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: $^{A}<em>{Z}\text{Cl}$, $^{35}</em>{17}\text{Cl}$, 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:
  $\bar m<em>{\text{element}} = \sum</em>i w<em>i\, m</em>i$
  where $wi$ = fractional abundance, $mi$ = isotopic atomic mass.

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

• 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:
  $\Delta m = \big(Z m<em>p + N m</em>n\big) - m_{\text{nucleus}} \gt 0$

• 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.