Comprehensive Study Notes on Atoms, Elements, and Atomic Structure

Early Philosophy of Matter and the Scientific Revolution

• Philosophical Origins of Atomic Theory:

  • Leucippus and Democritus: Proposed that matter was ultimately composed of tiny, indivisible particles.

  • Plato and Aristotle: Argued that matter was continuous and infinitely divisible.

  • Historical Precedence: Due to the absence of experimental testing methods in antiquity, philosophical debates were settled by argument quality; Aristotle's viewpoint was accepted as correct for centuries.

• The Scientific Revolution:

  • Established in the late 16th century, introducing a systematic empirical approach to understanding nature.

  • Over the subsequent 150+ years, cumulative experimental observations contradicted the concept of infinitely divisible matter.

Fundamental Laws of Matter

• Law of Conservation of Mass (Antoine Lavoisier, 1743–1794):

  • In a chemical reaction, matter is neither created nor destroyed.

  • The total mass of materials present before a reaction equals the total mass of materials present after the reaction:         $\text{Total Mass of Reactants} = \text{Total Mass of Products}$

  • Experimental Reaction Example:         $\text{Sodium metal } (s) + \text{Chlorine gas } (g) \rightarrow \text{Sodium chloride } (s)$         $7.7\,\text{g}\text{ Na}(s) + 11.9\,\text{g}\text{ Cl}_2(g) \rightarrow 19.6\,\text{g}\text{ NaCl}(s)$

• Law of Definite Proportions (Joseph Proust, 1754–1826):

  • All samples of a given compound, regardless of their source or method of preparation, possess the exact same proportions of their constituent elements by mass.

  • Proportions in Sodium Chloride ($\text{NaCl}$):

    • $100.0\,\text{g}$ sample: Contains $39.3\,\text{g}$ sodium and $60.7\,\text{g}$ chlorine:             $\frac{\text{mass Cl}}{\text{mass Na}} = \frac{60.7\,\text{g}}{39.3\,\text{g}} = 1.54$

    • $200.0\,\text{g}$ sample: Contains $78.6\,\text{g}$ sodium and $121.4\,\text{g}$ chlorine:             $\frac{\text{mass Cl}}{\text{mass Na}} = \frac{121.4\,\text{g}}{78.6\,\text{g}} = 1.54$

    • $58.44\,\text{g}$ sample: Contains $22.99\,\text{g}$ sodium and $35.44\,\text{g}$ chlorine:             $\frac{\text{mass Cl}}{\text{mass Na}} = \frac{35.44\,\text{g}}{22.99\,\text{g}} = 1.541$

• Law of Multiple Proportions (John Dalton, 1766–1844):

  • When two elements ($A$ and $B$) combine to form two different compounds, the masses of element $B$ that combine with $1.00\,\text{g}$ of element $A$ can be expressed as a ratio of small whole numbers.

  • Oxides of Carbon Example:

    • Carbon monoxide ($\text{CO}$): Contains $1.33\,\text{g}$ of oxygen for every $1.00\,\text{g}$ of carbon.

    • Carbon dioxide ($\text{CO}_2$): Contains $2.67\,\text{g}$ of oxygen for every $1.00\,\text{g}$ of carbon.

    • Ratio of oxygen masses per gram of carbon:             $\frac{\text{Mass of oxygen in CO}_2}{\text{Mass of oxygen in CO}} = \frac{2.67\,\text{g}}{1.33\,\text{g}} = 2$

Fundamental Properties of Electrical Charge

• Nature and Behavior of Charges:

  • Electric charge exists in two distinct forms: positive ($+$, represented visually in red) and negative ($-$, represented visually in yellow).

  • Opposite charges attract ($+$ attracts $-$).

  • Like charges repel ($+$ repels $+$, $-$ repels $-$).

  • Electrical neutrality requires an absence of charge or equal quantities of opposite charges:         $+1 + (-1) = 0$

• Charge Behavior in Chemical Reactions:

  • In chemical reactions, reacting elements do not transform into other elements; they rearrange their atomic attachments (Statement 4 of Dalton's Atomic Theory).

  • The number of protons determines elemental identity and remains unchanged in chemical reactions.

  • Chemical reactions frequently involve the transfer of electrons between participating atoms.

