The Quantum-Mechanical Model of the Atom

Vocabulary flashcards covering key terms from the lecture notes on light, spectra, quantum theory, and atomic orbitals.

Electromagnetic radiation

Radiant energy that propagates through space; travels as both waves and particles (photons).

Wavelength (λ)

Distance between corresponding points on adjacent waves; determines color and energy of light.

Amplitude

Height of a wave crest; relates to the brightness of light.*

Frequency (ν)

Number of waves passing a point per unit time; measured in hertz (Hz).

Speed of light (c)

Constant 3.00 × 10^8 m/s; c = λν.

Visible spectrum range

Visible light spans about 4.0 × 10^-7 m to 7.5 × 10^-7 m in wavelength.

Interference

Interaction of waves that can constructively or destructively alter amplitude.

Constructive interference

Waves in phase; amplitudes add, increasing overall brightness.

Destructive interference

Waves out of phase; amplitudes cancel, reducing brightness.

Diffraction

Bending of waves around obstacles or through openings; enables color separation and X-ray applications.

Planck's constant (h)

Fundamental constant 6.626 × 10^-34 J·s; relates energy to frequency.

Photon energy (E)

Energy of a single quantum of light: E = hν = hc/λ.

Photoelectric effect

Emission of electrons from a metal surface when illuminated; requires a minimum (threshold) frequency.

Work function (φ)

Minimum energy needed to eject an electron from a material’s surface.

Quantum of energy

Energy comes in discrete packets (photons) rather than a continuous stream.

de Broglie wavelength

Matter has wave properties; λ = h/p, where p = mv.

Momentum (p)

Product of mass and velocity (p = mv).

Heisenberg Uncertainty Principle

More precisely knowing momentum reduces certainty of position (ΔxΔp ≥ h/4π).

Schrödinger equation

Wave equation that blends particle and wave descriptions; yields wavefunctions for electrons.

Wavefunction (ψ)

Mathematical function whose square (ψ^2) gives the probability density of finding an electron.

Orbitals

Solutions to the Schrödinger equation that describe electron density distributions and energies.

Principal quantum number (n)

Energy level of an orbital; n is an integer ≥ 1.

Angular momentum quantum number (l)

Describes orbital shape; 0 ≤ l ≤ n−1; corresponds to s (l=0), p (l=1), d (l=2), f (l=3).

Magnetic quantum number (m_l)

Orbital orientation; −l ≤ m_l ≤ l; determines how many orbitals exist in a subshell.

Spin quantum number (m_s)

Electron spin; values are +1/2 or −1/2.

Shells and subshells

Principal level (shell) contains subshells (s, p, d, f) with the same n.

1s orbital

Lowest-energy orbital: n=1, l=0; spherical shape.

2s and 2p orbitals

n=2; 2s is s-type (l=0); 2p (l=1) comprises three orbitals with ml = −1, 0, +1.

3d orbitals

n=3, l=2; five orbitals with ml = −2, −1, 0, +1, +2.

4f orbitals

n=4, l=3; seven orbitals with ml = −3 to +3; complex shapes.

Orbital shapes

s: spherical; p: dumbbell; d: four-lobed or doughnut; f: more complex shapes.

Nodes

Regions where electron probability density is zero; increase with higher n (e.g., 2s has a radial node).

Line spectra

Spectra consisting of discrete lines (not continuous); arises from transitions between energy levels.

Bohr model

Electrons occupy fixed, quantized orbits with specific energies; light emission/absorption occurs during transitions between levels (E = hν).

Emission colors (Hydrogen lines)

Visible emission lines at specific wavelengths (e.g., 434 nm violet, 486 nm blue-green, 657 nm red) from hydrogen.

Limitations of Bohr model

Does not explain spectra of all elements; fails to account for electron wave nature and complex orbital shapes.

Wave-particle duality

Matter and light exhibit both wave-like and particle-like properties.

Probability density

Spatial distribution describing where an electron is likely to be found; given by ψ^2.

Orbitals vs. shells vs. subshells

Shells are principal energy levels (n); subshells are sets of orbitals with the same n and l (s, p, d, f).