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: $m<em>p \approx 1.007 \, AU$; Neutron mass: $m</em>n \approx 1.008 \, AU$; Electron mass: $m_e \approx 5.485 \times 10^{-4} \, AU$.
• Electron mass is about $m<em>e/m</em>p \approx 1/1836$. 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: $\bar{m} = \sum<em>i f</em>i m<em>i$ 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 $0.8 \times 5 + 0.2\times 6 = 5.2 \text{ AU}$.