Ch 9: Electrons in Atoms and the Periodic Table: Light, Atomic Models, Electron Configurations, and Periodic Trends

Electrons in Atoms and the Periodic Table

Electromagnetic Radiation and Light

Electromagnetic radiation is a form of energy that travels through space at a constant speed of $3.0 \times 10^8$ m/s. Light, a type of electromagnetic radiation, exhibits both wave-like and particle-like properties, and is fundamental to understanding atomic structure.

• Wavelength (\(\lambda\)): The distance between adjacent wave crests. Determines the color of visible light. Measured in meters (m) or nanometers (nm).

• Frequency (\(\nu\)): The number of wave cycles passing a point per second. Measured in hertz (Hz).

• Relationship: Wavelength and frequency are inversely related: $c = \lambda \nu$, where $c$ is the speed of light.

• Photon: A particle of light; the energy of a photon is given by $E = h \nu = \frac{hc}{\lambda}$, where $h$ is Planck's constant.

• Energy and Wavelength: Shorter wavelength means higher frequency and higher energy per photon.

Example: Red light (750 nm) has a longer wavelength and lower energy than violet light (400 nm).

The Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, from gamma rays to radio waves. Visible light is only a small portion of this spectrum.

• Gamma Rays: Shortest wavelength ($10^{-16}$ m), highest energy. Produced by stars and radioactive nuclei.

• X-Rays: Longer wavelength than gamma rays. Used in medical imaging.

• Ultraviolet (UV) Light: Causes sunburn; higher energy than visible light.

• Visible Light: 400 nm (violet) to 750 nm (red). Enables vision.

• Infrared (IR) Light: Longer wavelength than visible; felt as heat.

• Microwaves: Used in cooking and communication.

• Radio Waves: Longest wavelength; used for broadcasting and communication.

Type	Wavelength Range
Gamma rays	$10^{-11}$ m to $10^{-15}$ m
X-rays	$10^{-9}$ m to $10^{-11}$ m
Ultraviolet	$10^{-7}$ m to $10^{-9}$ m
Visible light	400 nm (violet) to 750 nm (red)
Infrared	$10^{-3}$ m to $10^{-6}$ m
Microwaves	$10^{-1}$ m to $10^{-3}$ m
Radio waves	$10^{5}$ m to $10^{-1}$ m

Visible Light Colors:

Color	Wavelength (nm)
Red	750
Orange	650
Yellow	600
Green	550
Blue	475
Violet	400

Applications: Ionizing radiation (X-rays, gamma rays) can damage biological molecules and is used in cancer therapy. Non-ionizing radiation (visible, IR, microwaves) is used in vision, heating, and communication.

Models of the Atom: Bohr and Quantum-Mechanical

Atomic models explain the arrangement and behavior of electrons in atoms, which in turn determine chemical properties.

The Bohr Model

• Electrons travel in fixed circular orbits around the nucleus, each with a specific energy (quantized energy levels).

• Electrons can move between orbits by absorbing or emitting energy as photons.

• The energy difference between orbits determines the wavelength of emitted or absorbed light.

• Explains the line spectrum of hydrogen but fails for multi-electron atoms.

Example: In hydrogen, a transition from $n=4$ to $n=2$ emits a photon of 486 nm; from $n=3$ to $n=2$ emits 657 nm.

The Quantum-Mechanical Model

• Electrons are described by orbitals—probability maps indicating where an electron is likely to be found.

• Orbitals are defined by quantum numbers: principal quantum number ($n$) and subshell letter ($s$, $p$, $d$, $f$).

• Electron positions are probabilistic, not fixed paths.

• Model explains the periodic law and underpins the structure of the periodic table.

Additional info: The quantum-mechanical model is foundational for modern chemistry and technology, including semiconductors and lasers.

Quantum Numbers, Orbitals, and Electron Configurations

Electrons occupy orbitals in a specific order, described by electron configurations. The arrangement of electrons determines the chemical behavior of elements.

• Principal Quantum Number (n): Indicates the energy level and size of the orbital. $n=1,2,3,...$

• Subshells: Each principal shell contains $n$ subshells, labeled $s$, $p$, $d$, $f$.

• Orbital Shapes: $s$ (spherical), $p$ (dumbbell), $d$ (cloverleaf), $f$ (complex).

• Number of Orbitals per Subshell:

  • $s$: 1 orbital (2 electrons max)

  • $p$: 3 orbitals (6 electrons max)

  • $d$: 5 orbitals (10 electrons max)

  • $f$: 7 orbitals (14 electrons max)

• Electron Configuration: Notation showing the distribution of electrons among orbitals. Example for carbon: $1s^2 2s^2 2p^2$.

• Orbital Diagrams: Visual representation using boxes (orbitals) and arrows (electrons with spin).

