Atoms and Atomic Structure

Foundations of Matter and the Atomic Concept

• Definition of Matter: Matter is anything that possesses mass and occupies volume in space. Mass measures the exact quantity of matter contained within an object.

• Classifications of Matter:

  • Elements: Pure substances that consist of only one type of atom and cannot be broken down into simpler substances by chemical processes. Elements maintain a fixed composition.

  • Compounds: Pure substances composed of two or more different elements chemically combined in fixed, definite mass ratios.

  • Mixtures: Physical combinations of two or more substances in variable proportions.

• The Atomic Concept:

  • An atom is defined as the smallest quantity of matter that still retains the fundamental physical and chemical properties of an element.

  • Matter can be subdivided into smaller portions until a single individual atom remains. Subdividing a single atom further produces subatomic components that no longer retain the properties of that element.

Historical Development of Atomic Theories and Chemical Laws

• Early Philosophical Ideas:

  • Democritus (460–370 BC): Proposed that all matter is composed of minute, indivisible, and indestructible particles termed atomos (Greek for "uncuttable").

  • Aristotle: Rejected atomism, proposing instead that matter is continuous and composed of four basic elements: air, water, earth, and fire.

• Foundational Laws of Chemistry:

  • Law of Conservation of Mass (Antoine Lavoisier): States that the total mass of a system remains constant during a chemical reaction; mass is neither created nor destroyed.

  • Law of Definite Proportions (Joseph Proust): States that all pure samples of a specific chemical compound contain the same elements combined in the exact same proportion by mass, regardless of the sample's source or method of preparation.

    • Example: Water ($\text{H}_2\text{O}$) formed via the reaction $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ maintains a hydrogen-to-oxygen mass ratio of $1:8$ whether sourced from a natural spring, a lake, or a laboratory container.

  • Law of Multiple Proportions: States that when two elements (designated A and B) combine to form more than one compound, the masses of element B that combine with a fixed mass of element A exist in ratios of small whole numbers.

    • Example: Hydrogen and oxygen combine to form two distinct compounds: water ($\text{H}_2\text{O}$) and hydrogen peroxide ($\text{H}_2\text{O}_2$).

    • In $\text{H}_2\text{O}$, $16\,\text{g}$ of oxygen combines with $2\,\text{g}$ of hydrogen.

    • In $\text{H}_2\text{O}_2$, $32\,\text{g}$ of oxygen combines with $2\,\text{g}$ of hydrogen.

    • The ratio of oxygen masses combining with a fixed $2\,\text{g}$ mass of hydrogen is $\frac{16\,\text{g}}{32\,\text{g}} = \frac{1}{2}$ (or $1:2$).

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

  • All matter consists of extremely small, indivisible particles called atoms.

  • Atoms of a given element are completely identical in mass and properties, but differ from the atoms of any other element.

  • Compounds are formed when atoms of different elements combine chemically in specific, fixed whole-number ratios.

  • Atoms of one element cannot be converted into atoms of another element during a chemical reaction.

  • In chemical reactions, atoms are rearranged, separated, or recombined, but are never created or destroyed.

  • Limitations of Dalton's Model: While it successfully derived and explained the basic laws of chemical combination, Dalton's model could not explain why or how atoms bond in specific ratios (e.g., why one oxygen atom bonds with two hydrogen atoms rather than three).

Basic Principles of Electrostatics and Magnetism

• Electrostatic Interactions:

  • Like charges repel one another ($+\text{ repels }+$; $-\text{ repels }-$).

  • Unlike (opposite) charges attract one another ($+\text{ attracts }-$).

• Magnetic Interactions:

  • Like magnetic poles repel one another (North repels North; South repels South).

  • Opposite magnetic poles attract one another (North attracts South).

Discovery and Physical Characterization of the Electron

• Cathode Ray Tube Experiments (J.J. Thomson, 1897):

  • When high electrical voltage is applied across electrodes inside an evacuated glass tube, a beam of negative electrical radiation called cathode rays streams from the cathode ($-$) to the anode ($+$).

  • Cathode rays travel in a straight path when no external electric or magnetic fields are applied.

  • Application of an external magnetic or electric field deflects the cathode ray beam toward the positive pole, proving that the ray consists of negatively charged subatomic particles, later named electrons.

  • Cathode rays are generated identically regardless of the metal composition of the cathode electrode.

• Thomson's Charge-to-Mass Ratio Calculation:

  • By measuring the precise deflection of cathode rays under calibrated electric and magnetic fields, Thomson calculated the charge-to-mass ratio ($\frac{e}{m}$) of the electron:         $\frac{e}{m} = -1.76 \times 10^8\,\text{C/g} \quad \left(\text{or } -1.759 \times 10^{11}\,\text{C/kg}\right)$

  • By comparison, the charge-to-mass ratio for a hydrogen ion ($\text{H}^+$) is $+9.58 \times 10^4\,\text{C/g}$ ($+9.58 \times 10^7\,\text{C/kg}$).

  • Comparing these two values established that the mass of an electron is approximately $\frac{1}{1800}$th the mass of the lightest known ion ($\text{H}^+$), proving that electrons are subatomic particles present within all matter.

• Millikan's Oil Drop Experiment (Robert Millikan, 1909):

  • Fine droplets of oil were sprayed into an apparatus and ionized using X-rays. Their movement was observed through a telescopic eyepiece in the presence of an adjustable electric field between brass plates.

