Modern Atomic Theory Study Guide

Principles of Chemistry

Chapter 11: Modern Atomic Theory

  • Author: Christopher G. Hamaker
  • Institution: Illinois State University
  • Source: Principles of Chemistry with Introductory Chemistry: A Foundation, 9th Edition by Zumdahl and DeCoste

Chapter 4: Wavelength Versus Frequency

  • Relationship between Wavelength and Frequency:
    • The shorter the wavelength of light, the higher the frequency.
  • Light as a Wave:
    • Light travels through space as a wave.
  • Definitions:
    • Wavelength (λ): The distance light travels in one complete cycle.
    • Frequency (ν): The number of cycles per second.

Light—A Continuous Spectrum

  • Definition of Light:
    • Refers to radiant energy that is visible to the human eye.
  • Visible Spectrum:
    • The range of wavelengths perceived as light is from 400 nm to 700 nm.
  • Invisible Radiation:
    • Radiant energy outside the ranges of 400 nm (ultraviolet region) and 700 nm (infrared region) is not visible to the human eye.

Radiant Energy Spectrum

  • Complete Spectrum:
    • The radiant energy spectrum is an uninterrupted band, or continuous spectrum.
  • Types of Radiation:
    • Includes various types of radiation, most of which are not visible to the human eye.

Bohr Model of the Atom

  • Concept of Electron Orbits:
    • Niels Bohr proposed that electrons orbit the nucleus in fixed energy levels.
  • Specific Energy Levels:
    • Electrons are located only in specific energy levels and nowhere else.
  • Quantization of Energy:
    • The electron energy levels are quantized, meaning electrons can only exist at certain energy levels.

Emission Line Spectra

  • Observation:
    • When an electrical voltage passes through a gas in a sealed tube, a series of narrow lines appears.
  • Emission Line Spectrum of Hydrogen:
    • The emission line spectrum for hydrogen gas displays three notable lines at wavelengths:
    • 434 nm
    • 486 nm
    • 656 nm

Evidence for Energy Levels

  • Electron Excitation:
    • An electric charge excites an electron to a higher orbit temporarily.
  • Energy Emission:
    • When the electron returns to its original state, radiant energy is released.
  • Bohr's Realization:
    • This phenomenon provided the evidence Bohr required to validate his atomic theory.

“Atomic Fingerprints”

  • Uniqueness of Emission Line Spectrum:
    • Each element has a unique emission line spectrum, akin to a fingerprint.
  • Identification of Elements:
    • The line spectrum can be utilized to identify elements based on their atomic fingerprints.

Critical Thinking: Neon Lights

  • Common Misconceptions:
    • Many signs labeled as “neon” do not actually contain neon gas.
  • True Neon Signs:
    • True neon lights emit red color.
  • Emission Spectra of Noble Gases:
    • Each noble gas has a distinct emission spectrum, resulting in different colors for signs made of various noble gases.

Energy Levels and Sublevels

  • Sublevels within Energy Levels:
    • Electrons occupy energy sublevels within each main energy level.
  • Sublevel Designations:
    • The sublevel designations are as follows: s, p, d, and f, corresponding to sharp, principal, diffuse, and fine lines seen in emission spectra.
  • Number of Sublevels:
    • The number of sublevels equals the number of the main energy level.

Quantum Mechanical Model

  • Definition of Orbital:
    • An orbital is the region of space where there is a high probability of finding an electron.
  • Orbital Properties:
    • In the quantum mechanical model of the atom, orbitals have specific sizes and shapes.
    • Higher energy orbitals are correspondingly larger in size.
  • Shapes of s Orbitals:
    • All s orbitals have spherical shapes.

Shapes of p Orbitals

  • Variability in p Orbitals:
    • There are three distinct p sublevels.
  • Shape of p Orbitals:
    • All p orbitals have dumbbell shapes.
  • Orientation in Space:
    • Each p orbital is oriented along a different axis in three-dimensional space.

Location of Electrons in an Orbital

  • Understanding Orbitals:
    • Orbitals are regions in space where electrons are most likely to be found.
  • Analogy for p Orbitals:
    • An analogy for an electron in a p orbital is likened to a fly trapped in two bottles connected end to end.

Shapes of d Orbitals

  • d Sublevels:
    • There are five different types of d orbitals.
  • d Orbital Shapes:
    • Four of the d orbitals exhibit a clover-leaf shape, while one has a unique dumbbell and doughnut shape.

