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:
  • $^{16}<em>{8}\text{O}$ – 8 p, 8 n, 8 e. • $^{31}</em>{15}\text{P}$ – 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): $\bar{m} = \sum<em>i \left( \text{fraction}</em>i \times A_i \right)$