Chapter 2 Notes: Atomic Theory, Structure, Formulas, and Periodic Table

2.1 Early Ideas in Atomic Theory

The concept of atoms originated with the Greek philosophers Leucippus and Democritus in the fifth century BC. They proposed atomos, from the Greek word for “indivisible,” as the basic, indivisible units of matter. They envisioned atoms as moving particles that could combine to form substances.
In contrast, Aristotle and many others argued that matter consisted of varying combinations of the four classical “elements”—fire, earth, air, and water. These ideas were conceptual and not experimentally tested.
In 1807, English schoolteacher John Dalton revived and formalized atomic ideas into a concrete atomic theory, laying groundwork for modern chemistry.

Dalton’s Atomic Theory (note: some parts have been disproved by later experiments)

Matter is composed of exceedingly small indivisible particles called atoms.
The atoms of a given element are identical. (This has been refined: atoms of the same element can have different masses due to isotopes.)
Atoms of one element differ in properties from atoms of all other elements.
Atoms of different elements combine in whole-number ratios to form compounds.
Atoms are neither created nor destroyed during a chemical change; they are rearranged to yield a different type of matter.
Law of Conservation of Matter: If atoms are neither created nor destroyed during a chemical change, then the total mass before and after the change remains constant. This is expressed as $m{ ext{initial}} = m{ ext{final}}.$
A common thought experiment from the transcript illustrates a potential challenge to Dalton’s idea: in a hypothetical reaction, “2 green + 2 blue → 1 green + 1 blue” would imply atoms were destroyed; however, if atoms are neither created nor destroyed, such a change would violate Dalton’s postulates. A different stoichiometry such as “2 green + 2 blue → 2 green + 2 blue” would be consistent with Dalton’s idea.

2.2 Evolution of Atomic Theory

The question arises: what are atoms made of? The early 20th century revealed three subatomic particles: neutrons, protons, and electrons, discovered through multiple experiments that mapped atomic structure.
Discovery of the Electron: J. J. Thomson
- The electron was discovered via the cathode ray tube experiment. A sealed glass tube with nearly all the air removed contained two metal electrodes. When a high voltage was applied, a visible beam (cathode ray) formed and was deflected toward the positive plate and away from the negative plate, irrespective of the electrode material.
- Thomson measured the charge-to-mass ratio $\frac{e}{m_e}$ of the cathode ray particles. The results showed the particles were much lighter than atoms, negatively charged, and were identical regardless of source material. These particles are the electrons, with a mass over a thousand times smaller than that of an atom.
- The era produced two influential models: Thomson’s Plum Pudding model (positively charged ‘pudding’ with embedded electrons) and the earlier Nagaoka/Planet model (planetary-like arrangement).
Discovery of the Nucleus: Ernest Rutherford
- Rutherford’s Gold Foil Scattering Experiment involved directing alpha particles (positively charged) at a very thin gold foil and observing their trajectories with a fluorescent screen. Most particles passed through, but a few were deflected slightly and a very small number were deflected at large angles.
- Rutherford concluded that atoms contain mostly empty space, with a very small, dense, positively charged nucleus at the center, housing most of the atom’s mass. The electrons surround the nucleus. The nucleus contains protons, positively charged subatomic particles.
- This led to the modern nuclear model of the atom, where a tiny nucleus (containing protons and neutrons) is surrounded by a cloud of electrons.
Other 20th-Century Discoveries
- Neutrons: Discovered by James Chadwick in 1932; neutrons are uncharged subatomic particles with a mass similar to protons and reside in the nucleus.
- Isotopes: Atoms of the same element with different numbers of neutrons, hence different masses. Example spotlighted: Carbon isotopes (e.g., Carbon-12, Carbon-13, Carbon-14), where Carbon-12 is the most abundant (≈ 98.9%), Carbon-13 is about 1.1%, and Carbon-14 is a trace radioactive isotope used in radiocarbon dating.

