Electronic Structure of Atoms and Quantum Mechanics

Comprehensive vocabulary flashcards covering electromagnetic radiation, wave-particle duality, atomic models, quantum numbers, and electron configurations from the lecture notes.

Electromagnetic Radiation

A propagating wave with both an electrical component and a magnetic component, which carries energy through space.

Wavelength ($\lambda$)

The distance between wave maxima or minima, directly related to the energy carried by the radiation.

Amplitude

The maximum extent of a wave's oscillation, which is related to the rate of change of the electric and magnetic fields.

Frequency ($\nu$)

The number of cycles (full waves) passing a point in space in a given amount of time (typically seconds), measured in Hertz ($1\,\text{Hz} = 1\,\text{s}^{-1}$).

Speed of Light ($c$)

The constant speed at which electromagnetic radiation propagates through a vacuum, equal to $2.9979 \times 10^8\,\text{m/s}$.

Electromagnetic Spectrum

The entire range of electromagnetic radiation wavelengths and frequencies, ordered from highest energy (gamma rays) to lowest energy (radio waves).

Quanta

Discrete packets of energy carried by electromagnetic radiation, where the energy of each packet is calculated as $E = h \cdot \nu$.

Planck's Constant ($h$)

A fundamental constant of proportionality relating electromagnetic energy to frequency, equal to $6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$.

Work Function

The minimum amount of energy necessary to free an electron from the surface of a metal ($E_{\min} = h \cdot \nu_{\min}$).

Photon

A quantized packet or particle of electromagnetic radiation postulated by Albert Einstein in 1905 to explain the photoelectric effect.

Discrete Spectrum (Line Spectrum)

An emission spectrum containing only specific narrow bands of frequencies or wavelengths, as produced by a gas discharge tube.

Bohr Model of the Hydrogen Atom

A model proposed in 1913 describing electrons moving in discrete circular orbits around the nucleus with quantized energy given by $E_n = -R_H \left(\frac{1}{n^2}\right)$, where $R_H = 2.18 \times 10^{-18}\,\text{J}$.

Matter Waves

The theoretical concept proposed by Louis de Broglie in 1924 stating that any moving particle has an associated wave with a wavelength of $\lambda = \frac{h}{m \cdot v}$.

Heisenberg Uncertainty Principle

A fundamental quantum principle proposed in 1927 stating that position and momentum cannot simultaneously be measured with arbitrary precision: $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.

Wave Function ($\psi$)

A mathematical solution to the Schrödinger wave equation that describes electron behavior but possesses no physical meaning on its own.

Probability Density ($\psi^2$)

The square of the wave function, which provides a three-dimensional spatial map indicating where an electron is most likely to be found.

Orbital

A three-dimensional region of space where an electron is most likely to be found, defined by the three quantum numbers $n$, $l$, and $m_l$.

Principal Quantum Number ($n$)

The quantum number ($n = 1, 2, 3, 4\dots$) that indicates the size of the region and the principal energy level of an electron.

Angular Momentum Quantum Number ($l$)

The quantum number with values $l = 0, 1, 2\dots (n-1)$ that defines the shape of the orbital ($s$, $p$, $d$, or $f$) and influences electron energy.

Magnetic Quantum Number ($m_l$)

The quantum number with integer values ranging from $-l$ to $+l$ that specifies the three-dimensional spatial orientation of an orbital.

Spin Quantum Number ($m_s$)

The quantum number describing an intrinsic property of the electron itself, taking values of either $+\frac{1}{2}$ or $-\frac{1}{2}$.

Shell

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

Subshell

A group of orbitals within a shell that have the same $n$ and $l$ quantum numbers and therefore have identical energy.

Pauli Exclusion Principle

The rule establishing that no two electrons in an atom can have the exact same set of four quantum numbers ($n$, $l$, $m_l$, and $m_s$), limiting each orbital to two electrons with opposite spins.

Hund's Rule

The principle stating that for orbitals of equal energy, the lowest energy state is achieved when electrons remain unpaired with parallel spins for as long as possible.

Aufbau Diagram

A graphical representation that illustrates the order in which atomic subshell energies increase and are filled by electrons.

Electron Configuration

A written notation describing the specific distribution of an atom's electrons among its various subshells.

Orbital Diagram

A pictorial representation that explicitly displays individual orbitals and their electron occupancies using directional arrows.

Subshell Stability Exceptions

Anomalous electron configurations occurring in elements like chromium ($\text{[Ar]}\,4s^1 3d^5$) and copper ($\text{[Ar]}\,4s^1 3d^{10}$) due to the enhanced stability of half-filled and completely filled $d$ subshells.