Chapter 6: Electronic Structure of Atoms – Study Notes

Electronic Structure of Atoms

Overview

The electronic structure of atoms describes how electrons are arranged around the nucleus. Understanding this structure is essential for explaining atomic properties, chemical bonding, and the periodic trends observed in the elements.

6.1 The Wave Nature of Light

Electromagnetic Radiation and Waves

• Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space.

• The wavelength ($\lambda$) is the distance between corresponding points on adjacent waves.

• The frequency ($\nu$) is the number of waves passing a given point per unit time (measured in s-1 or Hz).

• All light travels at the same velocity in a vacuum: $c = 3.00 \times 10^8$ m/s (speed of light).

• The relationship between wavelength and frequency is given by:

$c = \lambda \nu$

• Wavelength and frequency are inversely related: as one increases, the other decreases.

• The electromagnetic spectrum includes (from shortest to longest wavelength): gamma rays, X-rays, ultraviolet (UV), visible light, infrared (IR), microwaves, and radio waves.

Example: Calculating Frequency

Calculate the frequency of light with a wavelength of 620 nm:

$\lambda = 620\ \text{nm} = 6.20 \times 10^{-7}\ \text{m}$ $c = 3.00 \times 10^8\ \text{m/s}$ $\nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8}{6.20 \times 10^{-7}} = 4.8 \times 10^{14}\ \text{s}^{-1}$

6.2 Quantized Energy and Photons

Particle Nature of Light

• Light also behaves as a stream of particles called photons.

• When objects (e.g., metals) are heated, they emit energy in discrete packets (photons).

• The photoelectric effect demonstrates that light can eject electrons from a metal surface if it has sufficient energy.

• The energy of a photon is related to its frequency by Planck's equation:

$E = h\nu$

• Where $h = 6.626 \times 10^{-34}\ \text{J} \cdot \text{s}$ (Planck's constant).

• The energy can also be related to wavelength:

$E = \frac{hc}{\lambda}$

Example: Calculating Photon Energy

Calculate the energy of light with a wavelength of 0.265 mm:

$\lambda = 0.265\ \text{mm} = 2.65 \times 10^{-4}\ \text{m}$ $c = 3.00 \times 10^8\ \text{m/s}$ $\nu = \frac{3.00 \times 10^8}{2.65 \times 10^{-4}} = 1.13 \times 10^{12}\ \text{s}^{-1}$ $E = 6.626 \times 10^{-34} \times 1.13 \times 10^{12} = 7.50 \times 10^{-22}\ \text{J}$

6.3 Line Spectra and the Bohr Model

Atomic Spectra and Electron Transitions

• Electrons occupy specific energy levels (orbitals) in an atom.

• When an atom absorbs energy, electrons are excited to higher energy levels.

• When electrons return to lower energy levels, they emit energy as light at specific wavelengths, producing a line spectrum.

• Each element has a unique set of energy levels, so its emission or absorption spectrum is unique (basis for spectroscopy).

Example: Identifying Elements

By analyzing the wavelengths of light emitted or absorbed, we can identify elements present in a sample.

6.5 Atomic Orbitals and 6.6 Quantum Numbers

Atomic Structure and Orbitals

• An atomic orbital is a region in space where there is a high probability of finding an electron.

• Orbitals are described by quantum numbers, which specify their size, shape, and orientation.

• There are four main types of orbitals: s, p, d, and f.

Quantum Numbers

• Principal quantum number (n): Indicates the main energy level (shell); n = 1, 2, 3, ...

• Angular momentum quantum number (l): Indicates the shape of the orbital; l = 0 (s), 1 (p), 2 (d), 3 (f)

• Magnetic quantum number (ml): Indicates the orientation of the orbital; ml = -l to +l

• Spin quantum number (ms): Indicates the spin of the electron; ms = +1/2 or -1/2

Quantum Number	Symbol	Values	Meaning
Principal	n	1, 2, ...	Energy level, size, and energy of orbital
Angular momentum	l	0, 1, ..., n-1	Shape of orbital (s, p, d, f)
Magnetic	ml	-l to +l	Orientation in space
Spin	ms	+1/2, -1/2	Spin state of electron

Shapes and Capacities of Orbitals

• s-orbital: Spherical, 1 orientation, holds 2 electrons

• p-orbital: Dumbbell-shaped, 3 orientations, holds 6 electrons

• d-orbital: Cloverleaf-shaped, 5 orientations, holds 10 electrons

• f-orbital: Complex shapes, 7 orientations, holds 14 electrons

6.8 Electron Configurations

Rules for Electron Arrangement

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers; each orbital can hold a maximum of two electrons with opposite spins.

• Hund's Rule: Electrons occupy degenerate (equal-energy) orbitals singly before pairing up, and all unpaired electrons have the same spin.

• Aufbau Principle: Electrons fill the lowest energy orbitals first.

Order of Orbital Filling

The order in which orbitals are filled is determined by their energy:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p

Electron Configuration Notation

• Electron configurations are written by listing the occupied orbitals in order of increasing energy, with the number of electrons in each orbital as a superscript.

• Example: Oxygen (O): 1s2 2s2 2p4

• Abbreviated notation: Use the symbol of the preceding noble gas in brackets, then continue with the configuration. Example: Sulfur (S): [Ne] 3s2 3p4

Periodic Table and Electron Configurations

• The periodic table is arranged so that elements in the same group have similar valence electron configurations.

• The s, p, d, and f blocks correspond to the type of orbital being filled.

Summary Table: Quantum Numbers and Orbitals

l (Azimuthal)	Sublevel	Orbital Shape
0	s	Spherical
1	p	Dumbbell-shaped
2	d	Cloverleaf-shaped
3	f	Complex

Key Takeaways

• Light exhibits both wave-like and particle-like properties.

• Electrons occupy quantized energy levels described by quantum numbers.

• Electron configurations explain the arrangement of electrons in atoms and the structure of the periodic table.

• Understanding atomic orbitals and quantum numbers is essential for predicting chemical behavior.