Atomic Structure & Quantum Mechanics Lecture

Vocabulary flashcards covering key terms, constants, principles, models and quantum numbers from the lecture on atomic structure and quantum mechanics.

Atom

Smallest unit of matter; consists of a nucleus surrounded by electrons.

Sub-atomic particle

Particle smaller than an atom (electron, proton, neutron).

Rutherford Gold-Foil Experiment

α-particles scattered by thin gold foil proved atoms have a small, dense, positively charged nucleus with empty space around it.

Nucleus

Central, dense region of an atom containing protons (and neutrons) that holds most of the atom’s mass.

Bohr Model

1913 atomic model with electrons in fixed circular orbits (energy levels) around the nucleus and quantised angular momentum.

Energy Level (Shell)

Stationary state around a nucleus where an electron can exist without radiating energy (designated K,L,M… or n=1,2,3…).

Quantum

Discrete packet of energy equal to hν (Planck’s relation).

Planck’s Constant (h)

Fundamental constant 6.63 × 10⁻³⁴ J s relating energy and frequency.

Rydberg Constant (RH)

1.097 × 10⁷ m⁻¹; appears in hydrogen spectral line formula.

Bohr Radius (a₀)

First Bohr orbit radius: 0.529 Å (5.29 × 10⁻¹¹ m).

Coulombic Force

Electrostatic attraction between charged particles, F = e²/4πϵ₀r² for electron–proton.

Reduced Mass (μ)

Effective mass μ = me mp /(me + mp) used in two-body (electron–nucleus) problems.

de Broglie Wavelength

λ = h/p; matter exhibits wave nature with wavelength inversely proportional to momentum.

Matter Wave

Wave associated with a moving particle, predicted by de Broglie and confirmed by electron diffraction.

Heisenberg Uncertainty Principle

Δx Δp ≥ ħ/2; position and momentum cannot be simultaneously known with arbitrary precision.

Wavefunction (ψ)

Solution of Schrödinger equation; its magnitude squared gives probability density of finding a particle.

Normalization

Condition ∫|ψ|² dτ = 1 ensuring total probability of finding the particle in all space equals one.

Eigenfunction

Wavefunction that returns a constant (eigenvalue) when operated on by a quantum mechanical operator.

Eigenvalue

Allowed measurement value obtained from an operator acting on its eigenfunction.

Hamiltonian Operator (Ĥ)

Total energy operator Ĥ = –ħ²/2m ∇² + V(x,y,z) in quantum mechanics.

Schrödinger Equation

Fundamental wave equation Ĥψ = Eψ describing quantum behavior of particles.

Laplacian (∇²)

Operator ∂²/∂x² + ∂²/∂y² + ∂²/∂z² representing spatial second derivatives.

Principal Quantum Number (n)

Specifies energy level and relative size of orbital; n = 1,2,3…

Azimuthal Quantum Number (l)

Determines subshell and orbital shape; l = 0…(n–1) (s,p,d,f…).

Magnetic Quantum Number (m_l)

Specifies orientation of orbital; m_l = –l … 0 … +l, giving 2l+1 values.

Spin Quantum Number (m_s)

Represents intrinsic electron spin; m_s = +½ or –½.

Orbit

Two-dimensional circular path in Bohr model where an electron orbits nucleus.

Orbital

Three-dimensional region of space with high probability of finding an electron; described by ψ.

Radial Node

Spherical surface where radial probability density equals zero; number = n – l – 1.

Angular Node

Plane or cone where angular part of wavefunction is zero; number = l.

Radial Probability Distribution

4πr²|R_{nl}(r)|²; probability of finding electron between r and r+dr from nucleus.

Aufbau Principle

Electrons fill orbitals in order of increasing (n + l) value; lower n fills first if (n + l) equal.

Pauli Exclusion Principle

No two electrons in an atom can have identical sets of four quantum numbers; max 2 electrons per orbital.

Hund’s Rule

Electrons occupy degenerate orbitals singly with parallel spins before pairing to maximize total spin.

Pairing Energy

Energy cost from electrostatic repulsion when two electrons occupy same orbital with opposite spins.

Exchange Energy

Stabilising energy gained from possible exchanges between electrons with parallel spins in degenerate orbitals; increases with number of exchanges.

Half-filled/Completely Filled Subshell Stability

Extra stability due to symmetrical electron distribution and maximal exchange energy when subshell is half- or fully filled.

Zeeman Effect

Splitting of spectral lines in presence of external magnetic field due to separation of m_l energy levels.

Stern–Gerlach Experiment

Silver atom beam deflection in non-uniform magnetic field showed quantised electron spin (two spots).

Black-Body Radiation

Continuous spectrum emitted by an ideal absorber/emitter; explained by Planck using energy quantization.

Planck’s Radiation Law

E = 8πhν³/c³ 1/(e^{hν/kT} – 1); accurately describes black-body radiation intensity vs frequency.

Rayleigh–Jeans Law

Classical approximation for black-body radiation that fails (ultraviolet catastrophe) at high frequencies.

Quantum (Angular) Momentum

Magnitude L = √[l(l+1)]ħ for orbital; S = √[s(s+1)]ħ for spin.

Degenerate Orbitals

Orbitals having equal energy; degeneracy removed by external fields (Zeeman or Stark effects).

Bohr–Sommerfeld (n+l) Rule

Energy ordering guideline: orbital with lower (n+l) is filled first; if equal, lower n fills first.

Rydberg Formula

1/λ = R_H(Z²)(1/n₁² – 1/n₂²); predicts wavelengths of hydrogen spectral lines.