Chemistry Chapter 4 - Electrons

How are waves measured

• Wavelength (λ): Distance between corresponding points on adjacent waves (measured in meters, m).

• Frequency (ν): Number of waves that pass a point in one second (measured in Hertz, Hz or s⁻¹).m)

What is the relationship between frequency and wavelength?

The speed of light (c) equals wavelength (λ) × frequency (ν) → c = λν.
Because c is constant, frequency and wavelength are inversely proportional — as one increases, the other decreases.

Photoelectric effect

Emission of electrons from metal when light hits it; only occurs if light has a high enough frequency.

Blackbody radiation

When metals are heated, they glow. This couldn’t be explained by wave theory, showing it needed to be revised.

Light as particles (Planck’s theory)

Max Planck proposed that light is emitted in packets called quanta — the smallest amount of energy an atom can gain or lose. Energy is related to the frequency of radiation.

Planck’s Equation

E=hν=λhc​

• E: energy of a photon (J)

• h: Planck’s constant (6.626 × 10⁻³⁴ J·s)

• ν: frequency

• λ: wavelength

What is a photon?

A photon is a particle of light with no mass that carries a quantum of energy. Light can be seen as a stream of photons.

Excited state of an atom

An atom in its lowest energy is in the ground state.
When it gains energy, it moves to an excited state.
Atoms absorb or release energy when moving between these states.

Bohr’s Model of Hydrogen

Bohr improved Rutherford’s model by introducing fixed energy levels for electrons.
Electrons absorb or emit light when they move between these levels.

Bohr Model of Hydrogen (electron behavior)

Electrons orbit in fixed energy levels and jump between them, releasing or absorbing energy.

De Broglie’s hypothesis

Electrons can act as waves with specific frequencies, which correspond to specific energy levels, like Bohr proposed.

de Broglie Equation

λ=mvh​

• λ: wavelength of a particle

• h: Planck’s constant (6.626 × 10⁻³⁴ J·s)

• m: mass (kg)

• v: velocity (m/s)

Heisenberg Uncertainty Principle

It is impossible to know both the position and velocity of an electron (or any subatomic particle) at the same time. You can know either one, but not both.

Schrödinger Wave Equation

Describes the probable locations of electrons.
Electrons are in atomic orbitals, not fixed orbits like Bohr predicted.

Atomic Orbitals

• Represent 90% probability of finding an electron.

• s: spherical

• p: two lobes (“dumbbell”)

• d: 4-leaf clover shapes

• f: more complex

• g, h, i: exist only in excited states

Effect of principal quantum number on orbitals

As the principal quantum number (n) increases, orbitals get larger, so electrons are more likely to be farther from the nucleus.

Quantum Numbers

Describe an electron in a multi-electron atom, including its energy, shape, orientation, and spin.
The four quantum numbers are: n, l, mₗ, mₛ.

First Quantum Number (n)

• n = principal energy level of an electron

• Determines the electron’s energy

• Can be 1–∞ (1–7 at ground state)

• Corresponds to period for s & p; varies for d & f sublevels

Second Quantum Number (l)

• l = angular momentum quantum number

• Determines the sublevel and shape of an orbital

• Values: 0 → s, 1 → p, 2 → d, 3 → f

• Energy increases with l (0 lowest, 3 highest)

Third Quantum Number (mₗ)

• mₗ = magnetic quantum number

• Specifies orbitals within a sublevel (-l to +l)

• Number of orbitals:

  • s: 1 (0)

  • p: 3 (-1, 0, +1)

  • d: 5 (-2 to +2)

  • f: 7 (-3 to +3)

Fourth Quantum Number (mₛ)

• mₛ = electron spin

• Electrons spin like a charged particle on an axis

• Can be +½ (up) or −½ (down)

• Spins can be parallel or opposite within an orbital

Pauli Exclusion Principle

No two electrons in an atom can have the same four quantum numbers.
Each orbital can hold 2 electrons with opposite spins.

Electron Configurations

Shows how electrons are arranged around an atom.
Three types:

1. Standard

2. Noble Gas (shorthand)

3. Orbital Notation (arrows show electrons in orbitals)

Aufbau Principle

Electrons fill the lowest energy levels and sublevels first, predicting the order of electron configuration.

Exceptions to the Aufbau Principle

Sometimes half-filled or fully filled sublevels are more stable than the expected order.
Examples: Chromium, Copper

Hund’s Rule

Electrons fill unoccupied orbitals first in a sublevel, all with the same spin, before pairing up.