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Wavelength (λ)

Distance between identical points on consecutive waves

Frequency (ν)

Number of wave cycles per second (units: 1/s or Hz)

Relationship between wavelength and frequency

Inverse relationship: as wavelength increases, frequency decreases

Wave equation

c = λν

Speed of light (c)

3.00 × 10⁸ m/s

Amplitude

Height of the wave; shows light intensity or brightness

Constructive interference

Two waves combine to make a larger amplitude

Destructive interference

Two waves cancel out, reducing amplitude

Diffraction

Bending of waves around obstacles or openings

Diffraction pattern

Series of light and dark bands from interfering waves

Double-slit experiment

EM radiation acts like a wave (shows interference and diffraction)

Photoelectric effect

Shows light can behave as particles (photons) that eject electrons

Photoelectric equation

E = hν = h(c/λ)

E = hν

Energy of a photon equals Planck's constant times frequency

de Broglie's equation

λ = h/mv

de Broglie's relationship

All matter, including electrons, has wave-like properties

Evidence electrons behave like waves

Electron diffraction patterns similar to light waves

Bohr Model

Electrons orbit the nucleus in fixed energy levels

Evidence for the Bohr Atom (Absorption Spectra)

Atoms absorb photons, electrons move to higher energy levels

Evidence for the Bohr Atom (Emission Spectra)

Electrons drop levels, emit photons of specific wavelengths

Problems with the Bohr Model

Only works for hydrogen, can't explain multi‑electron atoms

Modern depiction of electronic transitions - Absorption

Arrows point upward; electron absorbs energy to move higher

Modern depiction of electronic transitions - Emission

Arrows point downward; electron emits light when falling lower

Relationship between energy, frequency, and wavelength

Energy ∝ frequency, Energy ∝ 1/wavelength

Heisenberg Uncertainty Principle

We cannot know both position and momentum of an electron exactly

Schrödinger

Contributed to the development of quantum mechanics

Used wave equations to describe electrons as wave functions

What do Schrödinger's results give us?

Quantum numbers that define atomic orbitals

What does quantum number n represent?

Energy level/shell (size and distance of orbital)

What does quantum number l represent?

Shape of orbital (0 = s, 1 = p, 2 = d, 3 = f)

What does quantum number ml represent?

Orientation of orbital in space

What does quantum number ms represent?

Electron spin (+½ or -½)

Shape of s orbital (l=0)

Spherical shape

Shape of p orbital (l=1)

Dumbbell shape, ml = -1, 0, +1

Define extended electron configuration.

Lists full electron arrangement (ex: 1s²2s²2p⁶3s²3p⁶4s¹)

Define condensed electron configuration.

Uses noble gas shorthand (ex: [Ne]3s²3p⁶4s¹)

What are valence electrons?

Outer shell electrons involved in bonding

How to find valence electrons in s block

Count ns electrons

How to find valence electrons in d block

Count ns and (n-1)d electrons

How to find valence electrons in p block

Count ns and np electrons

Shortcut for group numbers (valence electrons)

Group number = number of valence electrons for s and p blocks

Define core electrons.

Inner electrons not involved in bonding, found using configuration

How to make ions (general rule)

Remove ns/np first for cations, add to np for anions

Examples of ion formation: O → O²⁻

Gains 2 electrons

Na → Na⁺

Loses 1 electron

Mn → Mn²⁺

Loses 2 electrons from 4s then 3d

Define Effective Nuclear Charge (Zeff or ENC).

The net positive charge experienced by an outer electron

Across a period, what happens to Zeff?

Increases; more protons pull electrons closer

Down a group, what happens to Zeff?

Stays about the same; shielding increases from core electrons

Effect of increasing Zeff on atomic radius

Radius decreases (electrons pulled in tighter)

Effect of increasing Zeff on ionic radius

Cations smaller, anions larger due to electron loss/gain

Isoelectronic radii trend

More protons → smaller radius

Effect of Zeff on ionization energy

Higher Zeff → higher ionization energy

Why atoms on the left form cations

Low Zeff and few valence electrons, easier to lose electrons

Why atoms on the right form anions

High Zeff and nearly full valence shells, easier to gain electrons