Comprehensive Notes on Atomic Theory, Subatomic Particles, and Chemical Formulas

Origins of Atomic Theory

• The Greek Scholars: The concept of a "smallest bit of matter" originated with the ancient Greeks, specifically Leucippus and Democritus. It is unclear which individual first proposed the idea, as one was the student of the other and the concept appears in both of their writings.
  • Atomos: The modern word "atom" comes from the Greek word for "indivisible." These scholars argued there is a "bottom" or a discrete, smallest chunk of matter.
• The Competing View: Aristotle championed an opposing idea, suggesting there is no "bottom" to matter. He argued that matter could be divided infinitely and that it was composed of combinations of elements.
• Early Elements: Aristotle and his contemporaries believed matter was composed of four elements: Earth, Air, Fire, and Water. Later, they added "ether," a bizarre substance supposed to permeate all space. The speaker compares this concept to "The Force" in Star Wars.
• Longevity of the Greek Hypothesis: This non-scientific view of matter as earth, air, fire, and water persisted as the prevailing hypothesis for nearly 2,000 years.

Dalton's Atomic Theory and the Scientific Method

• John Dalton (1807): A schoolteacher who revived the ideas of Leucippus and Democritus about 200 years ago. This is remarkably recent compared to the work of Copernicus (1500s) or Newton (1600s). Dalton was unique because he performed experiments to support his ideas.
• Dalton's Postulates: A postulate is a proposal made without complete evidence. Dalton's summary included:
  • Atoms as Units: Elements consist of atoms, which are the smallest units that participate in chemical changes (bond breaking and formation).
  • Characteristic Mass: Each element consists of only one type of atom, and all atoms of that element have a characteristic mass.
  • Correction to Dalton's Mass Postulate: Through the scientific method, it was later discovered (about 100 years after Dalton) that atoms of the same element can have different masses. These are called isotopes (e.g., all Hydrogen atoms have 1 proton, but can have 0, 1, or 2 neutrons, changing their mass).
  • Unique Properties: Atoms of one element differ in properties from atoms of all other elements. While different elements can have the same number of electrons, they cannot have the same number of protons.
  • Whole Number Ratios: Atoms combine in simple, whole-number ratios to form compounds (e.g., $1:1$, $1:2$, $2:5$). This implies a "bottom" to matter because you cannot have a formula like $\text{NaCl}_{1.5}$.
  • Conservation of Matter: Atoms are neither created nor destroyed during chemical change, only rearranged. This contradicted 1,000 years of alchemy, which suggested lead could be transmuted into gold (an impossibility since gold is heavier than lead).

Evolution of Atomic Structure: Subatomic Discovery

• J.J. Thompson (1897): Used electricity and magnetic fields to study the atom after the discovery of magnetism and electric charges.
  • Cathode Ray Tube: Thompson generated a beam in a vacuum using high voltage across charged plates. He used a phosphorus-painted screen that would glow when struck by the beam.
  • Discovery of Electrons: By using a magnet, he could deflect the beam, proving it was composed of charged particles. He calculated the charge-to-mass ratio ($1.8 \times 10^{11}\,\text{C/kg}$).
  • Arbitrary Charge Assignment: Electrons were assigned a "negative" charge arbitrarily; they could just as easily have been called positive.
• Millikan's Oil Drop Experiment (1909):
  • Used an X-ray source to knock electrons loose from oil droplets, making them charged. By applying an electric field between plates, he suspended the droplets in mid-air.
  • Charge Calculation: He determined the charge of an individual electron is $-1.6 \times 10^{-19}\,\text{C}$.
  • Mass Calculation: Combining his result with Thompson's ratio, he calculated the mass of an electron as approximately $9.1 \times 10^{-31}\,\text{kg}$ (within $1\%$ of the modern known value of $9.10938356 \times 10^{-31}\,\text{kg}$).
• Atomic Models:
  • Plum Pudding Model (Thompson): Atoms as a "pudding" of positive charge with electron "chunks" floating in it.
  • Saturnian Model (Japanese physicist): A central ball of positive charge surrounded by rings of electrons.

