2.1 Atomic Theory and Subatomic Particles

Historical Foundations and Philosophy of Atomic Matter

• Definition of an atom: An atom is the smallest particle of an element that retains the chemical and physical characteristics of that element.

• Philosophical debate in $400\,\text{B.C.}$:

  • Democritus: Proposed that nature's basic particle is the atom, which is indivisible and invisible. This concept was illustrated by imagining a rock pounded into progressively smaller pieces until it is reduced to particles so minute they can no longer be seen.

  • Aristotle: Opposed the atomic view, maintaining that matter is continuous and indivisible. He asserted that all matter is composed of combinations of four fundamental elements: earth, air, fire, or water.

Chemical Foundations and Pre-Daltonian Laws

• Contributions of early alchemists and the Renaissance:

  • Ancient alchemists pursued two primary historical objectives:

  • Attempting transmutation: Seeking methods to turn lead and other base metals into gold.

  • Synthesizing the elixir of life: Creating a magical potion that could grant eternal life.

  • Renaissance technological developments, such as precision glass blowing, enabled formal, quantitative laboratory experimentation and systematic chemical analysis.

• Chemical principles established by the $1700\text{s}$:

  • Definition of an Element: A fundamental substance that cannot be broken down into simpler substances by ordinary chemical means.

  • Law of Conservation of Matter (Antoine Lavoisier): Mass is neither created nor destroyed during a chemical reaction; the total mass of reactants equals the total mass of products.

  • Law of Definite Proportions: A chemical compound always contains its component elements in fixed, definite whole-number mass ratios regardless of the source or sample size. For example, the mass ratio of hydrogen to oxygen in pure water is always $1:8$.

  • Law of Multiple Proportions: When two elements combine to form more than one compound, the different masses of one element that combine with a fixed mass of the second element are in ratios of small whole numbers. For example, combining hydrogen and oxygen in a mass ratio of $1:16$ yields hydrogen peroxide instead of water, proving that different compounds can be created from the same constituent elements by varying their proportions.

John Dalton's Atomic Theory and Electrical Charge Principles

• John Dalton's Atomic Theory ($1808$):

  • Dalton formulated the first comprehensive atomic theory consisting of four primary postulates:

  • 1. All matter is composed of extremely small, invisible, and indivisible particles called atoms.

  • 2. All atoms of a given element are identical in mass and properties, and atoms of different elements differ in mass and properties. (Modern qualification: It is now known that isotopes exist, meaning not all atoms of an element are $100\%$ identical in mass, but they remain identical in essential chemical characteristics).

  • 3. Atoms of two or more different elements combine in simple whole-number ratios to form chemical compounds. A specific compound is always composed of the same kinds of atoms combined in the exact same numerical ratio.

  • 4. Chemical reactions involve the rearrangement, separation, or combination of intact atoms. Atoms are neither created nor destroyed during a chemical reaction.

• Electrical charges in matter ($1800\text{s}$ discoveries):

  • By the $1800\text{s}$, experimental evidence revealed that atoms were not indivisible solid spheres, but were built from subatomic particles bearing electrical charges.

  • Fundamental electrostatic rules:

  • Electrical charge occurs in two distinct states: positive ($+$) and negative (-$access).

  • Like electrical charges repel one another ($+$ repels $+$, and -$access repels -$access).

  • Opposite electrical charges attract one another ($+$ attracts -$access).

Discovery of the Electron and Cathode Ray Experiments

• Cathode Ray Tube (CRT) Experiments ($1877$–$1897$):

  • Equipment construction: An evacuated glass tube (vacuum tube) fitted with two metal electrodes—a negative cathode (-$access) and a positive anode ($+$)—connected to a high-voltage electrical power supply, along with a downstream fluorescent screen.

  • Beam generation: Applying high electricity to the electrodes generates a stream of cathode rays originating from the negative cathode, shooting through a hole in the positive anode inside the vacuum toward the screen to produce a visible glowing spot.

• J.J. Thomson's discoveries ($1897$):

  • Beam deflection: Thomson exposed cathode rays to external electric fields and magnetic forces, observing that the rays were consistently deflected away from negatively charged plates and attracted toward positively charged plates.

  • Charge determination: The deflection direction confirmed that cathode rays consist of streams of negatively charged particles.

  • Charge-to-mass ratio: Thomson measured the charge-to-mass ratio ($e/m$) of these particles and discovered that the ratio was constant and identical, regardless of the material used for the cathode electrodes or the trace gas inside the tube.

  • Particle identity: Thomson concluded that cathode rays consist of identical subatomic particles, later named electrons.

  • Size and mass: Electrons were calculated to be vastly smaller than whole atoms and to possess extraordinarily small masses.

  • Nobel Prize: J.J. Thomson was awarded the Nobel Prize in Physics in $1906$ for discovering the electron.

• Robert Millikan's Oil Drop Experiment:

  • Millikan determined the precise unit magnitude of charge carried by an individual electron, proving that all electrons possess the exact same fundamental electrical charge.

  • Nobel Prize: Robert Millikan was awarded the Nobel Prize in Physics in $1923$.

