CHEM 1201 Chapter 6

Chapter 6: Electronic Structure of Atoms

6.1 The Wave Nature of Light

• Definition: Electromagnetic radiation (or radiant energy) is characterized by its wave nature.

• Examples of Electromagnetic Radiation:

  • Visible light

  • Radio frequency

  • Infrared waves

Key Characteristics of Waves

• Water Waves vs. Electromagnetic Waves

• Wavelength (BB): The distance between two adjacent peaks of a wave.

• Frequency (Bν): The number of complete wavelengths that pass a given point each second.

• Speed of Light: All electromagnetic radiation moves through a vacuum at $3.00 imes 10^8 ext{ m/s}$.

Relationships and Equations

• There exists an inverse relationship between frequency and wavelength, expressed in the equation:

  • c = Bλ Bν

  • Where:

    • $c$ = speed of light

    • BB = wavelength

    • Bν = frequency

• High Frequency: Waves with high frequency have a relatively short wavelength (and vice versa).

Frequency Measurement

• Frequency is reported in hertz (Hz), equivalent to $s^{-1}$ (or $1/s$), which is read as "per second".

• Relation of Frequency, Wavelength, and Energy:

  • Investigative question on whether they correlate directly or inversely.

Calculating Frequency and Wavelength

• Example Calculation:

  • Sodium Vapor Lamp: Yellow light with a wavelength of 589 nm.

  • FM Radio Broadcasts: At 89.3 MHz.

6.2 Quantized Energy and Photons

• While the wave model of light explains many behaviors of light, it fails to account for several phenomena.

1. Quantization of Energy (Max Planck)

• Concept: Electromagnetic energy can only be released or absorbed by atoms in fixed amounts, called quanta.

  • Energy Equation:

  • E = hBν

  • Where:

    • $E$ = energy of a single quantum

    • $h = 6.626 imes 10^{-34} ext{ J-s}$ (Planck's constant)

    • Bν = frequency of the light (radiation)

• Matter can absorb or emit energy only in whole-number multiples of hBν (e.g., 2hBν, 3hBν).

2. The Photoelectric Effect (Albert Einstein)

• Description: When photons of sufficient energy strike a metal's surface, electrons are emitted as energy is transferred.

• Photon Energy Equation:

  • E_{ ext{photon}} = hBν

  • Where:

    • $E_{ ext{photon}}$ = energy of a single photon

Energy of a Photon Calculation

• Example: Calculate the energy of one photon of yellow light with a wavelength of 589 nm.

• Example: A laser emits light with a frequency of $4.69 imes 10^{14} ext{ s}^{-1}$; find the energy of one photon of this radiation.

6.3 Line Spectra and the Bohr Model

• Monochromatic vs. Polychromatic Radiation:

  • Monochromatic: Radiation with a single wavelength (e.g., laser).

  • Polychromatic: Radiation with multiple wavelengths (e.g., white light).

• Spectrum: The division of radiation into its component wavelengths (e.g., rainbow).

• Continuous Spectrum: Contains all wavelengths.

Line Spectra

• Description: Certain radiation sources emit line spectra, which do not contain all wavelengths when passed through a prism; only a few are present in the emission spectrum.

• Observation: These spectra are primarily in the visible region.

Bohr's Model for Hydrogen

• Explanation for Line Spectra:

  • Discrete spectral lines are attributed to the quantized jumps of electrons between energy levels.

  • Only specific radii orbits corresponding to specific energies are allowed for the hydrogen atom.

• Energy Emission/Absorption: Energy is emitted or absorbed as the electron transitions between allowed energy states. The energy of the emitted or absorbed photon is given by:

  • E_{ ext{photon}} = h Bν.

Calculation of Energies

• Bohr’s Energy Calculation:

  • Energy of allowed orbit equation:

  • $E = - rac{hcR_H}{n^2}$

  • Where:

    • $R_{H}=1.0968\cdot10^7{ m}^{-1}$

    • $n$ = principal quantum number

• Energy Gaps Analysis: Noticeable trends in energy gaps with increasing energy.

