Atomic Structure & Isotopes

The Atom

• All matter is constructed from elements found on the periodic table.
• The atom is the smallest unit of an element that still preserves the element’s chemical identity.
• Everyday examples: A sheet of aluminum foil is simply a very large collection of individual aluminum atoms.

Dalton’s Atomic Theory (1808)

• First fully-formed scientific atomic model; answered why elements combine into compounds.
• Core postulates:
  • Matter consists of tiny, indestructible atoms.
  • Atoms of the same element are identical; atoms of different elements differ.
  • Compounds form when atoms of ≥2 different elements combine in fixed, whole-number ratios.
  • Chemical reactions merely rearrange, separate, or recombine atoms; atoms themselves are not created nor destroyed.
• Significance: Provided a quantitative, conservation-of-matter explanation for the Law of Constant Composition and Law of Conservation of Mass.

Discovery of Subatomic Particles

• Late 1800s experiments with electricity revealed that atoms are not indivisible; they contain smaller parts called subatomic particles.
• Three fundamental subatomic particles:
  • Proton (p⁺) – positively charged.
  • Neutron (n⁰) – neutral.
  • Electron (e⁻) – negatively charged.
• Charge interactions follow simple electrostatics: like charges repel; unlike charges attract.

J. J. Thomson’s Cathode-Ray Experiment (1897)

• Observed cathode rays bend toward a positive plate → concluded they are streams of negatively-charged particles (electrons).
• Proposed the “plum-pudding” model: a diffuse, positively-charged “pudding” with negatively-charged “plum” electrons embedded randomly.
• Conceptual leap: atoms contain internal charges that can be separated.

Rutherford’s Gold-Foil Experiment (1911)

• Fired α-particles (He nuclei) at thin Au foil.
• Most particles passed straight through → atom mostly empty space.
• Few deflected/ bounced back → presence of a tiny, dense, positively-charged nucleus.
• New atomic picture:
  • Nucleus (p⁺ + n⁰) at center.
  • Electrons occupy the vast surrounding space.
• Overturned the plum-pudding model; established the nuclear model of the atom.

Modern Structure of the Atom

• Components & locations:
  • Nucleus: contains all p⁺ and n⁰ → accounts for ~99.97 % of atomic mass.
  • Electron cloud: e⁻ move in the large empty volume around the nucleus.
• Mass hierarchy (atomic mass units, amu):
  • m_{\text{proton}} \approx 1.007\,\text{amu}
  • m_{\text{neutron}} \approx 1.008\,\text{amu}
  • m_{\text{electron}} \approx 0.00055\,\text{amu}
• Atomic Mass Unit (amu) definition: 1\,\text{amu}=\tfrac{1}{12} \text{mass of }\,^{12}\text{C} (i.e., ^{12}\text{C}=12\,\text{amu} by definition).

Summary Table of Subatomic Particles

Practice: Identifying Subatomic Particles

• Found outside nucleus → electron.
• Positive charge → proton.
• Mass but no charge → neutron.
• Misconception check: “Mass of e⁻ > mass of p⁺” → False.

Atomic Number (Z)

• Definition: whole number equal to number of protons in the nucleus.
• Unique identifier for an element; appears above element symbol on periodic table.
• Examples: Z{\text{H}}=1\;,\; Z{\text{C}}=6\;,\; Z{\text{Cu}}=29\;,\; Z{\text{Au}}=79.

Neutral Atoms

• In an uncharged atom:
  #\,\text{protons}=#\,\text{electrons} → net charge 0.
• E.g., Ca: Z=20\Rightarrow 20\,\text{p⁺ and }20\,\text{e⁻}.

Mass Number (A)

• Definition: total particles in nucleus, i.e.
  A=Z+\text{neutrons}.
• Not printed on periodic table because each specific atom (isotope) has its own A.
• To find neutrons:
  \text{neutrons}=A-Z
  Example (K): A=39,\, Z=19 \Rightarrow\text{neutrons}=20.

Quick Reference Equations

• Z = \text{protons}
• A = \text{protons} + \text{neutrons}
• \text{neutrons} = A - Z

Isotopes

• Atoms of the same element (same Z) with different A values.
• Hence identical numbers of p⁺ and e⁻, but differing n⁰ counts.
• Chemical behavior nearly identical; physical properties (mass, density, stability) can differ.