Energy Levels and Sublevels (Continued)

  • First Energy Level:
    • Contains one sublevel: 1s.
  • Second Energy Level:
    • Comprises two sublevels: 2s and 2p.
  • Third Energy Level:
    • Has three sublevels: 3s, 3p, and 3d.

Electron Occupancy in Sublevels

  • Maximum Electrons per Sublevel:
    • The capacity of each sublevel is as follows:
    • s sublevel: holds a maximum of 2 electrons.
    • p sublevel: holds a maximum of 6 electrons.
    • d sublevel: holds a maximum of 10 electrons.
    • f sublevel: holds a maximum of 14 electrons.
  • Maximum Electrons per Level:
    • The total maximum number of electrons per main energy level is the sum of the maximum number of electrons in its sublevels.

Electron Orbitals for Elements 1-10

Table 10.1: Orbital Filling for the First Ten Elements

Electron Configuration
  • Atomic Number (1): H
    • Orbitals: 1s
    • Electron Configuration: 1s¹
  • Atomic Number (2): He
    • Orbitals: 1s
    • Electron Configuration: 1s²
  • Atomic Number (3): Li
    • Orbitals: 1s, 2s
    • Electron Configuration: 1s²2s¹
  • Atomic Number (4): Be
    • Orbitals: 1s, 2s
    • Electron Configuration: 1s²2s²
  • Atomic Number (5): B
    • Orbitals: 1s, 2s, 2p
    • Electron Configuration: 1s²2s²2p¹
  • Atomic Number (6): C
    • Orbitals: 1s, 2s, 2p
    • Electron Configuration: 1s²2s²2p²
  • Atomic Number (7): N
    • Orbitals: 1s, 2s, 2p
    • Electron Configuration: 1s²2s²2p³
  • Atomic Number (8): O
    • Orbitals: 1s, 2s, 2p
    • Electron Configuration: 1s²2s²2p⁴
  • Atomic Number (9): F
    • Orbitals: 1s, 2s, 2p
    • Electron Configuration: 1s²2s²2p⁵
  • Atomic Number (10): Ne
    • Orbitals: 1s, 2s, 2p
    • Electron Configuration: 1s²2s²2p⁶
  • Note: Boxes represent the orbitals grouped by sublevel. Electrons are represented by arrows.

Electron Configurations

  • Arrangement of Electrons:
    • Electrons arrange themselves systematically around the nucleus.
    • Electrons fill the energy sublevel closest to the nucleus first.
  • Filling Order:
    • Electrons continue filling each sublevel until it is full, then progress to the next closest sublevel.
  • Example of Energy Sublevels:
    • The order of increasing energy for the sublevels includes:
    • 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d …

Writing Electron Configurations

  • Definition:
    • The electron configuration represents the electron location around the nucleus in a shorthand format.
  • Structure of Configuration:
    • Each sublevel is followed by a superscript indicating the number of electrons in that sublevel.
    • Example: If the 2p sublevel contains two electrons, it is denoted as 2p².

Blocks and Sublevels in the Periodic Table

  • Using the Periodic Table:
    • The periodic table assists in predicting which sublevel is being filled for specific elements.

Filling Diagram for Energy Sublevels

  • Order of Filling:
    • The order of filling does not conform strictly to numerical sequence (1, 2, 3, etc.).
  • Reference Fig 4.16:
    • Utilize this figure to predict the order of sublevel filling appropriately.

Continuing Process: Writing Electron Configurations for Specific Elements

  • Example for Bromine:
    • Determine the number of electrons in the atom (Bromine has 35 electrons; atomic number = 35).
    • Arrange energy sublevels according to increasing energy:
    • Order: 1s 2s 2p 3s 3p 4s 3d 4p
    • Fill sublevels until all electrons are accounted for:
    • Configuration: Br: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵
    • Superscripts:
    • The sum of the superscripts equals Bromine's atomic number (35).

Ionization Energy Trend

  • Trends in Ionization Energy:
    • Figure 5.8 illustrates the trend in ionization energy across the elements in the periodic table.

Atomic Radius

  • Atomic Radii for Main Group Elements:
    • Figure 5.4 displays atomic radii for the main group (representative) elements.
    • General Trend:
    • This trend specifically applies to main group elements, excluding transition elements.