Quantum Mechanics and Atomic Orbitals

A comprehensive vocabulary review set covering atomic transitions, wave-particle duality, standing waves, the Heisenberg uncertainty principle, and quantum numbers.

Absorption of Energy

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

Emission of Energy

A process occurring when an electron moves to a lower energy level, resulting in the release of energy from the system.

Matter Waves

The concept proposed in 1924 asserting that particles of matter exhibit wave-like behavior in addition to particle-like properties, characterized by the equation $\lambda = \frac{h}{m v}$.

Standing Wave

A continuous wave whose orbit path length is an exact multiple of its wavelength, allowing it to propagate without experiencing a phase jump or discontinuity.

Allowed Orbit

An electron orbital path whose circumference is an exact integer multiple of the electron's wavelength, forming a stable standing wave.

Joule

The derived SI unit of energy, equivalent to $1\,\text{kg}\,\text{m}^2/\text{s}^2$.

Heisenberg Uncertainty Principle

The fundamental quantum mechanical principle stating that it is impossible to simultaneously measure both the position and momentum of a particle with absolute certainty, satisfying $\Delta x \cdot \Delta(m v) \ge \frac{h}{4\pi}$.

Wave Function ($\Psi$)

A mathematical solution to the wave equation, denoted by the Greek letter capital psi ($\Psi$), whose square ($\Psi^2$) represents the probability of finding an electron in a specific volume of space around the nucleus.

Orbital

A defined region or volume of space around an atomic nucleus where an electron is likely to be found based on quantum mechanical probability.

Principal Quantum Number ($n$)

The primary quantum number, which is always a positive integer ($n = 1, 2, 3, 4, 5, \dots$), that designates the main energy level and orbital shell of an atom.

Shell

A collection of atomic orbitals that share the same principal quantum number ($n$).

Angular Momentum Quantum Number ($l$)

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

s Orbital

An orbital defined by the angular momentum quantum number $l = 0$, historically named after 'sharp' lines observed in atomic spectroscopy.

p Orbital

An orbital defined by the angular momentum quantum number $l = 1$, historically named after the 'principal' line observed in atomic spectroscopy.

d Orbital

An orbital defined by the angular momentum quantum number $l = 2$, historically named after 'diffuse' lines observed in atomic spectroscopy.

Magnetic Quantum Number ($m_l$)

The quantum number that defines the spatial orientation of an orbital relative to the standard Cartesian axes ($x, y, z$), taking integer values from $-l$ to $+l$.