Atomic Electronic Structure

Electronic Structure of Atoms

• Atoms' electronic structure is explored, beginning with light's wave properties and leading to modern quantum mechanics.

The Wave Nature of Light

• Electromagnetic radiation transmits energy through space.
• Wavelength ($\lambda$) measures the distance between wave crests.
• Frequency ($\nu$) is the number of waves passing a point per second.
• Amplitude is the wave's height from center to crest.
• The speed of light (c) is constant at $2.998 \times 10^8$ m/s, and is related to wavelength and frequency by the formula: $c = \lambda \nu$.
• The electromagnetic spectrum arranges radiation types by wavelength, from gamma rays ($10^{-12}$ m) to radio waves ($10^2$ m).

Quantized Energy and Photons

• Energy releases or absorptions happen in discrete quanta, as described by Planck's equation: $E = h\nu$.
• h denotes the Planck constant at $6.626 \times 10^{-34}$ J s.
• The photoelectric effect explains electron ejection from a metal surface when exposed to irradiation, with its equation being: $E = h\nu = KE + BE$.
• KE is kinetic energy
• BE is the binding energy of an electron.
• Photons are particles of energy.

Line Spectra and the Bohr Model

• Line spectra contain radiation at specific wavelengths.
• Bohr's model posits that electrons occupy fixed orbits with specific energies and energy emissions/adsorptions occur when electrons transition between levels.
• Energy is related is given by: $E = -2.18 \times 10^{-18} J (\frac{1}{n^2})$, where n is the principle quantum number.
• Change in energy is calculated by: $\Delta E = -2.18 \times 10^{-18} J (\frac{1}{n_f^2} - \frac{1}{n_i^2})$, with initial ($n_i$) and final ($n_f$) quantum numbers.

Wave Behavior of Matter

• Matter exhibits wave-like properties, shown by the equation: $\lambda = \frac{h}{mv}$, relating wavelength to momentum (mv).
• The Heisenberg Uncertainty Principle states that one cannot simultaneously know a particle's position and momentum, as described by: $\Delta x \Delta (mv) \geq \frac{h}{4\pi}$.

Quantum Mechanics and Atomic Orbitals

• Schrodinger's equation combines wave and particle behaviors, yielding wave functions ($\Psi$) whose square ($\Psi^2$) indicates electron probability.

Quantum Numbers

• The principle quantum number (n) denotes the energy level, where n = 1, 2, 3, 4,....
• The angular momentum quantum number (l) defines orbital shape, where l = 0 to n-1 and l = 0 is s, l = 1 is p, l = 2 is d, l = 3 is f.
• The magnetic quantum number ($m_l$) specifies spatial orientation: $-l \le m_l \le l$, leading to 1 s orbital, 3 p orbitals, 5 d orbitals, and 7 f orbitals per energy level.
• The spin quantum number ($m_s$) describes two possible electron spin orientations: +1/2 and -1/2.

Representation of Orbitals

• s orbitals have a spherical shape and their radius increases with n.
• p orbitals have two lobes and exist in three orientations: $p_x$, $p_y$, and $p_z$.
• d orbitals: Four of the five have four lobes, and one resembles a $p_z$ orbital with a doughnut at the center.

Energies of Orbitals

• Orbitals at the same energy level in hydrogen atoms are degenerate, or have the same energy.
• In multi-electron atoms, the increased electron repulsion removes degeneracy from orbitals at the same energy level.

Electron Spin and the Pauli Exclusion Principle

• The Pauli Exclusion Principle states that two electrons in the same atom cannot have the same energy, placing a maximum of two electrons in each orbital.
• Aufbau Principle dictates filling orbitals in ascending energy order.
• Hund's Rule says that for degenerate orbitals, the lowest energy configuration maximizes the number of electrons with the same spin.

Electron Configurations

• Electron configurations show electron arrangement in each orbital.
• Valence electrons reside in the outermost shell and are involved in bonding.

Periodic Table

• The periodic table organizes elements by electronic configuration and properties.
• Elements in the same group possess similar valence electron configurations.