Atomic Theory, Structure, and Mass Relationships Notes

Philosophical Atomic Theory in Antiquity

• Leucippus (5th century BC): Traditionally credited as the founder of atomism. He proposed that atoms exist in constant motion within a deterministic world, where everything results from the collisions of atoms.

• Democritus (460-371 BC): Developed the philosophical basis for atomism.

  • All matter is composed of atoms, which are bits of matter too small to be seen.

  • Atoms are indivisible and completely solid.

  • Atoms are homogeneous and lack any internal structure.

  • The "void" is the empty space existing between atoms.

  • Atoms differ in their sizes, shapes, and weights.

• This theory was largely ignored and forgotten for more than 2,000 years.

The Scientific Revolution and Atomic Structure

• Robert Boyle (1627-1691):

  • Performed detailed experiments with gases.

  • Provided physical evidence for the atomic makeup of matter.

  • Defined an "element" as a substance that cannot be chemically broken down further.

  • Proposed that atoms of different elements join together in various ways to yield chemical compounds.

• Joseph Priestley (1733-1804):

  • Prepared and isolated oxygen gas ($O_2$).

  • Reaction: $2HgO \rightarrow 2Hg + O_2$.

• Antoine Lavoisier (1743-1794):

  • Demonstrated the role of oxygen in combustion.

  • Observed that in a closed container, the mass of the products exactly equals the mass of the starting reactants.

  • Conclusion: Mass is neither created nor destroyed.

  • Established the Law of Mass Conservation.

Fundamental Laws of Chemistry

• Law of Conservation of Mass:

  • Example: Mixing Potassium Iodide ($KI$) and Mercury(II) Nitrate ($Hg(NO_3)_2$).

  • Equation: $Hg(NO_3)_2(aq) + 2KI(aq) \rightarrow HgI_2(s) + 2KNO_3(aq)$.

  • Quantitative Proof: $3.25\,g + 3.32\,g = 6.57\,g$ (reactants) yields $4.55\,g + 2.02\,g = 6.57\,g$ (products).

• Law of Definite Proportions (Law of Constant Composition):

  • Proposed by Joseph Proust (1754-1826).

  • A given chemical compound contains its constituent elements in a fixed mass ratio regardless of the source or method of preparation.

  • A substance is defined by the specific proportions of its elements, not just the types.

  • Example: By mass, water ($H_2O$) is always $8/9$ oxygen and $1/9$ hydrogen.

• Law of Multiple Proportions:

  • In compounds containing two particular elements (A and B), the amount of element A per measure of element B is a simple integer number.

  • Example: Nitrous oxide contains $7\,g$ of nitrogen per $8\,g$ of oxygen; nitrogen dioxide contains $7\,g$ of nitrogen per $16\,g$ of oxygen.

Dalton’s Atomic Theory (1803)

• John Dalton (1766–1844):

  • Solid Sphere Model: Imagined atoms as tiny, solid spheres resembling billiard balls.

  • Atoms of the same element are identical in mass and properties.

  • Atoms cannot be created, divided, or destroyed.

  • Compounds form when atoms of different elements combine in fixed ratios.

  • Chemical reactions involve rearranging how atoms are combined; the atoms themselves do not change.

• A Quantitative Theory:

  • The cardinal point of Dalton's theory was its quantitative nature.

  • He used measured mass ratios of elements in compounds and assumed molecular structures to convert mass ratios into relative atomic weights.

  • He asserted that atoms of different elements have different weights, which are proportions by weight in which elements combine (or simple multiples/sub-multiples).

• Impact of Dalton's Model:

  • Linked atoms to quantitative laws and scientific models based on experimental evidence.

  • Atomic weights became essential for explanations.

  • Laid the groundwork for modern chemistry; atoms became central explanatory entities rather than just metaphors.

The 19th-Century Debate on Atomism

• Resistance to Atoms:

  • Much of 19th-century chemistry functioned perfectly well without asserting the reality of atoms; stoichiometry could be done by mass and laws established empirically.

  • Atoms were unobservable, leading many chemists (like Ernst Mach and Wilhelm Ostwald) to treat them as "useful fictions."

