Chapter 2 The Quantum-Mechanical Model of the Atom
Light & Waves
Wavelength (λ) → Distance between corresponding points on waves.
Frequency (ν) → Number of waves passing a point per second.
Frequency unit → Hz or s⁻¹.
Wavelength vs. frequency → Inverse: λ ↑ = ν ↓
Speed of light (c) → 3.00 × 10⁸ m/s
Light equation → c = λν
Frequency formula → ν = c/λ
Wavelength formula → λ = c/ν
Photon Energy ⭐
Photon → Packet of light energy.
Planck's equation → E = hν
Planck's constant (h) → 6.626 × 10⁻³⁴ J·s
Energy using wavelength → E = hc/λ
Energy vs. frequency → ν ↑ = E ↑
Energy vs. wavelength → λ ↑ = E ↓
Photoelectric effect → Light can cause a metal to release electrons if the light has enough energy.
🔥 Relationship to Memorize
λ ↑ → ν ↓ → E ↓
λ ↓ → ν ↑ → E ↑
Memory: Short wavelength = High frequency = High energy.
Bohr Model & Spectra
Line spectrum → Specific/discrete wavelengths emitted by an atom.
Bohr model → Electrons can occupy only specific allowed energy levels.
Electron absorbs energy → Moves to a higher energy level.
Electron emits energy → Moves to a lower energy level.
Why do atoms produce specific colors? → Electron transitions release specific energies/wavelengths of light.
Bohr model worked especially well for → Hydrogen.
Major Bohr limitation → Does not fully explain other atoms or electron wave behavior.
Wave Behavior of Matter
de Broglie idea → Matter, including electrons, can behave like waves.
de Broglie equation → λ = h/mv
Momentum → mv
Heisenberg Uncertainty Principle → You cannot precisely know both an electron's position and momentum simultaneously.
Quantum Mechanics
Schrödinger's model → Treats electrons using both wave and particle behavior.
ψ² → Probability density of where an electron may be found.
Orbital → Spatial distribution/probable region of an electron.
How many quantum numbers describe an electron? → 4
Quantum Numbers ⭐ VERY IMPORTANT
n → Energy level/shell.
Allowed n values → 1, 2, 3, 4...
ℓ → Orbital shape/type.
Allowed ℓ values → 0 to n − 1
ℓ = 0 → s
ℓ = 1 → p
ℓ = 2 → d
ℓ = 3 → f
mₗ → Orbital orientation.
Allowed mₗ values → −ℓ to +ℓ
mₛ → Electron spin.
Allowed mₛ values → +½ or −½
Orbitals ⭐
s orbital shape → Sphere.
p orbital shape → Dumbbell/two lobes.
d orbital shape → Mostly four lobes.
Number of s orbitals → 1
Number of p orbitals → 3
Number of d orbitals → 5
Number of f orbitals → 7
🔥 Highest Priority
If you're short on time, memorize these first:
c = λν
E = hν
E = hc/λ
λ ↑ → ν ↓ → E ↓
Absorb energy → electron goes UP
Emit energy → electron goes DOWN
de Broglie: λ = h/mv
Heisenberg → can't precisely know position + momentum together
n = energy level
ℓ = shape (0=s, 1=p, 2=d, 3=f)
mₗ = orientation (−ℓ to +ℓ)
mₛ = spin (±½)
Orbitals: s=1, p=3, d=5, f=7
Shapes: s=sphere, p=dumbbell