Atomic Mass Unit & Average Atomic Mass

Scale & Purpose of Atomic Mass Units

• Chemistry examines phenomena at atomic/sub-atomic scale; requires specialized mass units for practicality.
• Conventional units (g, kg) are impractical for particles; chemists use the atomic mass unit.

Unified Atomic Mass Unit (u)

• Modern standard: unified atomic mass unit (symbol $u$).
• Definition: $1\,\text{u} = 1.660540 \times 10^{-27}\,\text{kg}$ (extremely small—$10^{-27}$ power).
• Chosen so common subatomic particles have masses near integer $u$ values, simplifying calculations.

Mass of Sub-Atomic Particles

• Proton: $\approx 1.007\,\text{u}$
• Neutron: $\approx 1.008\,\text{u}$
• Electron: $\approx \tfrac{1}{2000}\,\text{u}$ (mass negligible vs. nucleus).

Atomic Number & Element Identity

• Atomic number (top of periodic-table tile) = number of protons in nucleus.
  • $Z=1$ → Hydrogen, $Z=20$ → Calcium, $Z=36$ → Krypton.
• Element identity is fixed by $Z$; changing proton count changes the element.

Isotopes

• Isotopes = atoms of same element (same $Z$) with different neutron counts.
• Example: Hydrogen
  • $^1\text{H}$ (99.98 %): 1 proton, 0 neutrons, mass $\approx 1\,\text{u}$.
  • Heavier isotopes contain 1 or 2 neutrons.

Average (Relative) Atomic Mass

• Periodic-table value is a weighted average of all naturally occurring isotopes.
• Weighted mean: $\bar{m} = \sum<em>i f</em>i m_i$
  • Example: $0.80\times5 + 0.20\times6 = 5.2\,\text{u}$.
• Older term atomic weight; more precise term average atomic mass (with unit $u$).
• When units omitted, numbers represent relative atomic mass (unitless ratio to $1\,\text{u}$).

Practical Takeaways

• Nuclear (protons + neutrons) mass dominates atomic mass; electrons usually ignored in rough estimates.
• Knowing isotope distribution and $u$ definition allows prediction of atomic and molecular masses, foundational for stoichiometry and further chemical calculations.