Quantum Mechanics and Atomic Theory Flashcards

Comprehensive vocabulary flashcards covering the key principles of Electromagnetic Radiation, Bohr's Model, Quantum Mechanics, and Electron Configurations based on Chapter 12 lecture notes.

Wavelength ($\lambda$)

The distance between the adjacent crests of a wave, measured in meters ($\text{m}$).

Frequency ($\nu$)

The number of crests passing through a given point per second, measured in Hertz ($\text{Hz}$) or reciprocal seconds ($s^{-1}$).

Speed of light ($c$)

The speed of the movement of a given crest; in a vacuum, it is a constant represented by the equation c = \nu \times \text{\textlambda}.

Constructive Interference

A fundamental property of waves where a crest of a wave meets a crest of another wave, causing their amplitudes to add together.

Destructive Interference

A fundamental property of waves where a crest of a wave meets a trough of another wave, causing the two waves to cancel each other out.

Black-body Radiation

The light emitted by all non-reflective objects; as the temperature increases, the color of the emitted light shifts from red to blue.

Ultraviolet Catastrophe

The false prediction by classical theory that the intensity of black-body radiation would increase indefinitely with decreasing wavelength.

Photons

A stream of particles that make up light, postulated by Max Planck to solve the ultraviolet catastrophe.

Planck’s Equation

The equation $E = h \nu$ which defines the energy of a photon, where $h$ is Planck’s constant.

Atomic Absorption Lines

A discontinuous spectrum produced when matter receives the energy of photons that match the energy difference between its final and initial states.

Atomic Emission Lines

A discontinuous spectrum produced when excited atoms emit energy as photons to relax to lower energy levels.

Hydrogen-like species

Atoms or ions that possess only one electron, such as $\text{H}$, $\text{He}^+$, $\text{Li}^{2+}$, and $\text{Be}^{3+}$.

Bohr Model

A model representing hydrogen-like species where an electron revolves around the nucleus in specific allowed circular orbits due to electrostatic attraction.

Balmer series

A set of hydrogen emission lines that occur when an electron relaxes to the $n = 2$ energy level.

Lyman series

A set of hydrogen emission lines that occur when an electron relaxes to the $n = 1$ energy level.

Ionization Energy

The specific amount of photon energy absorbed that is just enough to remove an electron from the ground state ($n = 1$) of a hydrogen atom.

Wave-Particle Duality

The proposal by de Broglie that small particles of matter display wave-like properties with a wavelength inversely proportional to momentum (\text{\textlambda} = \frac{h}{mu}).

Heisenberg’s Uncertainty Principle

The principle stating a fundamental limit to the precision with which the position ($x$) and momentum ($p$) of a particle can be measured simultaneously, defined as \text{\textDelta} x \text{\textDelta} p \text{\textge} \frac{h}{4\text{\textpi}}.

Schrödinger Equation

A differential equation in quantum mechanics used to obtain wave functions (\text{\textpsi}_n(x)) and energies ($E_n$) for quantum states.

Wave function (\text{\textpsi}(x))

A mathematical function in quantum mechanics that describes a particle exhibiting wavelike properties.

Probability Density (\text{\textpsi}^2)

The square of the wave function which represents the probability of finding a particle at a given position.

Nodes

Specific positions where the wave function (\text{\textpsi}) equals zero, resulting in a probability density of zero.

Radial Wave Function ($R(r)$)

A component of the electron wave function for hydrogen-like species that describes the distance ($r$) from the nucleus.

Angular Wave Function (Y(\text{\texttheta}, \text{\textphi}))

A component of the electron wave function for hydrogen-like species that describes the orientation in space based on angles.

Principal Quantum Number ($n$)

A quantum number (n = 1, 2, 3, \text{\textdots}) that determines the size and energy of an atomic orbital.

Angular Momentum Quantum Number ($l$)

A quantum number (l = 0, 1, 2, \text{\textdots}, (n - 1)) that determines the shape of the orbital and defines the subshell.

Magnetic Quantum Number ($m_l$)

A quantum number (m_l = -l, \text{\textdots}, 0, \text{\textdots}, +l) that specifies the orientation of an orbital within a subshell.

Radial Node

A spherical surface where the radial wave function becomes zero and changes sign ($R(r) = 0$), calculated as $n - l - 1$.

Angular Node

A node of any shape other than spherical occurring at angles where the angular wave function ($Y = 0$), the number of which is equal to $l$.

Electron Spin Quantum Number ($m_s$)

The fourth quantum number ($m_s = +\frac{1}{2}$ or $-\frac{1}{2}$) that describes the direction an electron spins on its axis.

Shielding Effect

The decrease in attraction between an electron and the nucleus in a multi-electron atom caused by inner electrons pushing away outer electrons.

Pauli Exclusion Principle

A rule stating that no two electrons in the same atom can have the same four quantum numbers.

Hund’s Rule

A rule stating that electrons initially occupy degenerate orbitals singly with parallel spins before they begin pairing up.

Aufbau Process

A hypothetical process of building up an atom by progressively adding electrons and protons to the lowest energy orbitals available.

$n + l$ Rule

The guideline stating that subshells with lower $n + l$ values are filled first, and if they are equal, the subshell with the lower $n$ value is filled first.