Quantum Mechanics and Hydrogen Atom - Vocabulary

Vocabulary flashcards covering hydrogen energy levels, transitions, wave–particle duality, and foundational quantum concepts from the lecture.

Hydrogen atom energy levels

Quantized energy states of the one-electron hydrogen atom, described by E_n = -13.6 eV / n^2; levels get closer together as n increases.

E_n = -13.6 eV / n^2

Energy of the nth level in hydrogen (Z = 1); negative values that approach zero as n grows.

Ground state (n=1)

The lowest energy level of hydrogen with E = -13.6 eV; electron most tightly bound.

Absorption

Process where an electron moves to a higher energy level by absorbing energy; delta E > 0.

Emission

Process where an electron drops to a lower level, emitting a photon; delta E < 0.

Delta E

Change in the electron’s energy: ΔE = Efinal − Einitial; its absolute value equals the photon's energy.

Photon energy

Energy of a photon given by E = hν = hc/λ; equals the energy difference between levels.

Planck’s constant (h)

Fundamental constant (≈ 6.626×10^−34 J·s) used in photon energy and wave relations.

Speed of light (c)

Constant (≈ 3.00×10^8 m/s) relating wavelength and frequency: ν = c/λ.

Nanometer (nm)

Unit of length equal to 10^−9 meters; common unit for wavelengths in the visible hydrogen spectrum.

Ionization energy

Energy required to remove the electron completely (to infinity); for hydrogen, 13.6 eV.

Balmer series

Hydrogen emission lines from transitions ending at n_f = 2; visible spectrum (red, blue/purple lines observed).

Hydrogen-like ions (Z^2 scaling)

For ions with nuclear charge Z, E_n = −13.6 Z^2 / n^2 eV; energy scales with Z^2.

Bohr model

Early quantum model with quantized electron orbits that explains hydrogen spectral lines.

de Broglie wavelength

Matter-wave concept: λ = h/(mv); particles such as electrons have wave-like properties.

Wave–particle duality

Idea that light and matter exhibit both wave-like and particle-like behavior depending on the experiment.

Schrödinger equation

Hψ = Eψ; describes the wavefunction of a quantum system; yields orbitals as probabilistic regions.

Orbital

Region in space with a high probability of finding the electron; shapes include s (sphere) and p (dumbbell).

Nodes

Points or regions where the probability density is zero in an orbital.

Principal quantum number (n)

Main quantum number labeling energy levels in atoms; higher n means higher energy and larger orbitals.

Quantum numbers (overview)

Set of integers labeling states (e.g., n, l, ml, ms); n is the primary label discussed here.

Wave–particle duality in measurements

Depending on the experiment, light and matter can exhibit wave-like or particle-like properties.

Electron diffraction (TEM) and waves

Electrons show interference and diffraction, demonstrating their wave nature in crystallography.

Avogadro’s number

6.022×10^23 mol^−1; converts between atoms and moles; used to relate per-atom energy to per-mole energy.

Excitation

Synonymous with absorption in this context; process of promoting an electron to a higher energy state.