| Quantity | Rule |
|---|---|
| # orbitals in level n | n² |
| # orbitals in subshell | 2ℓ+1 |
| angular nodes | ℓ |
| radial nodes | n−ℓ−1 |
| total nodes | n−1 |
| # maxima (R², RDF) | n−ℓ |
RDF = 4πr²·R(r)²; peak = r_mp. 1s of H: r_mp = a₀ = 52.9 pm (memorize).
n=1 ground; E negative (0 at n=∞); as n↑ levels get closer together. Electron drops → emits (ΔE<0), jumps → absorbs (ΔE>0). mvr = nh/2π.
Matter has wave nature (λ_dB=h/mv); only matters for tiny masses. Can't know position+momentum together → no exact electron path.
n size · ℓ shape (0s,1p,2d,3f) · mₗ orientation (−ℓ…+ℓ) · mₛ ±½. For H, energy on n only (3s=3p=3d). Orbital = Ψ whose |Ψ|² = probability.
Shapes: s sphere (0 ang nodes) · p dumbbell (1 nodal plane) · d cloverleaf. +/− on lobes = PHASE of Ψ, not charge.
Plot reading: R-vs-r starts at max@r=0 → s; at 0 → p/d/f. Axis crossings = radial nodes → use n−ℓ−1 to get n.
Multielectron: same-shell orbitals SPLIT s<p<d<f (repulsion/shielding). Energy on n and ℓ. ↑Z → orbital contracts (E↓, size↓).
subshell max e⁻: s2 p6 d10 f14 · shell max = 2n² (2,8,18,32).
Pauli: no 2 e⁻ share 4 QN → 2/orbital opposite spin. Aufbau: lowest n+ℓ first (tie→lower n). Hund: singly fill degenerate, parallel, before pairing.
Cr=[Ar]4s¹3d⁵ · Cu=[Ar]4s¹3d¹⁰ (not "half-full stability" myth)
Build neutral, then remove highest-n FIRST. d-block: strip ns before (n−1)d.
Mn²⁺=[Ar]3d⁵ Fe³⁺=[Ar]3d⁵ Br⁺=[Ar]4s²3d¹⁰4p⁴
Valence e⁻: grp≤12 = group#; grp≥13 = group#−10.
| Property | → period | ↓ group |
|---|---|---|
| Atomic radius | ↓ | ↑ |
| Ionization energy | ↑* | ↓ |
| e⁻ affinity (mag) | ↑ | ↓ |
| Electronegativity | ↑ | ↓ |
IE/EA/EN → top-right (F=4.0); radius → bottom-left.
On Test 2: octet · Lewis structures · formal charge · resonance. That's it.
Atoms gain/lose/share → noble-gas config (ns²np⁶). Ionic = metal+nonmetal (transfer). Covalent = 2 nonmetals (share).
Total valence e⁻ = Σvalence − charge (add for anion).
Steps: single-bond skeleton → fill terminal octets → central → make double/triple to complete C/N/O/F octets.
H=1 bond terminal · C/N/O/F never exceed octet · period 3+ may expand (S,P,Cl,Br,I,Xe) · central = least-EN.
Neutral patterns: B 3bd/0lp · C 4/0 · N 3/1 · O 2/2 · F 1/3 · term. O⁻ 1/3.
ΣFC = overall charge. Best structure: smallest FC; negative FC on more-EN atom; avoid like charges adjacent.
e.g. nitrate N: 5 − (0 + 4) = +1; terminal −O: 6 − 7 = −1.
Same skeleton, move only π electrons & lone pairs (never break σ). Needs ≥1 double/triple bond. Real molecule = hybrid average → identical bonds.
Equivalent (same FC pattern) → equal; non-equivalent → major/minor.
Light = EM radiation (oscillating E & B fields). c = λν & E = hν = hc/λ (both given). ↑ν → ↑E → ↓λ (λ and ν inversely proportional).
radio → microwave → IR → visible (400–750 nm) → UV → X-ray → γ. Going right: λ↓, ν↑, energy↑. Violet ~400 → red ~700.
| Experiment | Key idea |
|---|---|
| Blackbody (Planck) | oscillator energy quantized: E = n·hν (packets) |
| Photoelectric (Einstein) | light = photons E = hν; ejects e⁻ only above a threshold frequency (not intensity) |
| Line spectra | atoms emit discrete lines → electron energies are quantized |
Photoelectric eqn (assemble from data sheet): hν = w + ½mₑv² (w = work function). Brighter light = more electrons, not faster. These set up the Bohr model (§2.4).
Groups = columns 1–18 · periods = rows · blocks s, p, d, f · metals left/centre, nonmetals upper-right (staircase). Atomic # = protons = electrons (neutral atom).
Valence e⁻ = group # (grp 1–2) or group # − 10 (grp 13–18). A Lewis symbol = element + its valence e⁻ as dots. This is how you get the electron count for a Lewis structure.
Pull on shared e⁻; increases toward top-right. Most EN: F > O > N ≈ Cl (F = 4.0). Put negative formal charge on the more electronegative atom.
Not directly tested — but you need these to draw Lewis structures.
Ionic = metal + nonmetal (criss-cross charges to net 0). Molecular = two+ nonmetals (covalent).
NH₄⁺ ammonium · OH⁻ hydroxide · NO₃⁻ nitrate · NO₂⁻ nitrite · CO₃²⁻ carbonate · HCO₃⁻ bicarbonate · SO₄²⁻ sulfate · PO₄³⁻ phosphate · CN⁻ cyanide · C₂H₃O₂⁻ acetate · MnO₄⁻ permanganate · ClO₄⁻/ClO₃⁻/ClO₂⁻/ClO⁻ (per-ate-ite-hypo).
Work in scientific notation, keep full precision, round at the end. Unit conversions (nm, pm) are on the data sheet. Watch negative exponents (visible λ ≈ 10⁻⁷ m).