  • Chief stumbling blocks included Dalton's arbitrary assumptions about compound formulae and the high number of different atoms required by the theory.

  • Thermodynamics and energetics were highly successful without requiring atomic theory.

• Collapse of Anti-Atomism (1900–1915):

  1. Brownian Motion: Albert Einstein (1905) and Jean Perrin (1908–1913) provided quantitative predictions tied to atomic size and number. Perrin experimentally measured Avogadro’s number.

  2. Electron Discovery: J.J. Thomson (1897) proved atoms had internal structure.

  3. X-ray Crystallography: Bragg (1912–1913) directly revealed atomic spacing in solids.

Discovery of the Electron and Cathode Rays

• Cathode Ray Tube Experiments:

  • A high voltage across electrodes in a hollow vessel causes negative particles to move from the cathode to the anode.

  • Julius Plücker (1801-1868): Observed rays are moved by magnets, implying they are electrically charged.

  • Eugen Goldstein (1850-1930): Observed rays cast shadows; coined the name "cathode ray."

  • William Crooks (1832–1919): Observed rays could rotate a wheel, proving they are particulate and negatively charged.

• Properties of Cathode Rays/Electrons:

  • Deflect parallel to an electrostatic field (toward the positive plate) and perpendicular to a magnetic field.

  • Deflection degree depends on magnetic/electric field strength, magnitude of negative charge, and mass of the electron.

• J.J. Thomson (1856-1940):

  • By balancing opposing magnetic and electric forces, he determined the charge-to-mass ratio ($e/m$) of an electron.

  • Determined that electrons are a part of all matter.

Millikan’s Oil Drop Experiment

• Robert A. Millikan (1868-1953):

  • Experiment: Oil droplets were sprayed into a chamber and allowed to reach terminal velocity to calculate mass. X-rays gave droplets a negative charge. Droplets were then suspended between charged plates.

  • Results: The charge on any droplet was always a whole-number multiple of $1.60 \times 10^{-19}\,C$.

  • Calculations: Using the charge-to-mass ratio ($1.76 \times 10^8\,C/g$), the mass of an electron was calculated.

  • Accepted Mass of Electron: $9.10939 \times 10^{-28}\,g$.

Evolution of Atomic Models

• Thomson’s Plum Pudding Model (1904):

  • The atom is a continuously distributed positive particle with point-like negative electrons inside.

  • The model was dynamic: electrons arranged in concentric rings rotating inside a uniform sphere of positive charge for stability.

  • Implied shell structure and attempted to relate structures to chemical periodicity.

• Radioactivity:

  • Henri Becquerel (1896): Discovered radiation from uranium salts.

  • Marie Curie (1867-1934): Coined the term "radioactivity"; discovered polonium and radium.

  • Alpha ($\alpha$) Particle: A helium nucleus consisting of $2$ protons and $2$ neutrons.

• Rutherford’s Gold Foil Experiment (1906/1911):

  • Ernest Rutherford and Hans Geiger fired $\alpha$ particles at thin gold foils.

  • Observations: Most particles passed through unimpeded; some deflected; 1 in 10,000 deflected by nearly $180^{\circ}$.

  • Conclusion: The atom contains a positively charged nucleus concentrated in a very small space. This nucleus is much heavier than the $\alpha$ particle.

• Rutherford’s Nuclear Model:

  • Determined that the number of positive charges equals the element's atomic number.

  • Problem: Classical electrodynamics suggested orbiting electrons should radiate energy and collapse into the nucleus (later resolved by Niels Bohr).

Discovery of Protons and Neutrons

• The Proton ($p^+$):

  • Discovered by Rutherford in 1917 via artificial disintegration of the atomic nucleus.

  • Irradiated nitrogen gas with $\alpha$ particles; observed hydrogen nuclei being ejected from nitrogen atoms.

  • Named the particle the "proton" in 1920.

• The Neutron ($n^0$):

  • Discovered by James Chadwick (1932).

  • Followed research by Irene Joliot-Curie and Frederick Joliot, who found a penetrating radiation when light elements were bombarded with $\alpha$ particles.