2.3 Atomic Structure and Symbolism

Symbols and notation: Atoms are described by a nuclear symbol that encodes the atomic number Z (number of protons), the mass number A (sum of protons and neutrons), and the charge when applicable. The standard nuclear symbol format is: $^{A}_{Z} ext{X}^{q}$ where X is the element symbol and q denotes the ionic charge.
Basic definitions:
- Atomic number, $Z$ : number of protons in the nucleus; identifies the element. e.g., Any atom with $Z=6$ is carbon.
- Mass number, $A$ : total number of protons and neutrons in the nucleus.
- Neutrons, $N = A - Z$ .
- Isotopes: atoms with the same $Z$ but different $A$ (different $N$ ).
Atomic mass unit:
- One atomic mass unit: $1 ext{ amu} = 1.6605 imes 10^{-24} ext{ g}.$
- Average atomic mass of an element is a weighted average of isotopic masses, reflecting natural abundances.
Subatomic particle masses and charges (typical values):
- Proton: mass $m_p = 1.0073 ext{ amu}, ext{ charge } +1$
- Neutron: mass $m_n = 1.0087 ext{ amu}, ext{ charge } 0$
- Electron: mass $m_e = 0.00055 ext{ amu}, ext{ charge } -1$
- Elementary charge: $e = 1.602 imes 10^{-19} ext{ C}$
Nucleus and electron distribution: A helpful analogy—if an atom were the size of a football stadium, its nucleus would be the size of a blueberry; the nucleus contains most of the mass, while electrons occupy most of the atom’s volume.
Protons, neutrons, and electrons:
- The nucleus holds protons and neutrons; electrons form surrounding shells.
Neutral atoms: A neutral atom has equal numbers of protons and electrons; thus the atomic number equals the number of electrons. Example: A carbon atom has $Z=6$ and therefore $6$ electrons.
Mass number and neutron calculation: $A = Z + N \ N = A - Z.$
Isotopes (example): Chlorine-35 and Chlorine-37 have the same $Z=17$ but different $A$ and neutron counts. For Chlorine-35: protons 17, electrons 17, neutrons 18; for Chlorine-37: protons 17, electrons 17, neutrons 20.
Ions and charges: When the number of protons and electrons differ, the atom is charged (an ion). Charge is given by $ext{Charge} = Z - Ne$ (where $Ne$ is the number of electrons).
- Cations: positively charged ions formed by losing electrons; Anions: negatively charged ions formed by gaining electrons. Examples:
- Oxygen neutral atom has 8 protons and 8 electrons; gaining 2 electrons yields an oxide ion with charge $2^{-}$ .
- Sodium neutral atom has 11 electrons; losing 1 electron yields a Na⁺ ion with charge $+1$ .
Chemical symbols and origins: A chemical symbol is a shorthand for an element. Some symbols derive from Latin names (e.g., Hg for mercury from hydrargyrum; Fe from ferrum; Cu from cuprum; Na from natrium). Capitalization: the first letter is capitalized; the second (if present) is lowercase.
Nuclear symbol for ions (practice): Commonly written as $^{A}{Z} ext{X}^{q+}$ or $^{A}{Z} ext{X}^{q-}$ . Example in the provided figure shows a mass number of 4, charge of 2+, etc.
Atomic mass concept: The mass of an atom in amu closely approximates its mass number for a single isotope, but natural elements are mixtures of isotopes, so the periodic table lists the weighted average atomic mass.
Example calculation: For boron with two isotopes, one with mass 10.0129 amu at 19.9% abundance and one with mass 11.0093 amu at 80.1% abundance, the average atomic mass is:
$\bar{m} = (0.199)(10.0129) + (0.801)(11.0093) \,=\, ext{approximately } 10.811 ext{ amu}.$
Practice problems from the transcript emphasize writing nuclear symbols for ions and interpreting neutron/proton/electron counts.