Discovery of the Electron and Cathode Ray Experiments

• Cathode Ray Tube Instrumentation:

  • Consists of a partially evacuated glass tube containing metal electrodes (cathode and anode).

  • When connected to a high-voltage power supply, a glowing ray emanates from the cathode toward the anode.

• J.J. Thomson's Experiments:

  • Hypothesized that cathode rays were composed of tiny electrically charged particles.

  • Designed an experimental apparatus using electrical plates and a magnet to measure the magnetic and electric force required to deflect the path of the beam.

  • Experimental Results:

    • Cathode rays were deflected toward the positive ($+$) electrical plate, proving the particles carry a negative charge.

    • Deflection was directly proportional to charge and inversely proportional to particle mass.

    • Identical negative particles were produced regardless of the metal electrode material used.

    • Measured charge-to-mass ratio of the particle:             $\text{Charge-to-mass ratio} = -1.76 \times 10^{8}\,\text{C/g}$

    • Comparison value for hydrogen ion charge-to-mass ratio:             $\text{Charge-to-mass ratio of H}^+ = +9.58 \times 10^{4}\,\text{C/g}$

• Thomson's Conclusions:

  • Assuming the particle possesses the same magnitude of charge as a hydrogen ion, its mass must be almost $2000 \times$ smaller than a hydrogen atom.

  • Proved that atoms are divisible and composed of subatomic constituents termed electrons.

  • Thomson postulated these electrons were fundamental building blocks of matter.

• Millikan's Oil Drop Experiment:

  • Utilized an atomizer and charged oil droplets between electrostatically charged plates to determine the fundamental unit charge of a single electron.

Atomic Models: From Plum Pudding to the Nuclear Atom

• Thomson's Plum Pudding Model:

  • Replaced John Dalton's model of hard, unbreakable marble-like spheres.

  • Proposed that negatively charged electrons are embedded within a diffuse sphere of uniform positive charge.

  • Model Rationale: Positive charge was required to achieve overall atomic neutrality, but no discrete positively charged particles had been isolated in cathode ray experiments.

  • Model Predictions:

    • The overall mass of the atom is due to the mass of its electrons.

    • The atom consists mostly of empty space to prevent negative electrons from repelling one another.

• Discovery of Radioactivity:

  • Discovered in the late 1800s by Henri Becquerel and Marie Curie, who identified that certain elements spontaneously emit energetic particles and radiation.

• Rutherford's Gold Foil Experiment:

  • Objective: Probe atomic structure by firing energetic particle "bullets" through thin target matter.

  • Target: Extremely thin gold foil (gold mass = $197\,\text{amu}$, highly malleable).

  • Projectiles: Alpha ($\alpha$) particles emitted from a radioactive source inside a lead container (mass = $4\,\text{amu}$, charge = $+2\,\text{c.u.}$).

  • Detection: Surrounded by a circular fluorescent screen that produced light flashes upon alpha particle impact.

  • Experimental Results:

    • Over $98\%$ of alpha particles passed straight through the foil with zero or negligible deflection.

    • A small fraction of alpha particles passed through but were deflected at moderate angles.

    • Approximately $1$ in $20\,000$ ($\approx 0.005\%$) bounced directly backward toward the source.

• Rutherford's Interpretation - The Nuclear Model:

  • 1. The atom contains a tiny, extremely dense center called the nucleus.

    • The space occupied by the nucleus is only about $\frac{1}{10\,\text{trillionth}}$ ($10^{-13}$) of the total volume of the atom.

  • 2. The nucleus contains essentially the entire mass of the atom.

    • Electrons possess so little mass that they contribute practically nothing to the atom's total weight.

  • 3. The nucleus is positively charged, balancing the total negative charge of the electrons.

  • 4. Electrons are dispersed throughout the extensive empty space surrounding the central nucleus.

Subatomic Particles: Protons, Neutrons, and Electrons

• Discovery and Properties of Protons:

  • Proposed by Ernest Rutherford based on measurements of elemental nuclear charge.

  • Protons possess an equal magnitude of charge as electrons but opposite sign.

