Quantum Mechanics, Atomic Orbitals, and Light-Matter Duality

Vocabulary flashcards covering atomic transitions, matter-wave duality, the Heisenberg uncertainty principle, the Schrödinger equation, and atomic quantum numbers.

Energy Absorption

A process where an electron transitions to a higher energy level, requiring energy to be taken in by the system.

Energy Emission

A process where an electron drops down to a lower energy level, causing energy to be released by the system.

Rydberg Equation

An equation used to calculate transition energies in a hydrogen atom: $\Delta E = R_H \left(\frac{1}{n_{\text{initial}}^2} - \frac{1}{n_{\text{final}}^2}\right)$.

de Broglie Wavelength

The wavelength associated with a particle of matter, calculated using the relationship $\lambda = \frac{h}{m v}$.

Standing Wave (Atomic Orbit)

An allowed orbital path whose circumference is an exact integer multiple of the electron's wavelength, preventing destructive interference or discontinuities.

Electron Diffraction

The phenomenon where electrons fired at a material produce an interference pattern analogous to that of X-rays, demonstrating the wave properties of matter.

Joule ($\text{J}$)

The derived SI unit of energy, expressed in fundamental units as $1\,\text{kg}\,\text{m}^2\,\text{s}^{-2}$.

Schrödinger Equation

A wave equation introduced in 1926 that abandons treating electrons as discrete particles and instead describes their behavior via wave functions ($\Psi$).

Heisenberg Uncertainty Principle

The principle stating that it is impossible to simultaneously know both the precise position and momentum of a particle, defined as $\Delta x \cdot \Delta(m v) \ge \frac{h}{4\pi}$.

Wave Function Squared ($\Psi^2$)

A value obtained from the wave equation that defines the probability of finding an electron within a given volume of space around the nucleus.

Principal Quantum Number ($n$)

A positive integer ($n = 1, 2, 3, \dots$) designating the main shell, orbital size, and energy level of an electron.

Angular Momentum Quantum Number ($l$)

A quantum number taking integer values from $0$ to $n - 1$ that defines the three-dimensional shape of an orbital.

Magnetic Quantum Number ($m_l$)

A quantum number with integer values ranging from $-l$ to $+l$ that defines the spatial orientation of an orbital relative to the coordinate axes.

$s$ Orbital

An atomic orbital characterized by an angular momentum quantum number of $l = 0$, historically named after the spectroscopic term "sharp."

$p$ Orbital

An atomic orbital designated by an angular momentum quantum number of $l = 1$, possessing three possible orientations ($m_l = -1, 0, +1$).