2.4 Chemical Formulas

Chemical formulas encode composition and stoichiometry of molecules and compounds.
- Molecular formula: shows the actual number of each type of atom in a molecule (e.g., benzene has formula $ext{C}6 ext{H}6$ ).
- Empirical formula: the simplest whole-number ratio of the elements in a compound (e.g., benzene’s empirical formula is $ext{CH}$ ).
- Structural formula: shows how atoms are bonded and arranged; conveys connectivity beyond the counts of atoms in a molecule.
For benzene and acetic acid:
- Benzene: Molecular formula $ext{C}6 ext{H}6$ ; Empirical formula $ext{CH}$ .
- Acetic acid: Molecular formula $ext{C}2 ext{H}4 ext{O}2$ ; Empirical formula $ext{CH}2 ext{O}$ .
Isomers: Compounds with the same molecular formula but different structures. Example: Acetic acid and methyl formate both have the formula $ext{C}2 ext{H}4 ext{O}_2$ but different structures and properties.
- Example drawings show Acetic acid (H3C–COOH) vs Methyl formate (HCOOCH3).
Exercises and concepts:
- Determine empirical formulas from given molecular formulas and vice versa.
- Understand that different arrangements (isomers) yield different properties despite identical formulas.
- Recognize that numeric subscripts convey counts of atoms, and their placement defines the molecule’s composition. The transcript cautions that the same symbols (like H, H2, H2O) can represent very different entities depending on context (single atoms vs molecules).
Sample problems from the transcript include:
- Writing both the molecular and empirical formulas for given structures (e.g., CO, H2O, etc.) and recognizing isomeric possibilities.

2.5 The Periodic Table

The Periodic Table organizes elements by recurring chemical properties. The key historical and conceptual points include:
- Dmitri Mendeleev laid the early groundwork for the modern table.
- Early tables were organized by atomic masses; later it became clear that atomic numbers better explain periodicity. The modern organizing principle is the increasing atomic number $Z$ .
- Periodic Law: The properties of the elements are periodic functions of their atomic numbers.
- The table is arranged in periods (horizontal rows) and groups (vertical columns, numbered 1–18).
- The modern table places elements in order of increasing $Z$ and groups similar-property elements together.
Structural layout and data: A representative section shows symbols, atomic masses, and notes about metals, metalloids, and nonmetals; the color code distinguishes metals, metalloids, and nonmetals; states of matter (solid, liquid, gas) can be indicated.
Classifications of elements:
- Metals: shiny, malleable, good conductors of heat and electricity.
- Nonmetals: dull, poor conductors.
- Metalloids: intermediate properties (some metal-like and some nonmetal-like).
- Main group (representative) elements: Groups 1, 2, and 13–18.
- Transition metals: Groups 3–13.
- Inner transition metals: Lanthanides (top row) and Actinides (bottom row).
Groupings and examples (from the transcript):
- Alkali metals: Group 1 (except hydrogen), highly reactive, solids at room temperature.
- Alkaline earth metals: Group 2, highly reactive but less than Group 1, solids at room temperature.
- Pnictogens: Group 15; Chalcogens: Group 16.
- Halogens: Group 17, extremely reactive nonmetals; states vary (gas, liquid, solid).
- Noble gases: Group 18, inert.
Classification exercise (from the transcript): Using the periodic table, classify several elements as metals vs. nonmetals and as main-group, transition, or inner-transition:
- Uranium: inner transition metal (actinide).
- Bromine: nonmetal (halogen, main-group).
- Strontium: alkaline earth metal (main-group).
- Neon: noble gas (nonmetal).
- Gold: transition metal.
- Americium: inner transition metal (actinide).
- Rhodium: transition metal.
- Sulfur: nonmetal (main-group).
- Carbon: nonmetal (main-group).
- Potassium: alkali metal (main-group).
Summary of periodic table organization:
- Elements are arranged by increasing $Z$ and grouped by similar chemical properties.
- The periodic table provides a framework to predict properties based on location (periods, groups, blocks).
- The table highlights trends in reactivity, electronegativity, and bonding tendencies across and down the table.
Note about sections not shown in the transcript:
- Sections 2.6 (Molecular and Ionic Compounds) and 2.7 (Chemical Nomenclature) are mentioned in the chapter outline but are not covered in detail in the provided transcript. The notes above focus on 2.1–2.5 content and core ideas relevant to early atomic theory, atomic structure, formulas, and the periodic table.
Key formulas and concepts to remember:
- Atomic number: $Z = ext{number of protons}$
- Mass number: $A = Z + N$ , where $N$ is the number of neutrons
- Neutrons: $N = A - Z$
- Neutral atom condition: number of protons equals number of electrons
- Empirical vs molecular formula: empirical = simplest whole-number ratio; molecular = actual number of atoms in a molecule
- Average atomic mass: $\bar{m} = \sumi fi mi$ where $fi$ are fractional abundances (or percent divided by 100)
- Electron charge: $e = 1.602 imes 10^{-19} ext{ C}$
- 1 amu = $1.6605 imes 10^{-24} ext{ g}$