The Plum-Pudding Atomic Model

• Theoretical formulation by J.J. Thomson:

  • Electrical neutrality requirement: Because bulk matter and individual atoms are electrically neutral overall, an atom containing negatively charged electrons must also contain an equal magnitude of positive electrical charge to balance them.

  • Mass distribution logic: Since electrons possess an extremely tiny fraction of the atom's total mass, the positive charge component must carry the vast bulk of the atomic mass.

• Structural depiction of the Plum-Pudding Model:

  • The atom was described as a uniform sphere of positively charged matter (the "pudding" or "cloud").

  • Tiny, negatively charged electrons (the "plums") were embedded and distributed equally throughout this positive cloud.

Rutherford's Gold Foil Experiment and the Nuclear Atom

• Background and setup ($1910$):

  • Conducted by Ernest Rutherford alongside his assistants Hans Geiger and Ernest Marsden.

  • Academic background: Rutherford had previously won the Nobel Prize in Chemistry in $1908$ for his investigations into radioactive decay types.

  • Initial objective: Designed to confirm and validate Thomson's plum-pudding model of the atom.

  • Experimental apparatus:

  • Alpha particle source: A radioactive emitter enclosed in a shielded block produced alpha particles ($\alpha$-particles), which are positively charged particles that are very small compared to a gold atom.

  • Target: A thin sheet of gold foil placed directly in the path of the narrow alpha particle beam.

  • Detector: A circular, fluorescent detecting screen coated with zinc sulfide placed around the gold foil to record scintillations where alpha particles hit after passing through or deflecting.

• Experimental observations and unexpected results:

  • Expected result: Under the plum-pudding model, positive charge was broadly dispersed, so heavy $\alpha$-particles were expected to pass straight through the foil with little to no deflection.

  • Actual findings:

  • The vast majority of alpha particles passed directly through the gold foil with zero deflection.

  • A very small fraction of alpha particles were deflected at wide angles.

  • An extremely minute fraction of particles bounced back almost directly toward the alpha source.

  • Famous quote by Rutherford: "It was as incredible as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

• Physical deductions and the Nuclear Model:

  • Collision dynamics: For a fast-moving particle to bounce back, it must collide with an object that is significantly heavier and denser than itself.

  • Positive concentrated core: The deflection of positively charged $\alpha$-particles required a concentrated, highly intense positive charge inside the atom that repelled them via strong electrostatic repulsion.

  • Nuclear parameters:

  • Nucleus: Located at the exact center of each atom is a tiny, dense, positively charged core called the nucleus, containing almost the entirety of the atom's mass.

  • Volume ratio: The nucleus occupies an extraordinarily tiny fraction of the atom's total volume (analogous to placing a marble inside a massive football stadium).

  • Dense concentration: The nucleus is extremely dense.

  • Atomic volume: The overwhelming majority of the atom consists of empty space through which electrons move.

  • Historical impact: Completely disproved the plum-pudding model.

Discoveries of the Proton and Neutron

• Discovery of the Proton ($1914$–$1917$):

  • Ernest Rutherford and his collaborators identified the fundamental positive subatomic particle in the nucleus: the proton.

  • Charge and mass specs:

  • Carries an electrical charge equal in magnitude to the electron but opposite in sign ($+1$).

  • Possesses a mass approximately $1840$ times greater than the mass of an electron ($1.007\,\text{amu}$).

• Prediction and Discovery of the Neutron ($1932$):

  • Missing mass problem: Rutherford noticed that protons alone could not account for the entire mass of atomic nuclei (e.g., nuclei had way bigger mass than protons provided), postulating the existence of an uncharged subatomic particle.

  • James Chadwick's discovery: In $1932$—almost $15$ years after Rutherford's speculation—James Chadwick conclusively identified the neutron.

  • Difficulty of detection: Because neutrons carry no electrical charge ($0$ charge), they do not interact with electric or magnetic fields, making them much more difficult to detect than charged protons or electrons.

  • Academic background and recognition: Chadwick studied directly under Rutherford and was awarded the Nobel Prize in Physics in $1935$ for discovering the neutron.

Fundamental Properties of Subatomic Particles

• Summary of subatomic particle parameters:

  • Proton:

  • Symbol: $p$ or $p^+$

  • Electrical Charge: $+1$ (or $1+$)

  • Relative Mass / Size: $1$

  • Atomic Mass Units: $1.007\,\text{amu}$

  • Spatial Location: Inside the nucleus

  • Neutron:

  • Symbol: $n$ or $n^0$

  • Electrical Charge: $0$ (neutral)

  • Relative Mass / Size: $1$

  • Atomic Mass Units: $1.008\,\text{amu}$

  • Spatial Location: Inside the nucleus

  • Electron:

  • Symbol: $e^-$

  • Electrical Charge: $-1$ (or $1-$)

  • Relative Mass / Size: $\frac{1}{1840}$

  • Atomic Mass Units: $0.00055\,\text{amu}$

  • Spatial Location: Outside of the nucleus (electron cloud surrounding the nucleus)