Mass spectroscopy is an essential analytical method that helps scientists determine the composition and structure of atoms by identifying their isotopes and relative abundance.
Understanding the Periodic Table and Atomic Mass
To begin, it’s important to understand how the periodic table reflects not only atomic number and symbol, but also atomic mass—a value that often includes decimals rather than whole numbers. This is because the atomic mass shown is not the mass of a single atom, but a weighted average of all the naturally occurring isotopes of that element.
Atomic number = number of protons in the nucleus (also equals the number of electrons in a neutral atom).
Atomic mass = weighted average of isotopic masses.
The Periodic Table. Image courtesy of Wikipedia
For example, carbon’s atomic mass is listed as 12.01 amu, which is not a whole number. This value comes from averaging the masses of its isotopes, weighted by their relative natural abundances.
Image courtesy of Science Info
What Are Isotopes?
Isotopes are atoms of the same element that contain the same number of protons but differ in their number of neutrons.
All isotopes of a given element have the same atomic number.
They have different mass numbers (protons + neutrons).
Chemical properties remain similar, but physical properties like mass vary.
Carbon Isotopes
Carbon exists naturally as three main isotopes:
Carbon-12 (¹²C)
Mass: 12 amu
Abundance: ~98.9%
Neutrons: 6 (12 - 6 protons)
Carbon-13 (¹³C)
Mass: 13 amu
Abundance: ~1.1%
Neutrons: 7 (13 - 6 protons)
Carbon-14 (¹⁴C)
Mass: 14 amu
Abundance: trace amounts
Radioactive and used in radiocarbon dating
Since carbon-14 is extremely rare, it has minimal influence on the average atomic mass calculation for carbon.
Calculating Average Atomic Mass
The average atomic mass (AAM) is determined using a weighted average of the masses of the isotopes based on their relative abundances.
Formula
Average Atomic Mass =
(abundance of isotope 1 × mass of isotope 1)
(abundance of isotope 2 × mass of isotope 2)
(abundance of isotope 3 × mass of isotope 3)
...and so on.
Important: Convert abundance percentages into decimals before using them in the formula.
Example: Carbon
Using carbon’s isotopes:
98.9% (0.989) Carbon-12
1.1% (0.011) Carbon-13
AAM = (0.989 × 12) + (0.011 × 13)
AAM = 11.868 + 0.143 = 12.011 amu
That’s why the periodic table lists carbon’s atomic mass as approximately 12.01 amu.
Changing Abundance
If the abundance of isotopes changes, the average atomic mass changes too.
For example, if carbon-12 made up only 75% and carbon-13 made up 25%:
AAM = (0.75 × 12) + (0.25 × 13)
AAM = 9 + 3.25 = 12.25 amu
This shows how sensitive atomic mass is to the natural distribution of isotopes.
Introduction to Mass Spectroscopy
Mass spectroscopy (MS) is a laboratory technique used to determine the mass and abundance of various isotopes in a sample. It provides highly accurate data about atomic composition.
How It Works
Ionization: The sample is bombarded with high-energy electrons, removing electrons from atoms to create positive ions.
Acceleration: The ions are accelerated in an electric field.
Deflection: The ions pass through a magnetic field, which bends their paths based on mass-to-charge ratio (m/z).
Detection: Lighter ions bend more and reach the detector sooner. The detector records the mass spectrum.
The mass spectrum is a graph that plots:
x-axis: mass-to-charge ratio (m/z), which typically reflects the atomic mass for singly charged ions.
y-axis: relative abundance of each isotope.
Mass Spectrum of Carbon
In a mass spectrum of carbon, you would typically see:
Image Courtesy of Professor Bensely
A large peak at m/z = 12 for carbon-12, reflecting its high abundance.
A smaller peak at m/z = 13 for carbon-13.
The height or area of each peak represents the relative abundance.
What Can You Learn?
From a mass spectrum, you can determine:
The number of isotopes.