  • $\text{Proton Charge} = +1.60 \times 10^{-19}\,\text{C}$

  • $\text{Proton Mass} = 1.67262 \times 10^{-24}\,\text{g}$

  • Mass Comparison Analogy: If a proton had the mass of a baseball, an electron would have the mass of a single grain of rice.

• Discovery and Properties of Neutrons:

  • Proposed by Rutherford to account for unassigned nuclear mass.

  • Neutrons carry zero electrical charge and reside within the nucleus.

  • $\text{Neutron Mass} = 1.67493 \times 10^{-24}\,\text{g}$ (slightly heavier than a proton).

• Comprehensive Subatomic Particle Comparison Table:

  • Proton ($p$, $p^+$, ${}^1\text{H}^+$):

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

    • Mass in amu: $1.00727\,\text{amu}$

    • Relative Charge: $+1$

    • Location: Nucleus

  • Electron ($e$, $e^-$):

    • Mass in grams: $0.00091 \times 10^{-24}\,\text{g}$

    • Mass in amu: $0.00055\,\text{amu}$

    • Relative Charge: $-1$

    • Location: Empty space surrounding nucleus

  • Neutron ($n$, $n^0$):

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

    • Mass in amu: $1.00866\,\text{amu}$

    • Relative Charge: $0$

    • Location: Nucleus

Atomic Structure, Symbols, Isotopes, and Ions

• Atomic Number ($Z$):

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

  • Uniquely defines the identity of an element.

  • Determines order on the Periodic Table.

  • In a neutral atom, $\text{Number of protons } (p^+) = \text{Number of electrons } (e^-)$.

• Mass Number ($A$):

  • Defined as the total whole number sum of protons and neutrons in the nucleus:         $A = Z + n^0$

  • $\text{Number of neutrons } (n^0) = A - Z$

  • For most stable nuclides, n^0 > p^+$.\n* **Isotopes (Discovered by Frederick Soddy):**\n * Atoms of the same element containing identical proton counts (Z$) but different neutron counts ($n^0$), yielding different mass numbers ($A).\n * All isotopes of an element are chemically identical and undergo identical chemical reactions.\n * **Natural Abundance:** The relative percentage of an isotope found in a naturally occurring sample of an element.\n * **Chlorine Example:** Natural chlorine consists of two isotopes: Cl-35 (\approx 35\,\text{amu}$) and Cl-37 ($\approx 37\,\text{amu}$), yielding a weighted average atomic mass of$35.45\,\text{amu}.\n* **Ions and Atomic Charge:**\n * Atoms acquire charge by gaining or losing electrons during chemical reactions.\n * **Anions:** Negatively charged ions formed when atoms gain electrons. Formed predominantly by nonmetals. Named by changing the elemental name ending to "-ide".\n * Fluoride example: Neutral \text{F}$($9\,p^+, 9\,e^-$) vs Fluoride anion$\text{F}^-$($9\,p^+, 10\,e^-).\n * Phosphide example: Neutral \text{P}$($15\,p^+, 15\,e^-$) vs Phosphide anion$\text{P}^{3-}$($15\,p^+, 18\,e^-).\n * **Cations:** Positively charged ions formed when atoms lose electrons. Formed predominantly by metals.\n * **Chemical Behavior Contrast:** Neutral sodium metal (\text{Na}$) is highly reactive and unstable; sodium cations ($\text{Na}^+) in table salt are stable and nonreactive.\n\n# Detailed Atomic Calculation Examples\n\n* **Example Calculation of Subatomic Particles ({}{24}^{52}\text{Cr}):**\n * **Given:** Chromium nuclide symbol {}{24}^{52}\text{Cr}$, where Mass Number$A = 52$and Atomic Number$Z = 24$.

  • Protons:         $\text{Protons } (p^+) = Z = 24$

  • Electrons: In a neutral atom:         $\text{Electrons } (e^-) = p^+ = 24$

  • Neutrons:         $\text{Neutrons } (n^0) = A - Z = 52 - 24 = 28$

  • Verification: $n^0 (28) > p^+ (24)$, which aligns with stable isotope trends.

The Periodic Table and Periodic Law

• Scanning Tunneling Microscope (STM):

  • Invented by Gerd Binnig and Heinrich Rohrer.

