Atomic Structure and Isotopes - Vocabulary Flashcards

Atomic Structure and Scales

  • Ordinary human senses perceive the world on a macroscopic scale (down to about 10^{-3} m), but actual chemistry happens on a nanoscopic scale (10^{-9} m or less).
  • The basic building blocks of matter are atoms: the kinds of atoms present (composition) and their arrangements (structure) determine observed macroscopic properties and behavior of matter.
  • Chemists must think in terms of tiny, invisible atoms to understand substances of the macroscopic world.
  • Atomic sizes and masses are very small:
    • Atoms are about 100 to 500 pm in diameter (1–5 Å; 1 Å = 100 pm = 10^{-10} m).
    • The heaviest atoms have masses on the order of 10^{-22} g.
  • Atoms are built from subatomic particles that matter for chemical behavior: protons, neutrons, and electrons.
  • Protons and neutrons reside in the nucleus (extremely small, on the order of 10^{-14} m) and account for virtually all the atom’s mass.
  • The vast majority of the atom’s volume is empty space occupied by a cloud of rapidly moving electrons, which contribute negligibly to the mass of the atom.
  • On the scale of atoms, the nucleus is tiny compared to the whole atom; if drawn to scale, the nucleus would be unnoticeably small relative to the atom.
  • Distances and scale:
    • Atom diameter: ~10^{2}–10^{3} pm; nucleus diameter is far smaller.
    • Nucleus: ~10^{-14} m; electron cloud extends to ~10^{-10} m.

Electrostatic Forces in Atoms

  • Electrons and protons are held together by an attractive electrostatic force.
  • The electrons do not fly away because they are attracted to the positively charged protons in the nucleus by an electrostatic force obeying Coulomb's law: F=kQ<em>1Q</em>2r2F = k \frac{Q<em>1 Q</em>2}{r^2} where:
    • $F$ is the electrostatic force magnitude,
    • $k$ is the Coulomb constant ($k \approx 8.9875 \times 10^{9}\ \mathrm{N}\,\mathrm{m}^2\ \mathrm{C}^{-2}$),
    • $Q1$ and $Q2$ are the interacting charges,
    • $r$ is the separation between charges.
  • Charge values for fundamental particles:
    • Electron: $e = -1.602 \times 10^{-19}$ C,
    • Proton: $+e = +1.602 \times 10^{-19}$ C,
    • Neutron: charge $q = 0$ (neutral).
  • Subatomic particle masses (relevant for units and comparisons):
    • Proton mass: $m_p = 1.6726 \times 10^{-27}$ kg,
    • Neutron mass: $m_n = 1.6749 \times 10^{-27}$ kg,
    • Electron mass: $m_e = 9.1094 \times 10^{-31}$ kg.
  • Relative contributions: nuclei carry most of the mass; electron cloud carries most of the volume but little mass.

Atomic Mass Units, Charge, and Subatomic Particles

  • For convenience, atomic units are defined:
    • Electric charge (au) is expressed as a multiple of the electron charge $e$ (i.e., $q \text{(au)} = Q/e$).
    • The atomic mass unit (amu or u) is defined as 1 amu=1.66054×10−24 g=1.66054×10−27 kg,1 \text{ amu} = 1.66054 \times 10^{-24} \text{ g} = 1.66054 \times 10^{-27} \text{ kg}, exactly 1/12 of the mass of carbon-12 (which has 6 protons and 6 neutrons).
  • Particle properties (typical values):
    • Proton: charge $q = +1.602 \times 10^{-19}$ C; charge in au $+1$; mass $m = 1.6726 \times 10^{-27}$ kg; mass in amu $\approx 1.0073$.
    • Neutron: charge $q = 0$ C; charge in au $0$; mass $m = 1.6749 \times 10^{-27}$ kg; mass in amu $\approx 1.0087$.
    • Electron: charge $q = -1.602 \times 10^{-19}$ C; charge in au $-1$; mass $m = 9.1094 \times 10^{-31}$ kg; mass in amu $\approx 5.486 \times 10^{-4}$.
  • The chemical identity of an atom is designated by its atomic number $Z$ (the number of protons).
  • An element is a collection of one or more atoms with the same number of protons (same $Z$).
  • There are about 100 naturally occurring or synthetic elements.
  • Isotopes are atoms with the same atomic number (same $Z$) but different numbers of neutrons.

