Chapter 4 – Isotopes & Atomic Mass

Definition of Isotopes

• Isotopes = atoms of the same element that differ in mass.
  • Same number of protons (atomic number Z is constant).
  • Different number of neutrons.
• Mass number (symbol A):
  • A = \text{protons} + \text{neutrons} (always a whole number).
  • Used to identify an isotope (e.g.
  • Hydrogen-1, Hydrogen-2, Hydrogen-3).
  • Distinct from atomic mass (a weighted average, often non-integer).

Naturally Occurring Isotopes – Examples

• Hydrogen
  • \text{H-1}: 1\,p^+, 0\,n^0 ⟶ mass number 1.
  • \text{H-2}: 1\,p^+, 1\,n^0 ⟶ mass number 2 (deuterium).
  • \text{H-3}: 1\,p^+, 2\,n^0 ⟶ mass number 3 (tritium).
• Neon
  • \text{Ne-20}: 10\,p^+, 10\,n^0 – 90.48 % abundance.
  • \text{Ne-21}: 10\,p^+, 11\,n^0 – 0.27 % abundance.
  • \text{Ne-22}: 10\,p^+, 12\,n^0 – 9.25 % abundance.

Isotopic Notation Systems

• Nuclide (nuclear) symbol:
  • ^{A}_{Z}\text{Symbol}
  • Superscript A = mass number, subscript Z = atomic number.
  • Example (neon): ^{20}{10}\text{Ne},\ ^{21}{10}\text{Ne},\ ^{22}_{10}\text{Ne}.
• Hyphen notation:
  • Element symbol/name – mass number.
  • Example: Ne-20, Ne-21, Ne-22 (atomic number understood & omitted).

Using Isotope Data to Find Subatomic Particles

• Given isotope notation, deduce:
  • Protons = atomic number Z (fixed for an element).
  • Electrons = protons if the atom is neutral (no charge specified).
  • Neutrons = A - Z.
• Worked example – ^{37}_{17}\text{Cl} (chlorine-37):
  • Protons = 17.
  • Electrons = 17 (neutral atom).
  • Neutrons = 37 - 17 = 20.

Practice Examples Highlighted in Video

1. Pb-204 (lead-204)
   • Atomic number Z = 82 ⟶ 82 protons & 82 electrons (neutral).
   • Mass number A = 204 ⟶ neutrons = 204-82 = 122.
   • Nuclide symbol ^{204}_{82}\text{Pb}.
2. Unknown element with 18 e⁻ and 20 n⁰ (neutral)
   • Electrons = protons ⇒ Z = 18 (argon, Ar).
   • Mass number A = 18 + 20 = 38.
   • Nuclide symbol ^{38}_{18}\text{Ar} or Ar-38.

Atomic Mass Units (amu)

• Need arose because individual atoms are too small for grams.
• Definition: 1\ \text{amu} = \frac{1}{12} \text{mass of }\, ^{12}\text{C}.
• Conversion: 1\ \text{amu} = 1.6606 \times 10^{-24}\ \text{g} (memorization not required but shows scale).

Weighted Average Atomic Mass

• Periodic-table value = weighted average of all naturally occurring isotopes.
• Formula (general): \overline{M} = \sum (\text{fractional abundance}) \times (\text{isotope mass})
  • Convert % to decimal before multiplying.
  • Sum over all isotopes.

Chlorine Example (two isotopes)

• Data
  • ^{35}\text{Cl}: 75.77 % ; mass 34.97\ \text{amu}.
  • ^{37}\text{Cl}: 24.23 % ; mass 36.97\ \text{amu}.
• Calculation
  \overline{M} = 0.7577 \times 34.97 + 0.2423 \times 36.97 = 35.45\ \text{amu}.
• Matches periodic table entry for chlorine (35.45 amu).

Gallium Example (worked in detail)

• Data
  • Ga-69: mass 68.9256\ \text{amu} ; abundance 60.11 %.
  • Ga-71: mass 70.9247\ \text{amu} ; abundance 39.89 %.
• Steps
  1. Convert % → decimals: 0.6011 and 0.3989.
  2. Multiply & add:
     0.6011 \times 68.9256 = 41.4312\ \text{amu}.
     0.3989 \times 70.9247 = 28.219\ \text{amu}.
     41.4312 + 28.219 = 69.7231\ \text{amu}.
  3. Apply sig-fig/decimal-place rules (2 decimal places) → 69.72\ \text{amu}.

Key Takeaways & Connections

• Changing neutron count → isotope; changing proton count → different element.
• Mass number aids in isotope identification but does not indicate actual mass; atomic mass (table) is average weighted by natural abundance.
• Atomic mass units permit convenient comparison of tiny masses.
• Weighted-average calculations illustrate statistical reasoning & significant-figure discipline—skill transferable to stoichiometry, solution concentrations, and error analysis across chemistry.

Formulas & Quick Reference

• Mass number: A = p^+ + n^0.
• Neutrons in an isotope: n^0 = A - Z.
• Weighted atomic mass:
  \overline{M} = (\%1 \div 100)\,M1 + (\%2 \div 100)\,M2 + \dots.
• Neutral atom: e^- = p^+.

Ethical & Practical Implications

• Isotopes such as \text{H-2} and \text{H-3} underpin nuclear fusion research & medical tracing.
• Accurate isotope abundance data critical in climate science (e.g., ^{18}\text{O}/^{16}\text{O} ratios), archaeology (radiocarbon dating), and pharmacology (drug metabolism tracking).