  • Passes a sharp metal tip across a flat conductive surface, measuring quantum tunneling current as distance changes.

  • Provides surface topographies at atomic resolution.

• Dmitri Mendeleev and Periodic Law:

  • Arranged elements in order of increasing atomic mass and identified repeating property patterns.

  • Periodic Law: When elements are arranged in order of increasing atomic mass, certain sets of properties recur periodically.

  • Grouped elements with similar chemical and physical properties into vertical columns.

  • Used periodic patterns to predict properties of undiscovered elements (e.g., Ekasilicon).

  • Reordered elements by chemical properties rather than strict mass order where conflicts arose (e.g., Tellurium and Iodine).

• Mendeleev's Predictions for Ekasilicon (Germanium):

  • Atomic Mass: Silicon = $28$, Tin = $118$; Predicted Ekasilicon = $72$; Measured Germanium = $72.6$

  • Color: Silicon = Grey, Tin = White metal; Predicted Ekasilicon = Grey; Measured Germanium = Grey-white

  • Density: Silicon = $2.32\,\text{g/cm}^3$, Tin = $7.28\,\text{g/cm}^3$; Predicted Ekasilicon = $5.5\,\text{g/cm}^3$; Measured Germanium = $5.4\,\text{g/cm}^3$

  • Acid Reaction: Silicon = Resists acid, Tin = Reacts with acid; Predicted Ekasilicon = Resists both; Measured Germanium = Resists both

• Oxide and Hydride Periodic Trends Across a Period:

  • Oxides: Basic ($\text{Na}_2\text{O}$, $\text{MgO}$) $\rightarrow$ Amphoteric ($\text{Al}_2\text{O}_3$) $\rightarrow$ Acidic ($\text{SiO}_2$, $\text{P}_2\text{O}_5$, $\text{SO}_3$, $\text{Cl}_2\text{O}_7$)

  • Hydrides: $\text{NaH}$, $\text{MgH}_2$, $(\text{AlH}_3)_x$, $\text{SiH}_4$, $\text{PH}_3$, $\text{H}_2\text{S}$, $\text{HCl}$

• Modern Periodic Table Layout:

  • Columns (Groups / Families): Elements with similar physical and chemical properties (designated by group number and letter $A$/$B$).

  • Rows (Periods): Sequential rows showing property patterns that repeat in subsequent periods.

  • Main Group (Representative Elements): Designated as "A" groups.

  • Transition Elements: Designated as "B" groups (all metals).

  • Inner Transition Elements (Rare Earth Elements): Bottom two rows (Lanthanides and Actinides, belonging to Periods 6 and 7; all metals).

• Elemental Classifications:

  • Metals: Account for $\approx 75\%$ of elements (located lower left). Solids at room temperature (except Mercury, $\text{Hg}$, liquid). Properties: Shiny, reflective, high electrical and thermal conductivity, malleable, ductile. Form cations in reactions.

  • Nonmetals: Located upper right (except Hydrogen, $\text{H}$). Found in all three physical states at room temperature ($\text{S}(s)$, $\text{Br}_2(l)$, $\text{Cl}_2(g)$). Poor conductors of heat and electricity; solids are brittle. Form anions in reactions.

  • Metalloids (Semiconductors): Located along the diagonal dividing line. Exhibit intermediate properties. Silicon ($\text{Si}$) is shiny and conducts electricity, but is brittle and a poor heat conductor.

Important Groups of the Periodic Table

• Group 1A - Alkali Metals ($\text{Li}, \text{Na}, \text{K}, \text{Rb}, \text{Cs}$; $\text{H}$ placed here structurally but is a nonmetal):

  • Properties: Soft metals with low melting points and low densities.

  • Flame Tests: Lithium ($\text{Li}$) = red, Sodium ($\text{Na}$) = yellow, Potassium ($\text{K}$) = violet.

  • Reactivity: Extremely reactive, never found uncombined in nature. Form water-soluble compounds. Extracted by electrolyzing molten salts.

  • Reaction with Water: React vigorously producing basic (alkaline) solutions and hydrogen gas:         $2\,\text{Na}(s) + 2\,\text{H}_2\text{O}(l) \rightarrow 2\,\text{NaOH}(aq) + \text{H}_2(g)$

• Group 2A - Alkali Earth Metals ($\text{Be}, \text{Mg}, \text{Ca}, \text{Sr}, \text{Ba}$):

  • Properties: Harder, denser, and higher melting than alkali metals.