Their exact masses.
Their natural abundances.
The average atomic mass, using the same weighted formula.
Identifying Elements Using Mass Spectrum
You can often identify an element by analyzing its mass spectrum.
Image Courtesy of Kenyaplex
Sample Problem
Suppose a spectrum shows peaks at:
m/z = 24 → 82.8%
m/z = 25 → 8.1%
m/z = 26 → 9.1%
Using the average atomic mass formula:
AAM = (0.828 × 24) + (0.081 × 25) + (0.091 × 26)
= 19.872 + 2.025 + 2.366 = 24.263 amu
Looking at the periodic table, the element with an average atomic mass of ~24.3 is magnesium (Mg).
Solving Reverse Mass Spectroscopy Problems
Sometimes, instead of calculating the average atomic mass, you are given the average atomic mass and asked to determine the percent abundances.
AP Exam Sample
Given:
Average atomic mass of neon = 20.18 amu
Neon has two isotopes: Ne-20 (mass = 19.99 amu) and Ne-22 (mass = 21.99 amu)
Let:
x = abundance of Ne-20
(1 - x) = abundance of Ne-22
Set up the equation:
20.18 = (x × 19.99) + [(1 - x) × 21.99]
Solve for x:
20.18 = 19.99x + 21.99 - 21.99x
20.18 = 21.99 - 2x
2x = 21.99 - 20.18 = 1.81
x = 0.905
So:
Ne-20 = 90.5%
Ne-22 = 9.5%
Tips for Solving These
Always convert percentages to decimals.
Remember that the total abundance must equal 1 (or 100%).
Assign x and 1 - x to the two isotopes when only two are involved.
Using Mass Spectroscopy for Stoichiometry
Mass spectroscopy can also be used to perform stoichiometric calculations, especially when dealing with specific isotopes.
Example Problem
You are asked to find the number of Ne-22 atoms in a 6.55 g sample of neon. Use:
Molar mass of neon = 20.18 g/mol
Percent abundance of Ne-22 = 9.5%
Avogadro’s number = 6.022 × 10²³ atoms/mol
Step 1: Convert grams to moles
6.55 g / 20.18 g/mol = 0.3244 mol
Step 2: Multiply by abundance of Ne-22
0.3244 mol × 0.095 = 0.0308 mol Ne-22
Step 3: Convert moles to atoms
0.0308 mol × 6.022 × 10²³ = 1.85 × 10²² Ne-22 atoms
Understanding how to do unit conversions using dimensional analysis is critical here.
Key Vocabulary to Know
Isotopes: Atoms with the same number of protons but different numbers of neutrons.
Mass spectrometry: Technique to measure the mass and abundance of isotopes.
Mass spectrum: Graph showing relative abundance vs. mass-to-charge ratio.
Average atomic mass: Weighted average of all isotope masses based on abundance.
Abundance: The percentage of a particular isotope in a natural sample.
Atomic mass unit (amu): Standard unit of atomic mass.
m/z ratio: Mass-to-charge ratio used in mass spectrometry.
Avogadro’s number: 6.022 × 10²³ particles/mol.
Dimensional analysis: Method of converting between units using conversion factors.
FAQ
Isotopes become unstable when the ratio of neutrons to protons in their nucleus is too far from the optimal balance, making the nucleus energetically unfavorable. These isotopes are known as radioactive isotopes. Over time, they decay into more stable forms, emitting radiation. In mass spectroscopy, radioactive isotopes can still appear if they are present in the sample and have not decayed, but their abundance is usually much lower than stable isotopes. Their signals may be weak or absent if the isotope has a short half-life or if the sample does not contain measurable amounts. Key points:
Unstable isotopes have an imbalance in the neutron-to-proton ratio.
They undergo radioactive decay, often transforming into a different element.
In mass spectra, they may produce small or undetectable peaks depending on stability.
Their limited natural presence typically means they contribute negligibly to average atomic mass calculations.
