Atomic Number, Isotopes & Average Atomic Mass of Chlorine

Atomic Number (Z) – The Element’s Fingerprint

  • Definition: The count of protons in the nucleus of an atom.

    • Z = \text{number of protons}

  • Determines elemental identity:

    • Z=1 \Rightarrow \text{Hydrogen}

    • Z=6 \Rightarrow \text{Carbon}

    • Z=17 \Rightarrow \text{Chlorine}

  • Periodic-table convention:

    • Small, whole number above/beside the symbol (e.g., the circled numbers the narrator refers to).

  • Connection to previous lecture: Earlier videos established that changing Z changes the element entirely (e.g., adding a proton to carbon turns it into nitrogen).

Mass Number (A) – Counts Nucleons

  • A = Z + N where N = neutrons.

  • Written in isotope notation at the upper-left of the element symbol: ^{A}{Z}\text{Cl}, ^{35}{17}\text{Cl}, etc.

  • Represents the total of massive nuclear particles; electrons are excluded because their mass is (<10^{-3}) of a nucleon and usually neglected for atomic-mass discussions.

Isotopes – Multiple Versions of the Same Element

  • Definition: Atoms with identical Z (protons) but differing N (neutrons).

  • Significance:

    • Chemically similar (same electron configuration when neutral) because chemistry is governed by proton count/electron structure.

    • Differ in mass, affecting density, diffusion rates, and nuclear stability.

  • Two stable chlorine isotopes discussed:

    1. Chlorine-35

    • Notation: ^{35}_{17}\text{Cl} or “Cl-35.”

    • Z = 17 ⇒ Chlorine.

    • A = 35 ⇒ N = 35-17 = 18 neutrons.

    1. Chlorine-37

    • Notation: ^{37}_{17}\text{Cl} or “Cl-37.”

    • Z = 17.

    • A = 37 ⇒ N = 37-17 = 20 neutrons.

  • Key take-away: Same Z (chlorine identity), different N (18 vs 20) ⇒ distinct isotopes.

Atomic Mass vs. Mass Number

  • Mass Number (A) is an integer count of nucleons.

  • Atomic Mass (m) is a measured mass expressed in unified atomic mass units (u, also “amu”).

    • 1 u ≈ mass of a single ^{12}\text{C}/12 atom.

    • Protons & neutrons ≈ 1 u each, but not exactly.

  • Why m ≠ A exactly:

    • Individual proton mass \neq 1.000\text{ u}; same for neutrons.

    • Mass defect: When nucleons bind, the system’s mass drops (energy released, E = \Delta m c^2).

    • Example: Cl-35’s actual atomic mass is slightly below 35 u.

Natural Abundance & Weighted Average Atomic Mass

  • Periodic-table “35.45” for chlorine is not any single isotope’s mass; it’s a weighted mean.

  • Given natural abundances:

    • Cl-35: 75.77\% = 0.7577 fraction.

    • Cl-37: 24.23\% = 0.2423 fraction.

  • Formula:
    \bar m{\text{element}} = \sumi wi\, mi
    where $wi$ = fractional abundance, $mi$ = isotopic atomic mass.

  • Chlorine example (symbols explained inline):
    \bar m{\text{Cl}} = (0.7577)(m{\text{Cl-35}}) + (0.2423)(m_{\text{Cl-37}}) \approx 35.45\ \text{u}

  • Practical use: Chemists use this average for molar-mass calculations (e.g., grams-per-mole numerics in stoichiometry).

Mass Defect ((\Delta m)) – Brief Mention

  • Combined nucleus mass is less than sum of isolated nucleons:
    \Delta m = \big(Z mp + N mn\big) - m_{\text{nucleus}} \gt 0

  • Significance: The “missing mass” is binding-energy credit, foundational for nuclear physics and applications (e.g., fission, fusion).

  • Linked concept: Even stable isotopes (Cl-35, Cl-37) exhibit a measurable mass defect despite chemical stability.

Key Take-Home Bullet List

  • Element identity = proton count (atomic number).

  • Isotopes: same Z, different N ⇒ different mass numbers.

  • Chlorine’s two stable isotopes: Cl-35 (18 n), Cl-37 (20 n).

  • Periodic table lists average atomic mass, not mass number.

  • Weighted average uses natural abundance: 35.45 u for chlorine.

  • Atomic mass slightly deviates from integer values due to nucleon mass differences and mass defect.

  • For routine chemistry, electrons’ mass is negligible in atomic-mass calculations.