Atoms, Subatomic Particles, Isotopes & Atomic Mass

The Atom: Fundamental Overview

• Atoms are the smallest particles of an element that retain that element’s chemical identity.
  • Example: Every sheet of aluminum foil is an immense collection of individual aluminum atoms.
• All elements on the periodic table are built from atoms; each element’s atoms have unique properties.

Dalton’s Atomic Theory (1808)

• Formulated by John Dalton (1766–1844) to explain fixed composition in compounds.
• Core postulates (modern wording):
  • All matter consists of tiny, indivisible particles called atoms.
  • Atoms of a given element are identical (same mass & properties) and differ from atoms of other elements.
  • Chemical compounds form when atoms of two or more elements combine in simple, fixed whole-number ratios.
  • Chemical reactions involve rearrangement, separation, or combination of atoms; atoms are neither created nor destroyed (law of conservation of mass).
• Significance: Provided the first coherent, testable framework for describing matter on the atomic scale and predicting stoichiometric relationships.

Discovery of Subatomic Particles

• By the late 1800s, experiments showed atoms are divisible and contain smaller constituents (subatomic particles):
  • Protons (p^+) – positive charge
  • Neutrons (n^0) – neutral
  • Electrons (e^-) – negative charge
• Charged-particle interaction rules:
  • Like charges ( (+,+) or (-,-) ) repel.
  • Unlike charges ( + and - ) attract.

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

• Observed cathode rays deflected by electric & magnetic fields, concluding they are streams of negatively charged electrons.
• Proposed “plum-pudding” model: electrons embedded in a diffuse, positively charged cloud (analogous to plums in pudding).
• Philosophical import: Demonstrated atoms were not indivisible, contradicting Dalton’s first postulate.

Rutherford’s Gold-Foil Experiment (1911)

• Fired α-particles at thin gold foil.
  • Most particles passed straight through (empty space).
  • Some deflected at large angles; a few rebounded.
• Conclusions:
  • Atom contains a dense, small, positively charged nucleus.
  • Electrons occupy the spacious region surrounding the nucleus.
• Led to planetary/nuclear model of the atom, superseding Thomson’s view.

Present-Day Atomic Structure

• Components & locations:
  • Nucleus – houses protons (+) and neutrons (0).
  • Electron cloud – vast, mostly empty space containing electrons (–).
• Approximate sizes: nucleus diameter \sim10^{-15}\text{ m} vs. whole atom \sim10^{-10}\text{ m} (factor of 10^5 difference).

Atomic Mass Unit (amu) & Particle Masses

• 1 amu is defined as \frac{1}{12} the mass of a ^{12}\text{C} atom (6 p, 6 n).
• Typical masses:
  • Proton: 1.007\text{ amu} (≈1 amu)
  • Neutron: 1.008\text{ amu} (≈1 amu)
  • Electron: 0.00055\text{ amu} (≈1/1836 of a proton)
• Practical consequence: Nearly all atomic mass resides in the nucleus; electrons dominate volume but not mass.

Tabulated Summary of Subatomic Particles

• Proton (symbol p\text{ or }p^+) – charge +1, mass 1.007\text{ amu}, in nucleus.
• Neutron (symbol n\text{ or }n^0) – charge 0, mass 1.008\text{ amu}, in nucleus.
• Electron (symbol e^-) – charge -1, mass 0.00055\text{ amu}, outside nucleus.

Electrical Neutrality of Atoms

• Any isolated atom has zero net charge.
  • Number of electrons = number of protons.
  • Example: Calcium (Z=20) contains 20 protons and 20 electrons.

Atomic Number (Z)

• Definition: Whole number unique to each element, equal to the number of protons.
• Placement: Shown above element symbol on periodic table.
• Examples:
  • Z=1 – Hydrogen (1 p)
  • Z=6 – Carbon (6 p)
  • Z=29 – Copper (29 p)
  • Z=79 – Gold (79 p)
• Critical outcome: Identifies an element; changing Z changes the element.

Mass Number (A)

• Definition: Total particles in nucleus:
  A = \text{protons} + \text{neutrons}
• Does not appear on the periodic table because each single atom may have a distinct A (isotopes).
• Determining neutrons:
  \text{Neutrons} = A - Z
  • Example: Potassium with A=39 and Z=19 → 20 neutrons.

Quick Reference / Study Tip

• Z = \text{number of protons}
• A = \text{protons} + \text{neutrons}
• \text{Neutrons} = A - Z
• Applies to individual atoms, not necessarily the bulk element.

