Electron Configurations, Atomic Models & Chemical Formulas

Empirical vs. Molecular Formulas

• Empirical formula
  • Gives the smallest whole‐number ratio of the different atoms present in a compound.
  • Example idea given in class: “How many atoms are actually bound together in the molecule versus just the smallest ratio?”
• Molecular formula
  • Tells the actual number of each type of atom in ONE molecule of the substance (the “true” formula).
• Relationship
  • Molecular formula is always an integer multiple of the empirical formula.
  • The multiple is determined experimentally (normally from molar mass data).

Molar Mass (Formula Mass)

• Always supplied or experimentally obtainable.
• Procedure to calculate yourself:
  1. Look up the atomic masses on the periodic table.
  2. Multiply each atomic mass by the number of that atom in the formula.
  3. Add the products.
• General expression: $M<em>{\text{compound}} = \sum</em>i n<em>i \times A</em>i$
  • $n_i$ = number of atoms of element $i$
  • $A_i$ = atomic mass of element $i$ (amu or g mol⁻¹)
• Will be used heavily in Chapter 5: Naming & Writing Chemical Formulas (preview mentioned).

Recap of Atomic Models

1. Bohr Model (historical but still instructive)

• Electrons occupy fixed, discrete energy levels (n = 1, 2, 3 …) and cannot exist between them.
• Visual “planets orbiting the nucleus” does NOT literally exist—instructor explicitly emphasized “that picture doesn’t exist.”

2. Quantum Mechanical Model (modern, probability based)

• Electrons are described by a wavefunction (ψ) which gives a probability distribution (electron cloud).
• Orbitals = regions in space with high probability (the “dust cloud” picture used on slides).
  • Dense near nucleus, sparse further out; at some distance probability ≈ 0.
• We know energy of an electron with some certainty; its exact position is uncertain (Heisenberg Uncertainty Principle underlying idea).

Energy Levels, Subshells, and Orbitals

• Principal Energy Level (n): 1, 2, 3 … (gets larger in size & energy).
• Each level splits into subshells (a.k.a. sublevels): $s, p, d, f$ (names only—letters).
  • $s$ is lowest in energy, $p$ slightly higher, then $d$, $f$ …
• Electron–electron repulsion
  • More electrons → stronger repulsion → shapes become more complex as they "try to find their own place to fit in."

Orbital Count & Capacity

Formula for electrons per subshell: $\text{e⁻}_{\max}=2(2\ell+1)$ (where $\ell$ = 0,1,2,3 for $s,p,d,f$).

Size Trend of $s$ Orbitals (same shape, growing size)

• $1s$: smallest
• $2s$: same sphere, bigger
• $3s$: same sphere, even bigger

Visualization Highlights Mentioned

• Dots on slides = individual points where electron might be; density ∝ probability.
• Moving away from nucleus → dot density fades → essentially zero probability beyond some boundary.

Spin & Pauli Principle (why only 2 e⁻ per orbital)

• Electrons possess spin (rotate on an axis).
  • One spin‐up (↑) and one spin‐down (↓) allowed → Pauli Exclusion Principle.

Building Electron Configurations

• Aufbau Principle: add electrons to lowest available energy state.
• Hund’s Rule and Pauli are implicitly followed (not verbally named but underlying logic).
• Example in lecture (12 e⁻):
  $1s^2\, 2s^2\, 2p^6\, 3s^2$ ← corresponds to Mg.
• Next element discussed → chlorine (17 e⁻) would add $3p^5$.
• d‐block caveat (explicitly warned):
  • For transition metals, $d$ subshell’s principal quantum number is one less than the $s$ that fills before it.
    Example teased in class: iron (Fe) 26 e⁻
    $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6$

Shorthand / Noble-Gas Core Notation

• Early sections of every configuration are identical ⇒ use preceding noble gas in brackets.
• Rule: Only noble gases (last column) may be used in brackets because all their subshells are completely full (chemically inert).
• Example (not fully written but principle stated):
  Fe → $[Ar]\,4s^2\,3d^6$ (since Ar is the previous noble gas).

Valence Electrons & Periodic Table Groups

• Valence electrons = $s$ and $p$ electrons in the highest n.
• Drive bonding & reactivity; outermost “surface” of atom.
• Periodic table A-group labeling (two styles shown on handout):
  • Columns 1A → 8A correlate with 1 → 8 valence electrons.
  • Instructor highlighted Group 3A (“that 3 is the number of valence e⁻, not 13”).
• Noble gases already have 8 valence e⁻ (an octet) → no tendency to react.

Ion Formation Tie-in (preview for Tuesday)

• Atoms tend to lose, gain, or share electrons to achieve a noble-gas configuration.
  • Example posed: an element with one valence electron “loses one to become the noble gas before it.”

Practical & Pedagogical Notes from Instructor

• Readings + videos must be completed before Tuesday’s class.
• A periodic table exactly like the one projected will be provided on exams.
• Emphasis on distinguishing “model pictures” (Bohr rings) from physical reality (probability clouds).

Ethical / Philosophical Angle Briefly Touched

• “We don’t know exactly where the electron is, only where it is likely to be” → foundational uncertainty philosophy in quantum mechanics.

Numerical / Formula Summary Cheat-Sheet

• Molar mass: $M = \sum<em>i n</em>i A_i$
• Max e⁻ in subshell: $2(2\ell+1)$
• $s,p,d,f$ orbital counts: 1, 3, 5, 7 (→ 2, 6, 10, 14 e⁻)
• Electron configuration order (through 4p):
  $1s\rightarrow 2s\rightarrow 2p\rightarrow 3s\rightarrow 3p\rightarrow 4s\rightarrow 3d\rightarrow 4p$ (use diagonal/energy chart).

These bullet-point notes capture every conceptual, numerical, and procedural detail mentioned in the transcript and are organized to serve as complete study material independent of the original video.