Mass spectroscopy analyzes individual isotopic patterns, not just average atomic mass. Two different elements may have similar average atomic masses, but their isotopic signatures—the number, position, and intensity of peaks in the mass spectrum—are distinct. This allows scientists to differentiate elements based on the exact mass of each isotope and their relative abundances. For instance, chlorine (with major isotopes at 35 and 37 amu) and argon (with isotopes near 36 and 40 amu) may appear close in average mass but show different isotope distributions. Mass spectrometry identifies:
Unique isotope count and spacing.
Precise m/z values for each isotope.
Different relative abundance ratios.
Fine resolution to detect subtle differences between elements.
Yes, mass spectroscopy is highly sensitive and can detect trace amounts of specific elements or isotopes in complex mixtures. Modern mass spectrometers can measure quantities as small as parts per trillion (ppt). This makes them essential in forensic science, environmental monitoring, and biomedical research. When a complex sample is ionized, the spectrometer can separate and detect even minute signals from rare isotopes or contaminants. Techniques like high-resolution MS or tandem MS/MS increase specificity and sensitivity. In practice:
Samples are often purified to reduce background noise.
Ionization techniques can be tuned to target specific substances.
Detectors can amplify low-abundance signals for accurate measurement.
Calibration with known standards helps verify low-level isotope presence.
In mass spectroscopy, the detector measures the mass-to-charge ratio (m/z) of ions. Most ions generated have a single positive charge (z = +1), so the m/z value corresponds directly to their mass. However, if an ion has multiple charges (e.g., z = +2), its m/z value is half its actual mass. This affects where the peak appears on the spectrum and must be accounted for in analysis. For elements with multiple charge states, this can result in overlapping or shifted peaks, especially in large biomolecules. Key implications:
m/z = mass / charge, so higher charges lower the measured value.
Peak identification requires knowing the charge state of each ion.
Multiply charged ions are common in protein or peptide analysis.
Charge state affects both spectral complexity and resolution.
Calibration is critical in mass spectroscopy to produce accurate and reproducible results. Instruments are calibrated using standard reference materials with well-known masses and isotope distributions. These standards help correct for systematic errors, drift, and instrument-specific biases. Calibration typically involves:
Running a standard sample with known m/z values.
Adjusting the detector and magnetic field settings to match expected outcomes.
Verifying peak position and resolution across the m/z range.
Using internal standards within a sample to correct for variations during analysis.
Practice Questions
A sample of element X is analyzed using mass spectrometry. The spectrum shows three isotopes with the following data: X-28 (mass = 28 amu, abundance = 91.5%), X-29 (mass = 29 amu, abundance = 4.5%), and X-30 (mass = 30 amu, abundance = 4.0%). Calculate the average atomic mass and identify the element based on this value.
The average atomic mass of element X is calculated using the formula: (0.915 × 28) + (0.045 × 29) + (0.040 × 30) = 25.62 + 1.305 + 1.2 = 28.125 amu. This value closely matches the atomic mass of silicon on the periodic table, which is approximately 28.09 amu. Therefore, the element in question is silicon. Mass spectrometry data allows us to determine this by measuring the mass and relative abundance of each naturally occurring isotope, which directly impacts the average atomic mass and helps identify the element. Silicon’s isotopes match both the given masses and the relative abundances.
Explain how mass spectrometry can be used to distinguish between two isotopes of the same element and how this information is used to calculate average atomic mass.
Mass spectrometry distinguishes isotopes by measuring the mass-to-charge ratio of ions. Since isotopes of the same element have the same number of protons but different numbers of neutrons, they have different masses. In a mass spectrum, each isotope appears as a separate peak along the x-axis (mass-to-charge ratio), with peak height reflecting relative abundance. By analyzing the position and intensity of these peaks, scientists calculate the average atomic mass using the formula: (relative abundance × mass) for each isotope. This method accurately reflects the weighted average of all isotopes naturally occurring in a sample of the element.
