of all the naturally occurring isotopes. Isotopes that are more common count more.
Think of a class grade. A test worth 70% of your grade counts more than a quiz worth 30%. In the same way, an isotope that makes up 75% of the atoms counts more than one that makes up 25%.
Since chlorine is 75.77% $^{35}\text{Cl}$ and 24.23% $^{37}\text{Cl}$, its average falls between 35 and 37. It is much closer to 35, because that isotope is more common. The average, 35.45, matches no single atom. That is why it is not a whole number.
A mass spectrum of element X shows only two peaks: one at 10 with a relative abundance of 20%, and one at 11 with a relative abundance of 80%. Which isotope is more…
A mass spectrum of element X shows only two peaks: one at 10 with a relative abundance of 20%, and one at 11 with a relative abundance of 80%. Which isotope is more abundant? Would you expect the average atomic mass of X to be closer to 10 or to 11?
Chlorine has two naturally occurring isotopes, $^{35}\text{Cl}$ (75.77%) and $^{37}\text{Cl}$ (24.23%). Explain why the average atomic mass of chlorine on the periodic…
Chlorine has two naturally occurring isotopes, $^{35}\text{Cl}$ (75.77%) and $^{37}\text{Cl}$ (24.23%). Explain why the average atomic mass of chlorine on the periodic table is 35.45 and not a whole number.
Calculating average atomic mass
You can also work backward. If you know the average mass and the isotope masses, you can find the abundances. Use $x$ for one fraction and $1 - x$ for the other.
When a problem gives only mass numbers (as in a simple spectrum), you can use them as the isotope masses. The answer is then a good estimate, and you can match it to the periodic table to identify the element.
Lithium has two isotopes: $^{6}\text{Li}$ with a mass of 6.015 u and $^{7}\text{Li}$ with a mass of 7.016 u. In a mass spectrum, the $^{6}\text{Li}$ peak has a relative…
Lithium has two isotopes: $^{6}\text{Li}$ with a mass of 6.015 u and $^{7}\text{Li}$ with a mass of 7.016 u. In a mass spectrum, the $^{6}\text{Li}$ peak has a relative abundance of 7.5% and the $^{7}\text{Li}$ peak has 92.5%. Calculate the average atomic mass of lithium to three decimal places.
Copper has two isotopes, $^{63}\text{Cu}$ (62.93 u) and $^{65}\text{Cu}$ (64.93 u). The average atomic mass of copper is 63.55 u. Determine the percent abundance of each…
Copper has two isotopes, $^{63}\text{Cu}$ (62.93 u) and $^{65}\text{Cu}$ (64.93 u). The average atomic mass of copper is 63.55 u. Determine the percent abundance of each isotope.
A student's mass spectrum of an element shows peaks at 24 (relative abundance 79.0), 25 (10.0), and 26 (11.0). Calculate the average atomic mass using the mass numbers…
A student's mass spectrum of an element shows peaks at 24 (relative abundance 79.0), 25 (10.0), and 26 (11.0). Calculate the average atomic mass using the mass numbers as the isotope masses, then identify the element.
Spectra of molecules and more complex cases
Bromine gas is made of $\text{Br}_2$ molecules. Atomic bromine has two isotopes, $^{79}\text{Br}$ and $^{81}\text{Br}$, in nearly equal amounts. A $\text{Br}_2$ molecule can contain any pair of them:
| Combination | Molecular mass number |
|---|---|
| $^{79}\text{Br}$–$^{79}\text{Br}$ | 158 |
| $^{79}\text{Br}$–$^{81}\text{Br}$ (either order) | 160 |
| $^{81}\text{Br}$–$^{81}\text{Br}$ | 162 |
The middle combination can form in two ways, so it is about twice as likely. With 50.7% and 49.3%, the probabilities are roughly $0.507^2 \approx 0.26$, $2(0.507)(0.493) \approx 0.50$, and $0.493^2 \approx 0.24$. The peaks are in a ratio of about 1 : 2 : 1.
So a molecule's spectrum differs from an atom's: the molecular peaks show every possible combination of isotopes.
Bromine exists as two isotopes of nearly equal abundance, $^{79}\text{Br}$ and $^{81}\text{Br}$. The mass spectrum of gaseous $\text{Br}2$ shows three peaks for the…
Bromine exists as two isotopes of nearly equal abundance, $^{79}\text{Br}$ and $^{81}\text{Br}$. The mass spectrum of gaseous $\text{Br}_2$ shows three peaks for the molecule. (a) Give the mass number of each molecular peak. (b) Predict the approximate relative heights of the three peaks, assuming the isotopes are 50.7% and 49.3% abundant, and justify your answer. (c) Explain why the spectrum of $\text{Br}_2$ differs from that of atomic bromine.
An element Z has three isotopes. The mass spectrum gives: $^{A}\text{Z}$ at 28.0 u, $^{B}\text{Z}$ at 29.0 u, and $^{C}\text{Z}$ at 30.0 u. The 28.0 u isotope is 90.0%…
An element Z has three isotopes. The mass spectrum gives: $^{A}\text{Z}$ at 28.0 u, $^{B}\text{Z}$ at 29.0 u, and $^{C}\text{Z}$ at 30.0 u. The 28.0 u isotope is 90.0% abundant, and the average atomic mass is 28.2 u. (a) Find the abundances of the other two isotopes. (b) Explain why the problem has a unique answer only because both the average mass and one abundance were given. (c) Describe how the spectrum would change if the sample were enriched in the heaviest isotope.
Back to the start: chlorine's 35.45 is a weighted average of $^{35}\text{Cl}$ and $^{37}\text{Cl}$, pulled toward 35 because that isotope makes up about three-fourths of all chlorine atoms.