Isotopes and Atomic Notation

  • Atoms of a given element can differ in the number of neutrons in their nuclei, yielding isotopes.
  • Hydrogen isotopes (naturally occurring):
    • Protium: most abundant (~99.98%), isotope mass number $A=1$ (no neutrons).
    • Deuterium: $A=2$ (one neutron), abundance ~0.0156%.
    • Tritium: $A=3$ (two neutrons), abundance ~4 × 10^{-15}% (radioactive).
  • Isotope notation uses mass number superscript and atomic number subscript:
    • Mass number $A$ = protons + neutrons, Atomic number $Z$ = protons.
    • Nuclear notation example: A<em>ZX^{A}<em>{Z}\mathrm{X} (e.g., 3</em>1H^{3}</em>{1}\mathrm{H} for tritium).
  • Because the atomic number $Z$ fixes the atomic symbol, the subscript is often omitted in practice (e.g., 12C^{12}\mathrm{C} or 612C^{12}_{6}\mathrm{C} both refer to carbon-12).
  • Examples of natural isotopes (illustrative): carbon isotopes 12C, 13C^{12}\mathrm{C}, \ ^{13}\mathrm{C}; uranium isotopes 235U, 238U^{235}\mathrm{U}, \ ^{238}\mathrm{U}; oxygen isotopes 16O, 17O, 18O^{16}\mathrm{O}, \ ^{17}\mathrm{O}, \ ^{18}\mathrm{O} (isotopes difficult to visualize, shown out of scale in diagrams).
  • Isotopes differ in mass but chemical behavior is largely governed by electronic structure; nuclei remain unchanged in chemical reactions.

Atomic Weight and Natural Abundances; Mass Spectrometry

  • In nature, elements exist as mixtures of isotopes with specific natural abundances.
  • Atomic weight (AW) is the weighted average of the masses of all isotopes present:
    AW=∑<em>i(m</em>i×f<em>i)\mathrm{AW} = \sum<em>i (m</em>i \times f<em>i) where $mi$ is the isotope mass and $f_i$ is its fractional natural abundance.
  • Example: naturally occurring carbon contains 98.93% 12C^{12}\mathrm{C} (mass 12 amu) and 1.07% 13C^{13}\mathrm{C} (mass 13.00335 amu).
    AW(C)=(0.9893)(12)+(0.0107)(13.00335)=12.01  amu.\mathrm{AW}(\mathrm{C}) = (0.9893)(12) + (0.0107)(13.00335) = 12.01\;\text{amu}.
  • Mass spectrometry: a precise method to determine isotope composition:
    • Atoms are ionized in vacuum and ejected electrons are removed.
    • Resulting ions travel in a magnetic field; their paths bend according to mass/charge ratio ($m/q$).
    • Ion detectors measure the relative abundances of ions with different masses, allowing calculation of isotopic distributions and AW.
  • The physical basis of the technique is the dependence of path curvature on $m/q$; heavier isotopes (larger $m$) bend less than lighter isotopes for the same charge.
  • The ability to determine isotope masses and abundances with mass spectrometry enables precise AW determinations for many elements (e.g., carbon, uranium). The figure references show naturally occurring isotopes such as 235U^{235}\mathrm{U} and 238U^{238}\mathrm{U}, among others.

Conservation of Mass and Nuclear Stability in Chemical Reactions

  • In chemical reactions, the nuclei remain unchanged; only the electron clouds reorganize during bonding and reorganization of electrons.
  • Consequently, atoms are not created or destroyed in chemical processes; the law of conservation of mass applies at the chemical level.
  • This conservation reflects that chemical changes involve only electrons and their configurations, not changes in nuclear composition.