  • Flame Tests: Calcium ($\text{Ca}$) = red, Strontium ($\text{Sr}$) = red, Barium ($\text{Ba}$) = yellow-green.

  • Reactivity: Reactive (less than Group 1A). Form stable insoluble oxides from which they are extracted.

  • Reactivity with Water:

    • Beryllium ($\text{Be}$): No reaction

    • Magnesium ($\text{Mg}$): Reacts with steam

    • Calcium ($\text{Ca}$), Strontium ($\text{Sr}$), Barium ($\text{Ba}$): React with cold water

• Group 7A - Halogens ($\text{F}, \text{Cl}, \text{Br}, \text{I}, \text{At}$):

  • Properties: Nonmetals existing as diatomic molecules ($\text{F}_2, \text{Cl}_2, \text{Br}_2, \text{I}_2$). Extremely reactive.

  • Physical States: Fluorine ($\text{F}_2$) and Chlorine ($\text{Cl}_2$) are gases; Bromine ($\text{Br}_2$) is liquid; Iodine ($\text{I}_2$) is solid.

  • Reactions: React with metals to form ionic compounds. React slowly with water:         $\text{Br}_2(l) + \text{H}_2\text{O}(l) \rightleftharpoons \text{HBr}(aq) + \text{HOBr}(aq)$

  • Hydrohalic Acid Strengths: $\text{HF} < \text{HCl} < \text{HBr} < \text{HI}$ (where $\text{HF}$ is weak, others are strong).

• Group 8A - Noble Gases ($\text{He}, \text{Ne}, \text{Ar}, \text{Kr}, \text{Xe}, \text{Rn}$):

  • Properties: All gases at room temperature with very low melting and boiling points. Extremely unreactive (chemically inert).

Atomic Mass Calculations and Mass Spectrometry

• Average Atomic Mass Calculation:

  • The atomic mass of an element is a weighted average that accounts for the mass and natural fractional abundance of each naturally occurring isotope:         $\text{Atomic Mass} = \sum_{i} (\text{fractional abundance of isotope}_i) \times (\text{mass of isotope}_i)$

• Example 2.5 Calculation (Atomic Mass of Copper):

  • Given:

    • Cu-63: $69.17\%$ abundance, mass = $62.9396\,\text{amu}$

    • Cu-65: $100\% - 69.17\% = 30.83\%$ abundance, mass = $64.9278\,\text{amu}$

  • Calculation:         $\text{Atomic Mass} = (0.6917 \times 62.9396\,\text{amu}) + (0.3083 \times 64.9278\,\text{amu})$         $\text{Atomic Mass} = 43.5353\,\text{amu} + 20.0172\,\text{amu} = 63.5525\,\text{amu} \approx 63.55\,\text{amu}$

• Mass Spectrometry:

  • Measures isotopic masses and abundances by ionizing sample atoms/molecules, accelerating them down a flight tube, and bending their trajectory with a magnetic field.

  • Separation is based on mass-to-charge ratio ($m/z$).

  • Fragmentation during ionization provides molecular structure details.

  • Mass Spectrum Plot: Displays Relative Abundance ($y$-axis, $0\%$ to $100\%$) versus Relative Mass ($x$-axis).

  • Chlorine Mass Spectrum Example: Shows two major peaks at mass $35$ ($100\%$ relative height / $75\%$ abundance) and mass $37$ ($33\%$ relative height / $25\%$ abundance).

Molar Mass, Avogadro's Number, and Quantitative Conversions

• The Mole Concept:

  • A mole ($\text{mol}$) is defined as the number of particles equal to the exact number of atoms in $12.000\,\text{g}$ of pure Carbon-12 (${}^{12}\text{C}$).

  • $\text{Avogadro's Number} = 6.0221421 \times 10^{23}\text{ particles/mol} \approx 6.022 \times 10^{23}$

  • $1\,\text{atom of C-12} = 12\,\text{amu}$ exactly; $1\,\text{mole of C-12} = 12\,\text{g}$ exactly.

