2: Quantum Theory and Electronic Structure
- Page ID
- 483507
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- 2.0: Introduction
- Big Power from Tiny Pulses: Quantum Ideas Behind the World's Strongest Lasers
- 2.1: The Nature of Light
- Understanding the electronic structure of atoms requires an understanding of the properties of waves and electromagnetic radiation. Waves are characterized by several interrelated properties, such as wavelength, frequency, speed, and amplitude. Electromagnetic radiation shows wavelike behavior, traveling at the speed of light, c. Electromagnetic radiation has also been shown to have particle characteristics with the energy of the photon proportional to the frequency of the light.
- 2.2: Atomic Spectra
- The line spectrum of an element is connected to its atomic structure. The Bohr model describes the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. He postulated that the electron was restricted to certain orbits characterized by discrete energies. While the idea of fixed orbits is incorrect, the discrete energy levels from the Bohr model help us relate atomic spectra to atomic transitions.
- 2.3: The Wave-Particle Duality of Matter
- An electron possesses both particle and wave properties. The modern model for the electronic structure of the atom is based on recognizing that an electron possesses particle and wave properties, the so-called wave–particle duality. Heisenberg’s uncertainty principle states that it is impossible to precisely describe both the location and the speed of particles that exhibit wavelike behavior.
- 2.4: The Quantum-Mechanical Model of the Atom
- The quantum mechanical model describes the three-dimensional position of the electron in a probabilistic manner with a mathematical function called a wavefunction, ψ. ψ2 gives the probability of finding the electron in a particular region in space. Therefore, atomic orbitals are regions of space in an atom where electrons are most likely to be found. Each atomic orbital can be described by quantum numbers and has an energy associated with it.
- 2.5: Characteristics of Many-Electron Atoms
- The Pauli exclusion principle states that an orbital can contain only two electrons (with opposite spin). The calculation of orbital energies in multi-electron system is complicated by repulsions between the electrons. The degree to which orbitals with different values of l and the same value of n penetrate filled inner shells results in different energies for different subshells for multi-electron atoms.
- 2.6: Electronic Configurations
- Based on the Pauli exclusion principle and orbital energies obtained using hydrogen-like orbitals, electron configurations of all of the elements can be determined. Electron configurations can be found by adding electrons to the lowest-energy available orbitals before occupying higher-energy levels (the aufbau principle). In addition, sub-shells are filled with one electron per orbital before pairing electrons and those unpaired electrons have the same spin (Hund's rule). For chemical purpose
- 2.7: Trends in Atomic Size
- Electron configurations allow us to understand many periodic trends. The atomic radius increases as we move down a group because the n level (orbital size) increases. Atomic radius mostly decreases as we move left to right across a period because the effective nuclear charge experienced by the electrons increases, and the electrons are pulled in tighter to the nucleus. Anionic radii are larger than the parent atom, while cationic radii are smaller, because the number of valence electrons has cha
- 2.E: Quantum Theory and Electronic Structure (Exercises)
- You should be able to answer all the following questions. The solutions to these problems are best used to check your final answers, rather than to provide you with step-by-step instructions to answer that question. Remember, that the questions are designed to help you practice using concepts, rather than memorizing the mechanics of that specific question. Learning to solve problems in science comes through active learning!