  • Millikan discovered that the electric charge on any given droplet was always an exact integer multiple of a single fundamental unit value:         $e = -1.6022 \times 10^{-19}\,\text{C}$

• Calculation of the Mass of an Electron:

  • Combining Millikan's charge measurement with Thomson's charge-to-mass ratio yielded the rest mass of an electron ($m_e$):         $\text{mass of an electron} = \frac{\text{charge}}{\text{charge/mass}} = \frac{-1.6022 \times 10^{-19}\,\text{C}}{-1.76 \times 10^8\,\text{C/g}} = 9.10 \times 10^{-28}\,\text{g}$

Atomic Structure Models: Thomson's Plum Pudding Model

• Because whole atoms are electrically neutral while containing negatively charged electrons, Thomson concluded that atoms must also contain an equal quantity of positive charge.

• Plum Pudding Model: Thomson proposed that an atom consists of a uniform sphere of diffuse positive charge with negatively charged electrons embedded throughout it, similar to raisins distributed inside a plum pudding.

The Nuclear Model of the Atom and Rutherford's Gold Foil Experiment

• Gold Foil Experiment (Ernest Rutherford):

  • A stream of positively charged alpha particles ($\alpha$ particles) emitted from a radioactive source (e.g., radium) was directed at an extremely thin sheet of gold foil.

  • Impacts were detected using a circular zinc-sulfide ($\text{ZnS}$) screen that produced flashes of light upon collision.

  • Predicted Outcome: Under Thomson's model, the diffuse positive charge would allow all $\alpha$ particles to pass straight through the foil with little to no deflection.

  • Actual Experimental Observations:

    1. The vast majority ($99\%$) of $\alpha$ particles passed straight through the foil without any deflection.

    2. A small fraction of $\alpha$ particles were deflected at very large angles (approximately $1$ in $8000$).

    3. Extremely rarely, $\alpha$ particles deflected directly backward toward the radiation source.

• Rutherford's Conclusions & Nuclear Model:

  • Because most $\alpha$ particles passed through undeflected, most of the space inside an atom is empty space.

  • All of an atom's positive charge and nearly all of its mass are concentrated in an extremely dense central region called the nucleus.

  • The positively charged nuclear particles are named protons.

  • Electrons are distributed in the surrounding space outside the nucleus.

  • For an atom to remain electrically neutral, the total number of nuclear protons must equal the total number of extranuclear electrons.

• Relative Size and Mass Scale:

  • The nucleus accounts for $99.7\%$ of an atom's total mass.

  • An entire atom has a diameter on the order of $\sim 10^{-10}\,\text{m}$, whereas the nucleus has a diameter on the order of $\sim 10^{-14}\,\text{m}$.

  • Relatively, if an atom were scaled to the dimensions of a football stadium, its nucleus would be equivalent to a marble sitting at the center field line.

Discovery of the Neutron and Properties of Subatomic Particles

• Discovery of the Neutron (James Chadwick, 1932):

  • Limitation of Rutherford's Model: The combined mass of an atom's protons and electrons accounted for less than half of its total measured mass.

  • In 1932, James Chadwick discovered a third subatomic particle residing within the nucleus, termed the neutron.

  • Neutrons possess no net electrical charge ($0\,\text{C}$) and have a mass of $1.67493 \times 10^{-24}\,\text{g}$, making them slightly heavier than protons.

• Physical Properties of Subatomic Particles:

  • Electron:

    • Mass in grams: $9.10938 \times 10^{-28}\,\text{g}$

    • Mass in atomic mass units: $5.4854 \times 10^{-4}\,\text{amu}$

    • Charge in coulombs: $-1.6022 \times 10^{-19}\,\text{C}$

    • Relative charge unit: $-1$

  • Proton:

    • Mass in grams: $1.67262 \times 10^{-24}\,\text{g}$

    • Mass in atomic mass units: $1.0073\,\text{amu}$

    • Charge in coulombs: $+1.6022 \times 10^{-19}\,\text{C}$

    • Relative charge unit: $+1$

  • Neutron:

    • Mass in grams: $1.67493 \times 10^{-24}\,\text{g}$

    • Mass in atomic mass units: $1.0087\,\text{amu}$

    • Charge in coulombs: $0\,\text{C}$

    • Relative charge unit: $0$

Atomic Number, Mass Number, and Element Notation

• Atomic Number ($Z$):

  • Defined as the total number of protons in an atom's nucleus.

  • The atomic number uniquely defines the identity of a chemical element. All atoms of a given element contain the exact same number of protons.

  • Example: Nitrogen has an atomic number of $Z = 7$; every nitrogen atom contains exactly $7$ protons.

• Mass Number ($A$):

  • Defined as the total sum of protons and neutrons in the nucleus ($A = Z + N$, where $N$ represents the number of neutrons).

  • Protons and neutrons reside within the nucleus and are collectively referred to as nucleons.

• Symbolic Element Notation:

  • An atom is symbolically denoted using the standard nuclide format ${}_Z^A\text{X}$:

    • $\text{X}$ = Chemical element symbol.

    • $A$ = Mass number (superscript, upper-left).

    • $Z$ = Atomic number (subscript, lower-left).