Atomic Theory and Quantum Mechanics

Comprehensive practice flashcards defining foundational atomic theories, electromagnetic radiation concepts, quantum principles, and quantum numbers based on Dr Ewan Cruickshank's lecture notes.

Solid Sphere Model

The atomic model proposed by John Dalton in 1803, based on the Ancient Greek concept of 'atomos' (indivisible), stating that atoms of a given element are identical, atoms of different elements differ, and compounds are combinations of different types of atoms.

Plum Pudding Model

The atomic model proposed by J.J. Thomson in 1904 following his 1897 discovery of electrons ('corpuscles'), which depicts the atom as negatively charged electrons scattered throughout a spherical cloud of positive charge with no nucleus.

Rutherford's Nuclear Model

The classical atomic model proposed in 1911 by Ernest Rutherford after firing positively charged alpha particles at a thin gold foil; it established that the atom is mostly empty space with positive charge concentrated in a small central nucleus orbited by negatively charged electrons.

Bohr Model

A 1913 modification of Rutherford's model by Niels Bohr stating that electrons move around the nucleus in orbits of fixed sizes and quantised energies, explaining the emission spectra of some elements but failing to explain why electrons would not collapse into the nucleus or work for heavier atoms.

Schrödinger Quantum Model

The widely accepted 1926 atomic model formulated by Erwin Schrödinger, stating that electrons move in waves rather than set paths and exist in 'clouds of probability' called orbitals where exact position is uncertain.

Atomic Orbitals

Regions of space around the nucleus where electrons are most likely to be found, corresponding to valid mathematical solutions of Schrödinger's wave equation.

Wave–Particle Duality

The quantum mechanical principle stating that subatomic particles (such as electrons) and light can display properties of both waves and particles.

Energy Quantisation

The principle that energy can only exist in discrete, indivisible packets called quanta rather than along a continuous spectrum.

Planck's Constant ($h$)

A fundamental constant of quantum mechanics equal to $6.63 \times 10^{-34}\,\text{J}\cdot\text{s}$, used to relate frequency and energy in electromagnetic radiation.

Electromagnetic Radiation

A form of energy that can be described as a sine wave consisting of mutually perpendicular electric and magnetic field vectors oscillating and propagating through space at the speed of light.

Wavelength ($\lambda$)

The physical distance between successive peaks or equivalent points of a wave, where longer wavelengths correspond to lower frequencies and shorter wavelengths correspond to higher frequencies.

Frequency ($\nu$)

The number of wave cycles that pass a given point per unit time, measured in reciprocal seconds ($\text{s}^{-1}$) or Hertz ($\text{Hz}$).

Speed of Light ($c$)

The velocity of electromagnetic radiation in a vacuum, defined as $c = 3.00 \times 10^8\,\text{m/s}$, which relates wavelength ($\lambda$) and frequency ($\nu$) via the formula $c = \lambda\nu$.

Photoelectric Effect

A quantum phenomenon in which incident light above a critical threshold frequency ejects electrons from a photocell cathode to generate a measurable current; the number of ejected electrons ($n$) depends on light intensity, while light energy is delivered as quantized packets called photons.

Photon

A discrete particle or quantum of light carrying a packet of energy proportional to the radiation frequency.

Planck's Equation

The mathematical equation $E = h\nu$ stating that the energy of radiation is directly proportional to its frequency ($\nu$), and for $n$ quanta or moles of photons, given as $E = nh\nu$.

Heisenberg Uncertainty Principle

A principle of quantum mechanics stating that the position and momentum of an electron cannot be simultaneously defined, meaning that while electron energy can be specifically known, its exact location cannot.

Wave Function ($\Psi$)

A mathematical solution to Schrödinger's wave equation that characterizes the quantum state of an electron without specifying its exact location.

Probability Density ($\Psi^2$)

The square of the wave function ($\Psi^2$), which is directly proportional to the probability of finding an electron in a specific region of space.

Principal Quantum Number ($n$)

The quantum number that designates the main electron shell and overall size of an orbital, taking positive integer values ($n = 1, 2, 3, 4, \dots$) based on the periodic table period in which the shell begins filling.

Angular (Azimuthal) Quantum Number ($l$)

The quantum number that defines the electron sub-shell and geometric shape of an orbital within a principal shell, taking integer values from $0$ to $n - 1$ ($l = 0 \rightarrow s$, $l = 1 \rightarrow p$, $l = 2 \rightarrow d$, $l = 3 \rightarrow f$).

Magnetic Quantum Number ($m_l$)

The quantum number that defines the spatial orientation of an orbital within a sub-shell along the $x$, $y$, or $z$ axis, with allowable integer values ranging from $-l$ to $+l$.

Degenerate Solutions

Multiple distinct wave function solutions to Schrödinger's equation that have the same energy level, corresponding to the different spatial orientations available for a sub-shell with given values of $n$ and $l$.

Spin Quantum Number ($m_s$)

The quantum number describing the intrinsic angular momentum or spin orientation of an electron, which cannot be zero and must equal either $+\frac{1}{2}$ (spin up) or $-\frac{1}{2}$ (spin down).

Orbital Description Parameters

The quantum numbers required for structural specification: an empty orbital is completely defined by three quantum numbers ($n$, $l$, and $m_l$), whereas an electron occupying an orbital is fully described by all four quantum numbers ($n$, $l$, $m_l$, and $m_s$).