Mass spectrometry of elements Knowledge-Based Study

Study notes

1. What is Mass Spectrometry?

   Mass spectrometry is an analytical technique used to determine the relative isotopic masses and relative abundances of isotopes in a sample of an element. This information allows scientists to calculate the element's relative atomic mass ($A_r$).

   Key Stages of a Time-of-Flight or Magnetic Deflection Mass Spectrometer

   1. Ionization: Atoms in the gaseous sample are converted into positive ions, typically by knocking off one or more electrons using high-energy electrons (electron impact) or electrospray ionization. The resulting species are predominantly singly charged positive ions, represented as $M^+$.
   2. Acceleration: An electric field accelerates the positive ions to give all ions of the same charge identical kinetic energy.
   3. Deflection / Drift: The ions are separated based on their mass-to-charge ratio ($m/z$). In magnetic deflection instruments, lighter ions and ions with higher charges are deflected more strongly by a magnetic field. In time-of-flight (TOF) instruments, lighter ions travel faster and reach the detector sooner.
   4. Detection: When positive ions hit the detector, they gain electrons, generating an electrical signal. The size of the current produced is directly proportional to the abundance of that specific ion.

   Reading the Spectrum

   The output of a mass spectrometer is displayed as a graph called a mass spectrum.

   • Horizontal Axis ($x$-axis): Displays the mass-to-charge ratio ($m/z$). Because most ions formed have a charge of $+1$, the $m/z$ value directly corresponds to the isotopic mass or mass number of each isotope.
   • Vertical Axis ($y$-axis): Displays the relative abundance or percentage abundance of each ion. The height of each peak indicates how abundant that isotope is relative to the others.

   Example: Naturally Occurring Neon

   A mass spectrum of elemental neon exhibits three distinct peaks:

   • Peak at $m/z = 20$ with a relative abundance of approximately 90.48%
   • Peak at $m/z = 21$ with a relative abundance of approximately 0.27%
   • Peak at $m/z = 22$ with a relative abundance of approximately 9.25%

   These peaks demonstrate that naturally occurring neon consists of three stable isotopes: $^{20}\text{Ne}$, $^{21}\text{Ne}$, and $^{22}\text{Ne}$.

   Determining Relative Atomic Mass ($A_r$)

   The relative atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes, relative to one-twelfth of the mass of a carbon-12 atom.

   Formula

   When abundances are given as percentages:

   $$A_r = \frac{\sum (\text{isotopic mass} \times \text{percentage abundance})}{100}$$

   Worked Calculation for Neon

   Using the data from neon's mass spectrum:

   $$A_r(\text{Ne}) = \frac{(20 \times 90.48) + (21 \times 0.27) + (22 \times 9.25)}{100}$$$$A_r(\text{Ne}) = \frac{1809.6 + 5.67 + 203.5}{100} = \frac{2018.77}{100} = 20.19$$

   Notice that the calculated relative atomic mass (20.19) is close to 20 because the $^{20}\text{Ne}$ isotope is by far the most abundant.

   Common Misconceptions

   • Mass Number vs. Relative Atomic Mass: The mass number of an individual isotope is an integer representing the sum of protons and neutrons. In contrast, relative atomic mass is usually a non-integer value because it represents a weighted average across all naturally occurring isotopes.
   • Doubly Charged Ions ($M^{2+}$): Occasionally, an atom loses two electrons during ionization to form a $+2$ ion. If a $^{24}\text{Mg}^{2+}$ ion forms, its mass-to-charge ratio will appear at $m/z = 24 / 2 = 12$, not 24.
   • Diatomic Elements: When elements that exist as diatomic molecules (such as chlorine, $\text{Cl}_2$) are analyzed, both individual atomic ions ($\text{Cl}^+$) and intact molecular ions ($\text{Cl}_2^+$) may be detected, producing multiple distinct sets of peaks.