Atomic Mass and Mass Spectrometry

Atomic Mass

• Protons and neutrons contribute approximately 1 amu each; electrons contribute far less.
• Atomic mass of a single atom ≈ its mass number: $A \approx \text{mass number}$
• Average atomic mass is a weighted average of isotopes present in a naturally occurring sample of that element.
• Formula: $ext{Average mass} = \sum<em>i (f</em>i \cdot m<em>i)$ or, for a simple case, $ext{Average mass} = (f</em>1 \cdot m<em>1) + (f</em>2 \cdot m<em>2) + \cdots$ where $f</em>i$ is the fractional abundance and $m_i$ is the isotopic mass.
• Example: Boron has two isotopes:
  • 10B: abundance $f=0.199$, mass $m=10.0129 \text{amu}$
  • 11B: abundance $f=0.801$, mass $m=11.0093 \text{amu}$
• Boron average mass:
  $ext{Boron average mass} = (0.199 \times 10.0129) + (0.801 \times 11.0093) \text{amu} = 10.81 \text{amu}$
• Important: No single boron atom weighs exactly 10.81 amu; it is the average mass of all boron atoms.
• Note: Most elements exist naturally as mixtures of two or more isotopes.

Mass Spectrometry

• Mass spectrometry (MS) determines the occurrence and natural abundances of isotopes.
• Applications: chemistry, forensics, medicine, environmental science, and many other fields.
• How a typical MS works:
  • The sample is vaporized and ionized by a high-energy electron beam, usually by removing one or more electrons, creating cations.
  • Cations pass through a variable electric or magnetic field; their path is deflected based on mass and charge, analogous to a magnet deflecting different-sized steel balls.
  • Ions are detected to produce a spectrum.
• Mass spectrum: a plot of the relative number of ions versus mass-to-charge ratio, $m/z$.
• Peak height is proportional to the fraction of cations with the specified $m/z$.
• MS has evolved into a powerful analytical tool across many disciplines since its early use in developing modern atomic theory.