Transition Energy Change

• Change in energy when an electron transitions from an initial state ($n<em>i$) to a final state ($n</em>f$) can be calculated with:

  • $riangle E = - rac{2.18 imes 10^{-18} ext{ J}}{n<em>f^2} - rac{2.18 imes 10^{-18} ext{ J}}{n</em>i^2}$

  • If $riangle E$ is negative, energy or a photon was emitted; if positive, absorbed.

Emission and Absorption Process

• Absorption of Energy:

  • Electron absorbs a photon, moving from lower to higher energy level; energy difference is positive ($+ riangle E$).

• Emission of Energy:

  • Electron releases a photon, moving from higher to lower energy level; energy difference is negative ($- riangle E$).

6.4 The Wave Behavior of Matter

• de Broglie's Hypothesis: Suggested that particles, such as electrons, behave like waves and possess a wavelength.

• Wavelength of Matter Equation:

  • BB_e = rac{h}{mv}

  • Where:

    • $m$ = mass

    • $v$ = velocity.

• Note: The wavelength of ordinary-sized objects is too large to be observable.

6.5 Quantum Mechanics and Atomic Orbitals

• Introduction of Quantum Mechanics: Erwin Schrödinger utilized quantum mechanics to describe subatomic particles, incorporating both wave-like and particle-like behaviors.

• Schrödinger's Equation: For hydrogen atom yields wave functions (C8). The square of the wave function (C8^2) indicates probability density, or where the electron might likely be.

Orbitals and Quantum Numbers

• Definition of Orbitals: Solutions to Schrödinger’s equation for hydrogen lead to orbitals with distinct energies and shapes.

• Three Quantum Numbers to characterize an orbital:

  1. Principal Quantum Number (n): Positive integral values (1, 2, 3…∞). Increased $n$ results in larger orbitals further from the nucleus.

  2. Angular Momentum Quantum Number (l): Integers from 0 to (n-1) defining orbital shape.

  • Values:

    • 0 (s)

    • 1 (p)

    • 2 (d)

    • 3 (f)

  1. Magnetic Quantum Number (m_l): Integral values from -l to +l, provides orientation in space.

  2. Spin Magnetic Quantum Number (m_s): Defines electron spin (+1/2 or -1/2).

Probability Functions of Electrons

• Radial Probability Function: Indicates the probability of finding an electron at a specific distance from the nucleus.

6.6 Representations of Orbitals

• Characteristics of various types of orbitals (s, p, d) regarding their electron distributions and shapes are examined, applying radial probability functions.

6.7 Many-Electron Atoms

• Pauli Exclusion Principle: Stipulates that no two electrons in an atom can have the same set of four quantum numbers (n, l, ml, and ms).

Quantum Numbers Analysis

• Discusses possible values for quantum numbers given specific electron configurations, identifying allowed and impossible combinations.

6.8 Electron Configurations

• Definition: Arrangement of electrons among various orbitals in an atom.

• Key Principles:

  • Aufbau Principle: Orbitals filled in order of increasing energy.

  • Pauli Exclusion Principle: No more than two electrons per orbital.

  • Hund's Rule: Electrons occupy empty degenerate orbitals with the same spin first.

Noble Gas Configuration

• Creation of Configurations: Electrons are represented through noble gas core notation, specifically indicating valence electrons.

Valence and Core Electrons

• Valence Electrons: Electrons in the outermost energy level that are involved in bonding.

• Core Electrons: Inner electrons that do not participate in bonding.

  • Example:

  • Nitrogen: 1s² 2s² 2p³ (5 valence, 2 core)

  • Chlorine: [Ne] 3s² 3p⁵ (7 valence, 10 core)

Isoelectronic Series

• Definition: Group of atoms and/or ions sharing the same electron configuration, such as:

  • $ext{N}^{3-}, ext{O}^{2-}, ext{F}^-, ext{Na}^+, ext{Mg}^{2+}, ext{Al}^{3+}$.

• Question: Identify which ions have a specified noble gas configuration and include d-block ions.