Practice Highlights (from Exercises)

• Identifying particles:
  • Outside nucleus → electron.
  • Positive charge → proton.
  • Mass but no charge → neutron.
• True/False checkpoints:
  • Electron mass > proton mass? → False.
  • Proton (+) and electron (-) charges? → True.
  • Nucleus contains only protons & neutrons? → True.
• Sample proton counts:
  • F atom → 9 p.
  • K atom → 19 p.
  • Ba atom → 56 p.
• Filling atomic-number tables (Na, Zn, S): each property equals Z because atoms are neutral.
• Lead-207 example: 82 p, 125 n, 82 e.
• Zinc-65 example: 30 p, 35 n; alt. isotope with 37 n has A=67.
• Unknown element with 14 p and 20 n → Z=14, A=34, element = silicon (Si).

Isotopes

• Definition: Atoms of the same element (same Z) with different A due to varying neutron counts.
• Atomic symbol (nuclide notation):
  ^{A}_{Z}\text{X} where X = element symbol.
• Example isotopes & particle counts:
  • ^{16}{8}\text{O} – 8 p, 8 n, 8 e. • ^{31}{15}\text{P} – 15 p, 16 n, 15 e.
  • ^{65}_{30}\text{Zn} – 30 p, 35 n, 30 e.

Carbon Isotopes (Exercise 13)

• ^{12}_{6}\text{C} → 6 p, 6 n, 6 e.
• ^{13}_{6}\text{C} → 6 p, 7 n, 6 e.
• ^{14}_{6}\text{C} → 6 p, 8 n, 6 e.
• Importance: ^{14}\text{C} is radioactive and useful for radiocarbon dating.

Additional Symbol Practice (Exercise 14)

• 8 p, 8 n, 8 e → ^{16}_{8}\text{O}.
• 17 p, 20 n, 17 e → ^{37}_{17}\text{Cl}.
• 47 p, 60 n, 47 e → ^{107}_{47}\text{Ag}.

Isotope Comparison (Exercise 15)

• Pair B with 6 p each are isotopes of carbon.
• Pair C are the atoms that both contain 8 n.

Atomic Mass (Weighted Average)

• Listed beneath each element symbol on periodic table (units: amu).
• Represents weighted average of all naturally occurring isotopes, not a single atom’s mass.
• Calculated relative to ^{12}\text{C} standard.
• Contrast: A is an integer for an individual atom; atomic mass is often fractional.

Examples from Periodic Table

• Ca → 40.08\text{ amu}
• Al → 26.98\text{ amu}
• Pb → 207.2\text{ amu}
• Ba → 137.3\text{ amu}
• Fe → 55.85\text{ amu}

Majority Isotope & Abundance Logic

• The isotope whose mass is closest to the average atomic mass is the most abundant.
  • Lithium: 6.941 amu → ^{7}\text{Li} predominates.
  • Potassium: 39.10 amu → ^{39}\text{K} predominates.

Formal Calculation of Atomic Mass

1. Obtain each isotope’s percent abundance and its individual atomic mass (A in amu).
2. Convert percent → decimal fraction.
3. Multiply: (\text{fraction})(\text{isotope mass}) for each isotope.
4. Sum contributions: \Sigma\,[(\text{fraction})(\text{mass})] = \text{average atomic mass}.

Chlorine Example (conceptual)

• Given atomic mass 35.45\text{ amu}.
• Chlorine has isotopes ^{35}\text{Cl} and ^{37}\text{Cl}.
• Cl-35 must have the larger percent abundance because 35.45 is nearer to 35 than 37.

Magnesium Isotopes Table (Key Data)

• Weighted average → 24.31\text{ amu} (agrees with periodic table value).

Practical & Conceptual Implications

• Understanding subatomic make-up enables:
  • Prediction of chemical behavior (valence depends on electrons).
  • Computation of molar masses (link macroscopic grams to microscopic atoms).
  • Use of isotopic signatures in geochemistry, medicine (PET scans), archeology (radiocarbon dating).
• Philosophically, atomic theory bridges empirical observations with an unseen microscopic world, embodying the reductionist approach in science.

Quick Reference Equation Set

• Atomic number: Z = #\text{protons}
• Mass number: A = Z + #\text{neutrons}
• Neutrons: #n = A - Z
• Atomic mass (average): \bar{m} = \sumi \left( \text{fraction}i \times A_i \right)