Atomic Symbol (Isotope Notation)

• Written as ^{A}_{Z}\text{X} where X = element symbol, Z = atomic number, A = mass number.
• Provides full subatomic inventory:
  • Protons = Z
  • Electrons = Z (for a neutral atom)
  • Neutrons = A-Z
• Examples discussed:
  • ^{16}_{8}\text{O} → 8 p⁺, 8 n⁰, 8 e⁻.
  • ^{31}_{15}\text{P} → 15 p⁺, 16 n⁰, 15 e⁻.
  • ^{65}_{30}\text{Zn} → 30 p⁺, 35 n⁰, 30 e⁻.

Worked Isotope Examples

1. Carbon family:
   • ^{12}_{6}\text{C} → 6 p⁺, 6 n⁰, 6 e⁻.
   • ^{13}_{6}\text{C} → 6 p⁺, 7 n⁰, 6 e⁻.
   • ^{14}_{6}\text{C} → 6 p⁺, 8 n⁰, 6 e⁻ (radioactive; used in radiocarbon dating).
2. Exercise: 8 p⁺, 8 n⁰, 8 e⁻ ⇒ ^{16}_{8}\text{O}.
3. Exercise pair analysis: atoms with same Z but different A are isotopes (e.g., both with Z = 6 are carbon isotopes).
4. Pair with both atoms having eight neutrons determined via A-Z=8.

Sample Calculations

• Lead example: ^{207}_{82}\text{Pb}
  • p⁺ = 82, n⁰ = 207 − 82 = 125, e⁻ = 82.
• Zinc example: given A=65
  • Z=30;\; n⁰=35;\; new isotope with 37 n⁰ → A=67.
• Unknown element: 14 p⁺, 20 n⁰ → Z=14 \Rightarrow \text{Si};\; A=34.

Atomic Mass (Average Atomic Weight)

• Displayed beneath each element symbol on periodic table (e.g., Ca 40.08 amu).
• Weighted average of all naturally occurring isotopes based on percent abundance; not the same as any single mass number.
• Relates to ^{12}\text{C} scale: each isotope’s mass is measured relative to 12 amu for carbon-12.

Key Elements & Their Atomic Masses (selected)

• Ca: 40.08 amu
• Al: 26.98 amu
• Pb: 207.2 amu
• Ba: 137.3 amu
• Fe: 55.85 amu

Calculating Atomic Mass – Procedure

1. Obtain each isotope’s mass (amu) and percent abundance (%).
2. Convert % to decimal fraction.
3. Compute \text{(fraction)} \times \text{(isotopic mass)} for each isotope.
4. Sum the contributions:
   \bar{m}=\sumi (\text{fraction}i \cdot m_i).

• Example: Chlorine average 35.45 amu lies closer to A=35, indicating ^{35}\text{Cl} is more abundant than ^{37}\text{Cl}.

Quick Insight Questions

• Li-6 & Li-7 → table value 6.941 amu → Li-7 more abundant (value closer to 7).
• K-39, K-40, K-41 → table value 39.10 amu → K-39 most abundant.

Isotopic Data Tables (Highlights)

• Magnesium natural isotopes:
  • ^{24}_{12}\text{Mg}\;(78.70\%)
  • ^{25}_{12}\text{Mg}\;(10.13\%)
  • ^{26}_{12}\text{Mg}\;(11.17\%)
  • Weighted average → 24.31 amu.
• Elements with one dominant isotope show an atomic mass very close to that single A (e.g., ^{19}\text{F} 100 % ⇒ 19.00 amu).

Ethical & Practical Implications

• Isotopic abundances underpin radio-dating (C-14), medical diagnostics (radioisotopes), and tracing environmental processes.
• Understanding atomic structure enables control of chemical reactions, nuclear power, and materials science innovations.
• Conservation of mass and nuclear stability considerations inform safety protocols and environmental regulations.

Study Tips & Mnemonics

• A-Z-N triangle: draw a triangle with A at top, Z bottom left, N bottom right; covering one corner shows calculation using the other two.
• Remember: “p⁺ defines the element, n⁰ defines the isotope, e⁻ defines the charge.”
• Practice with plenty of isotope notation problems to cement proton-neutron relationships.

Key Equations Recap

• Z=#\,\text{p⁺}
• A=Z+#\,\text{n⁰}
• #\,\text{n⁰}=A-Z
• \text{Average atomic mass}=\sum (\text{fraction}\times\text{isotopic mass})
• \text{Neutral atom}: #\,\text{p⁺}=#\,\text{e⁻}
• Charge interactions: ++/-- \text{ repel};\; +- \text{ attract}.

With these consolidated notes, you should be able to: identify subatomic particles, determine atomic & mass numbers, write isotope symbols, calculate neutrons, infer relative isotopic abundance, and understand the historical evolution of atomic models.