• Pauli Exclusion Principle: Each orbital holds a maximum of two electrons with opposite spins.

• Hund’s Rule: Electrons occupy orbitals singly with parallel spins before pairing.

• Order of Filling: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d$

Example: Electron configuration for magnesium (Mg): $1s^2 2s^2 2p^6 3s^2$ or [Ne]$3s^2$.

Valence and Core Electrons

Electrons are classified as valence or core electrons based on their location and role in chemical bonding.

• Valence Electrons: Electrons in the outermost principal shell (highest $n$). Involved in chemical bonding.

• Core Electrons: All other electrons not in the outermost shell.

• Example: Silicon (Si): $1s^2 2s^2 2p^6 3s^2 3p^2$; 4 valence electrons (in $n=3$), 10 core electrons.

Electron Configurations and the Periodic Table

The periodic table is structured to reflect the filling of electron orbitals, which determines the chemical properties of elements.

• Groups (Columns): Elements in the same group have the same number of valence electrons and similar chemical properties.

• Periods (Rows): Indicate the highest principal quantum number ($n$) for valence electrons.

• Blocks:

  • s-block: Groups 1A, 2A, and He

  • p-block: Groups 3A to 8A

  • d-block: Transition metals (row number minus one for $d$-orbitals)

  • f-block: Lanthanides and actinides

• Noble Gas Notation: Electron configurations can be abbreviated using the symbol of the previous noble gas in brackets. Example: Sodium (Na): [Ne]$3s^1$.

• Exceptions: Some transition metals (e.g., Cr, Cu) have unique configurations for stability.

Element	Electron Configuration	Noble Gas Notation
Magnesium (Mg)	1s22s22p63s2	[Ne]3s2
Sulfur (S)	1s22s22p63s23p4	[Ne]3s23p4
Gallium (Ga)	1s22s22p63s23p64s23d104p1	[Ar]4s23d104p1

Periodic Trends

Periodic trends describe how certain properties of elements change across periods and down groups in the periodic table.

Atomic Size

• Increases down a group (due to additional electron shells).

• Decreases across a period (due to increasing nuclear charge pulling electrons closer).

• Example: Potassium (K) is larger than lithium (Li); carbon (C) is larger than oxygen (O).

Ionization Energy

• Energy required to remove an electron from an atom in the gaseous state.

• Decreases down a group (outer electrons are farther from the nucleus).

• Increases across a period (nuclear charge increases, holding electrons more tightly).

• Equation: $\mathrm{Na} + \text{ionization energy} \rightarrow \mathrm{Na}^+ + e^-$

Metallic Character

• Refers to how easily an atom loses an electron.

• Increases down a group; decreases across a period.

• Metals are found on the left and center of the periodic table; nonmetals on the right.

Chemical Properties and Valence Electrons

The chemical properties of elements are largely determined by the number of valence electrons.

• Elements in the same group have similar chemical properties due to similar valence electron configurations.

• Noble gases have full valence shells (eight electrons, except helium with two), making them stable and inert.

• Alkali metals (Group 1) have one valence electron and tend to lose it to form $1^+$ cations.

• Alkaline earth metals (Group 2) have two valence electrons and form $2^+$ cations.

• Halogens (Group 17) have seven valence electrons and tend to gain one to form $1^-$ anions.

• Isoelectronic species have the same electron configuration (e.g., $\mathrm{Na}^+$ and $\mathrm{Ne}$).

Summary Table: Periodic Trends

Trend	Across a Period (Left to Right)	Down a Group
Atomic Size	Decreases	Increases
Ionization Energy	Increases	Decreases
Metallic Character	Decreases	Increases

Key Equations

• Speed of Light: $c = \lambda \nu$

• Photon Energy: $E = h \nu = \frac{hc}{\lambda}$

Applications and Health Connections

• Ionizing Radiation: X-rays and gamma rays can ionize atoms, damaging biological molecules. Used in cancer therapy.

• Ion Pumps in Biology: Sodium and potassium ions are transported across cell membranes, essential for nerve function. Potassium ions are larger than sodium ions.

Examples and Practice

• Electron Configuration for Aluminum (Al): $1s^2 2s^2 2p^6 3s^2 3p^1$ or [Ne]$3s^2 3p^1$

• Electron Configuration for Bromine (Br): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^5$ or [Ar]$4s^2 3d^{10} 4p^5$

• Electron Configuration for Strontium (Sr): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2$ or [Kr]$5s^2$

• For ions: Remove or add electrons according to the charge. Example: $\mathrm{Al}^{3+}$: $1s^2 2s^2 2p^6$

Conclusion

Understanding the quantum-mechanical model, electron configurations, and periodic trends is essential for predicting the chemical and physical properties of elements. The periodic table is a powerful tool for organizing this information and understanding the behavior of atoms in chemical reactions.