Atomic Mass Unit, Isotopes, and Relative Atomic Mass

Unified atomic mass unit (AU)

  • AU defined as 1.66054 \times 10^{-27} \text{ kg}; historically AMU; modern term AU.
  • A mass scale for atoms; 1 AU is extremely small.
  • Mass units connect to grams/kilograms via this scale.

Mass composition and fundamental particles

  • Atoms are composed of protons, neutrons, electrons; mass mainly from protons and neutrons.
  • Proton mass: mp \approx 1.007 \, AU; Neutron mass: mn \approx 1.008 \, AU; Electron mass: m_e \approx 5.485 \times 10^{-4} \, AU.
  • Electron mass is about me/mp \approx 1/1836. Thus the nucleus dominates atomic mass.

Atomic numbers and element identity

  • Atomic number Z equals number of protons; defines the element.
  • Hydrogen: Z = 1; Calcium: Z = 20; Krypton: Z = 36.

Isotopes and common forms of hydrogen

  • Isotopes: same Z, different neutrons; different masses.
  • Hydrogen most common isotope: protium, nucleus: 1 proton, 0 neutrons; neutral atom has 1 electron.
  • Most hydrogen in the universe (~99.98%) has 1 proton, 0 neutrons.
  • Mass of protium is approximately the mass of a proton plus electron; roughly \approx 1.008 \, AU; actual weighted average for hydrogen is close to this value.

Average atomic mass and relative atomic mass

  • Average atomic mass: the weighted average of isotopic masses, using natural abundances.
  • Formula: \bar{m} = \sumi fi mi where (fi) are fractional abundances.
  • Atomic weight (older term) refers to this mass concept; modern term is average atomic mass.
  • Relative atomic mass: unitless ratio of an atom's mass to 1/12 of carbon-12; expression: (A_r).
  • Examples: (Ar(\mathrm{C}) \approx 12), (Ar(\mathrm{H}) \approx 1).
  • The numbers on the periodic table are unitless, i.e., relative atomic masses.

Quick illustrate example

  • Example: if 80% of sample is isotope with mass 5 AU and 20% with mass 6 AU, then the average mass is 0.8 \times 5 + 0.2\times 6 = 5.2 \text{ AU}.