Lecture 4: Atomic Theory, Isotopes, and Atomic Mass

Early Theories of Matter

• Leucippus and his student Democritus proposed that matter is composed of small, indestructible particles called atoms.

• Plato and Aristotle did not accept the atom idea; they proposed the theory of four elements: fire, earth, air, and water.

• We now know matter is made of small particles (atoms), but the historical debate set the stage for modern atomic theory.

Dalton's Atomic Theory and the Modern Atomic Theory

• John Dalton (early 1800s) proposed that matter is made of tiny indestructible particles called atoms and that atoms behave according to fixed rules in reactions.

• Dalton's Atomic Theory (four postulates):

  • 1) Each element is composed of tiny indestructible particles called atoms. ext{Atoms are the fundamental units of elements.}

  • 2) All atoms of a given element have the same mass and other properties that distinguish them from atoms of other elements. ext{e.g., O atoms differ from H atoms.}

  • 3) Atoms combine in simple whole-number ratios to form compounds. For example, water is formed from two hydrogen atoms and one oxygen atom (2:1 in terms of atoms). ext{H}_2 ext{O}

  • 4) Atoms of one element cannot change into atoms of another element in a chemical reaction. They only rearrange how they are bound together.

• From these ideas, the modern atomic theory includes three key laws:

  • 1) Law of Conservation of Mass: In a chemical reaction, matter is neither created nor destroyed. m{ ext{reactants}} = m{ ext{products}}.

  • 2) Law of Definite Proportions (Definite Proportion Law): All samples of a given compound have the same ratio of constituent elements by mass (a constant mass ratio).

  • Example (water): Decomposition of water (as discussed) shows an 8:1 mass ratio of oxygen to hydrogen. In the lecture, an example is given: 18 g of water decomposes to 60 g of oxygen and 2 g of hydrogen, illustrating a fixed mass relationship for that compound in this context.

  • In chemistry this is commonly interpreted as the definite proportionality of elements within a given compound.

  • 3) Law of Multiple Proportions: When two elements form more than one compound, the masses of one element that combine with a fixed mass of the other element are in simple whole-number ratios.

  • Example given: For carbon and oxygen forming CO and CO₂, with one unit of carbon combining with one unit of oxygen to form CO, and with two units of oxygen to form CO₂ (mass ratios reflect small whole numbers).

• These laws supported the idea that matter is composed of small, structured particles (atoms) that combine in fixed ways to form substances.

Discovery of the Electron and Atomic Models

• J.J. Thomson and the cathode ray experiment:

  • Discovered the electron travels in a straight line and carries a negative charge. e = -1.6 imes 10^{-19} ext{ C}.

  • Charge-to-mass ratio experiment yielded a value for the ratio rac{e}{m_e}. The oil drop experiment by Millikan provided the elementary charge value above, enabling calculation of the electron mass when combined with the charge-to-mass ratio.

  • Calculated electron mass from the ratio: m_e \approx 9.1 imes 10^{-28} ext{ g}. (This is the number given in the lecture.)

• Thomson proposed the plum pudding (or blueberry muffin) model: the atom is a positively charged sphere with electrons embedded inside like blueberries in a muffin.

• Ernest Rutherford and the gold foil experiment:

  • A beam of positively charged particles was directed at a thin gold foil.

  • Most particles went straight through; a small fraction were deflected, and about 1 in ~1000 bounced back.

  • Conclusion: Atoms are not uniform; they contain a small, dense, positively charged nucleus at the center with most of the atom's mass, surrounded by mostly empty space where electrons travel.

• Nuclear atom model (Rutherford-inspired) has three key parts:

  • The nucleus at the center contains protons (positive) and neutrons (neutral/nearly equal mass to protons).

  • Most of the atom’s volume is empty space (the electron cloud around the nucleus).

  • The nucleus contains almost all the mass; the electrons provide the atom’s size and charge distribution around the nucleus.

• Neutral atoms have equal numbers of protons and electrons; the positive and negative charges balance out.

• Neutrons: similar in size to protons but carry no electric charge; they reside in the nucleus along with protons.

• Summary of subatomic particles:

  • Proton: roughly the same mass as neutron; charge +1.

  • Neutron: roughly the same mass as proton; charge 0.

  • Electron: much smaller mass; charge -1.

• Atomic schematic concepts:

  • Nucleus (central region) contains protons and neutrons (collectively, the nucleons).

  • Electron cloud surrounding the nucleus contains electrons.

  • The nucleus is positively charged and is the source of most of the atom’s mass.

Subatomic Particles and Atomic Structure: Key Quantities

• Protons, neutrons, and electrons: their masses and charges summarized:

  • Protons and neutrons have nearly identical masses; electrons have negligible mass in comparison. $$m_p \