  • Chadwick proved this radiation consisted of neutral particles with approximately the same mass as a proton.

Nuclear Arithmetic and Isotopes

• Subatomic Particle Comparison:

  • Proton: Charge $+1$ ($1.602 \times 10^{-19}\,C$); Mass $\approx 1.007\,amu$.

  • Neutron: Charge $0$; Mass $\approx 1.008\,amu$.

  • Electron: Charge $-1$ ($-1.602 \times 10^{-19}\,C$); Mass $\approx 0.0005\,amu$.

  • Nucleons: Collective term for protons and neutrons.

• Atomic Number ($Z$): Number of protons; defines the element and its periodic table position. In neutral atoms, $Z = \text{number of electrons}$.

• Mass Number ($A$): Total number of nucleons ($Z + N$). Symbol $A$ comes from German Atomgewichtzahl.

• Isotopes: atoms with identical $Z$ but different $A$ (different number of neutrons).

  • Notation: ${^A_Z}E$ (Example: Uranium-235 is ${^{235}_{92}}U$).

  • Stability:

    • For light elements ($Z \le 20$): $N \approx Z$ and $A \approx 2Z$.

    • For heavier elements (Z > 20): Stability requires N > Z to counteract proton-proton repulsion. The $N/Z$ ratio reaches $\approx 1.5$ for heavy elements (e.g., Lead-208 has $N/Z \approx 1.54$).

Atomic Mass and Atomic Weight

• Atomic Mass: The mass of a single atom measured in atomic mass units ($amu$) or Daltons ($Da$).

  • Standard: One atom of ${^{12}C}$ is exactly $12\,amu$.

  • Mass Defect: The actual atomic mass is less than the sum of its individual nucleons due to energy released during nuclear formation ($E=mc^2$).

  • Mass of atom in $amu \approx$ atom's mass number ($A$).

• Atomic Weight (Relative Atomic Mass): A weighted average of the atomic masses of an element's naturally occurring isotopes.

  • Formula: $\text{Atomic weight} = \sum(\text{isotopic mass} \times \text{fractional abundance})$.

  • It is a dimensionless number.

  • Example for Carbon: $(12\,amu)(0.9889) + (13.0034\,amu)(0.0111) = 12.01\,amu$.

The Mole and Molar Mass

• The Mole (mol): The SI unit for amount of substance.

  • Historical Definition: Amount of substance containing as many entities as there are atoms in $12\,g$ of ${^{12}C}$.

  • 2019 Revised Definition: Exactly $6.02214076 \times 10^{23}$ specified entities (Avogadro's number, $N_A$).

• Molar Mass ($M$): The mass of one mole of a substance, expressed in $g/mol$.

  • Numerically equivalent to an element's atomic weight.

• Calculations:

  • $\text{Moles (n)} = \frac{\text{Mass (m)}}{\text{Molar Mass (M)}}$

  • $\text{Moles (n)} = \frac{\text{Volume (v)}}{\text{Molar Volume (V)}}$

  • $\text{Number of Particles} = n \times 6.022 \times 10^{23}$

Worked Examples

• Interpreting Uranium-235 (${^{235}_{92}}U$):

  • Protons: $92$

  • Electrons: $92$

  • Neutrons: $235 - 92 = 143$

• Calculating Atomic Weight of Chlorine:

  • Isotope 1: ${^{35}Cl}$ ($34.969\,amu$, $75.76\%$

  • Isotope 2: ${^{37}Cl}$ ($36.966\,amu$, $24.24\%$

  • Calculation: $(34.969 \times 0.7576) + (36.966 \times 0.2424) = 35.45\,amu$.

• Mass to Moles/Atoms for Silicon ($10.53\,g$, Atomic Mass $28.0855\,amu$):

  • Moles: $10.53\,g\,Si \times \frac{1\,mol}{28.0855\,g} = 0.3749\,mol\,Si$

  • Atoms: $0.3749\,mol \times (6.022 \times 10^{23}) = 2.258 \times 10^{23}\,atoms\,Si$