  • Average carbon atom mass = $12.01\,\text{amu}$; $1\,\text{mole}$ of natural carbon weighs $12.01\,\text{g}$ and contains $6.022 \times 10^{23}$ atoms.

  • Visual Scale: 22 copper pennies contain approximately $1\,\text{mol}$ of copper atoms.

• Molar Mass Relationships:

  • Molar mass is the mass in grams of one mole of atoms ($\text{g/mol}$).

  • The molar mass of an element in grams is numerically equal to its atomic mass in $\text{amu}$.

  • The lighter the atom, the less a mole weighs.

  • The lighter the atom, the greater the total number of atoms in a $1.00\,\text{g}$ sample.

• Mole and Mass Relationships Table:

  • Hydrogen ($\text{H}$): $1\,\text{atom} = 1.008\,\text{amu}$, $1\,\text{mole} = 6.022 \times 10^{23}\text{ atoms}$, $1\,\text{mole mass} = 1.008\,\text{g}$

  • Carbon ($\text{C}$): $1\,\text{atom} = 12.01\,\text{amu}$, $1\,\text{mole} = 6.022 \times 10^{23}\text{ atoms}$, $1\,\text{mole mass} = 12.01\,\text{g}$

  • Oxygen ($\text{O}$): $1\,\text{atom} = 16.00\,\text{amu}$, $1\,\text{mole} = 6.022 \times 10^{23}\text{ atoms}$, $1\,\text{mole mass} = 16.00\,\text{g}$

  • Sulfur ($\text{S}$): $1\,\text{atom} = 32.06\,\text{amu}$, $1\,\text{mole} = 6.022 \times 10^{23}\text{ atoms}$, $1\,\text{mole mass} = 32.06\,\text{g}$

  • Calcium ($\text{Ca}$): $1\,\text{atom} = 40.08\,\text{amu}$, $1\,\text{mole} = 6.022 \times 10^{23}\text{ atoms}$, $1\,\text{mole mass} = 40.08\,\text{g}$

  • Chlorine ($\text{Cl}$): $1\,\text{atom} = 35.45\,\text{amu}$, $1\,\text{mole} = 6.022 \times 10^{23}\text{ atoms}$, $1\,\text{mole mass} = 35.45\,\text{g}$

  • Copper ($\text{Cu}$): $1\,\text{atom} = 63.55\,\text{amu}$, $1\,\text{mole} = 6.022 \times 10^{23}\text{ atoms}$, $1\,\text{mole mass} = 63.55\,\text{g}$

• Quantitative Conversion Worked Examples:

  • Example 2.6: Atoms in $2.45\,\text{mol}$ of Copper:

    • Given: $2.45\,\text{mol Cu}$

    • Relationship: $1\,\text{mol Cu} = 6.022 \times 10^{23}\text{ atoms Cu}$

    • Calculation:             $\text{Atoms Cu} = 2.45\,\text{mol Cu} \times \frac{6.022 \times 10^{23}\text{ atoms}}{1\,\text{mol Cu}} = 1.48 \times 10^{24}\text{ atoms Cu}$

  • Example 2.7: Moles of Carbon in $0.0265\,\text{g}$ of Pencil Lead:

    • Given: $0.0265\,\text{g C}$

    • Relationship: $1\,\text{mol C} = 12.01\,\text{g C}$

    • Calculation:             $\text{Moles C} = 0.0265\,\text{g C} \times \frac{1\,\text{mol C}}{12.01\,\text{g C}} = 2.21 \times 10^{-3}\,\text{mol C}$

  • Example 2.8: Copper Atoms in a $3.10\,\text{g}$ Penny:

    • Given: $3.10\,\text{g Cu}$

    • Relationships: $1\,\text{mol Cu} = 63.55\,\text{g Cu}$, $1\,\text{mol Cu} = 6.022 \times 10^{23}\text{ atoms}$

    • Calculation:             $\text{Atoms Cu} = 3.10\,\text{g Cu} \times \frac{1\,\text{mol Cu}}{63.55\,\text{g Cu}} \times \frac{6.022 \times 10^{23}\text{ atoms}}{1\,\text{mol Cu}} = 2.94 \times 10^{22}\text{ atoms Cu}$