The Nuclear Atom and the Gold Foil Experiment

• Ernest Rutherford: His work was largely carried out by a 20-year-old undergraduate specifically using the Gold Foil Experiment.
  • Source: Radioactive radium in a lead block emitted a beam of positively charged alpha particles.
  • Observation: Most particles went straight through the gold foil, but some ricocheted at odd angles or bounced straight back.
  • The Metaphor: Rutherford described this as being as surprising as firing a 15-inch artillery shell at a piece of tissue paper and having it bounce off.
  • Conclusion: All positive charge and most mass must be concentrated in a tiny area called the nucleus.
  • Empty Space: The rest of the atom is almost entirely empty space. If the nucleus were a blueberry at midfield in a football stadium, the electron cloud would extend past the library and gymnasium, and the electrons themselves would be smaller than grains of sand.
• Missing Pieces:
  • Frederick Soddy: Discovered isotopes (atoms of the same element with different masses).
  • James Chadwick (1932): Discovered the neutron, the uncharged high-mass particle in the nucleus that accounts for the mass difference in isotopes.

Modern Atomic Structure and Units

• Subatomic Particle Properties:
  • Protons: Found in the nucleus, charge of $+1$, mass approximately $1\,\text{amu}$.
  • Neutrons: Found in the nucleus, charge of $0$, mass approximately $1\,\text{amu}$.
  • Electrons: Found in the cloud, charge of $-1$, mass is approximately $\frac{1}{2000}$ of a proton ($5 \times 10^{-4}\,\text{amu}$).
• Units of Measurement:
  • Length: The Angstrom (1 \, \text{Å}) is $10^{-10}\,\text{m}$. The nucleus is $10^{-15}\,\text{m}$.
  • Mass: The Atomic Mass Unit (amu) is defined as precisely $\frac{1}{12}$ the mass of a Carbon-12 atom ($6$ protons, $6$ neutrons).
  • Fundamental Unit of Charge (e): The charge of a single electron ($1.6 \times 10^{-19}\,\text{C}$).
• Atomic Definitions:
  • Atomic Number (Z): The number of protons. This defines the identity of the element.
  • Mass Number (A): The sum of protons and neutrons.
  • Neutral Atom: An atom where the number of protons equals the number of electrons.

Isotopes and Ions

• Isotope Notation: Written as ${}^A_Z \text{X}$, where $A$ is the mass number, $Z$ is the atomic number, and $\text{X}$ is the chemical symbol.
  • Hydrogen Isotopes: Protium ($0$ neutrons), Deuterium ($1$ neutron), and Tritium ($2$ neutrons).
  • Natural Abundance: The fixed percentage of each isotope found in nature, which does not vary by geography.
• Average Atomic Mass: The number on the periodic table is a weighted average of all isotopes of that element.
  • Calculation: Convert natural abundance percentages to decimals, multiply by the mass of each isotope, and sum the results.
  • Example: Boron is a weighted average of Boron-10 ($19.9\%$, $10.01\,\text{amu}$) and Boron-11 ($80.1\%$, $11.01\,\text{amu}$).
• Ions: Charged atoms formed by the transfer of electrons.
  • Anion: A negatively charged ion that has gained electrons (e.g., $\text{Cl}^-$).
  • Cation: A positively charged ion that has lost electrons (e.g., $\text{Na}^+$).

Chemical Formulas and Molecules

• Representations:
  • Molecular Formula: Shows the exact number of atoms of each element ($\text{CH}_4$ for methane).
  • Structural Formula: Shows how atoms are connected via bonds (lines representing shared electrons).
  • Ball-and-Stick Model: Shows bonding and 3D geometry but with inaccurate atom sizes.
  • Space-Filling Model: Shows the actual relative sizes of the atoms and the overlapping electron clouds.
• Diatomic Elements: Elements that naturally occur as pairs in their pure state. There are 7: Nitrogen ($\text{N}_2$), Oxygen ($\text{O}_2$), Fluorine ($\text{F}_2$), Chlorine ($\text{Cl}_2$), Bromine ($\text{Br}_2$), Iodine ($\text{I}_2$), and Hydrogen ($\text{H}_2$).
• Empirical Formulas: The simplest whole-number ratio of atoms in a substance.
  • Example: Benzene molecular formula is $\text{C}_6\text{H}_6$; its empirical formula is $\text{CH}$.
  • Example: Acetic acid molecular formula is $\text{C}_2\text{H}_4\text{O}_2$; its empirical formula is $\text{CH}_2\text{O}$.
• Isomers: Compounds with the same molecular formula but different structures.
  • Structural Isomers: Differ in how atoms are connected (e.g., Acetic acid vs. Methyl formate).
  • Spatial Isomers (Enantiomers): Mirror images with the same connectivity but different 3D arrangements. This is critical in pharmacy, as one mirror image might be a drug while the other is toxic or inactive (e.g., optical activity).