AP Physics 2 Unit 7 Notes: Quantum, Atomic, and Nuclear Physics

Quantization

The idea that certain physical quantities (like exchanged energy) can take only specific discrete values rather than any value in a continuous range.

Photon

A particle-like quantum of electromagnetic radiation that carries a discrete amount of energy.

Planck’s constant (h)

A fundamental constant that relates photon energy to frequency in E = hf (h ≈ 6.63×10⁻³⁴ J·s).

Frequency (f)

The number of wave cycles per second (Hz); for light, higher frequency means higher energy per photon.

Wavelength (λ)

The distance between repeating points of a wave; shorter wavelength corresponds to higher frequency and higher photon energy.

Photon energy (E = hf)

The relationship stating that the energy of a single photon equals Planck’s constant times the light’s frequency.

Photon energy–wavelength relation (E = hc/λ)

A formula for photon energy using wavelength (in vacuum): energy is inversely proportional to wavelength.

Intensity (light)

Power per unit area carried by light; at fixed frequency it mainly changes the number of photons per second, not the energy per photon.

Electron-volt (eV)

A convenient energy unit at atomic scales; 1 eV = 1.60×10⁻¹⁹ J (energy gained by charge e across 1 V).

Photoelectric effect

The emission of electrons from a metal surface when light shines on it, demonstrating quantized energy transfer.

Threshold frequency (f₀)

The minimum light frequency needed to eject electrons from a given metal; below it, no emission occurs regardless of intensity.

Work function (Φ)

The minimum energy required to liberate an electron from a metal surface (a property of the material).

Einstein photoelectric equation (K_max = hf − Φ)

Energy-conservation model for the photoelectric effect: maximum electron kinetic energy equals photon energy minus the work function.

Maximum kinetic energy (K_max)

The greatest kinetic energy of emitted photoelectrons; it increases with light frequency (above threshold), not with intensity at fixed frequency.

Stopping potential (V_s)

The smallest reverse voltage that reduces the photocurrent to zero; used to measure the maximum electron kinetic energy.

Stopping-potential relation (Kmax = eVs)

The connection between stopping potential and maximum photoelectron kinetic energy: K_max equals (elementary charge)(stopping potential).

Wave-particle duality

The principle that quantum objects (photons, electrons) can show wave-like or particle-like behavior depending on the experiment.

de Broglie wavelength (λ = h/p)

The wavelength associated with a particle of momentum p; larger momentum implies smaller wavelength.

Momentum (p)

A measure of motion; for nonrelativistic speeds p = mv, used in the de Broglie relation.

Diffraction

Wave spreading/bending that can produce patterns; electron diffraction is evidence that matter has wave behavior.

Line spectrum

A spectrum consisting of discrete wavelengths, indicating that atomic energy changes occur in quantized steps.

Quantized energy levels

Discrete allowed energies for electrons in atoms; transitions between levels produce or absorb photons with specific energies.

Bohr model

An early quantum model (especially for hydrogen) with electrons in allowed orbits of specific energies; photons are emitted/absorbed during jumps between levels.

Principal quantum number (n)

An integer (1, 2, 3, …) labeling allowed energy levels in the Bohr model of hydrogen.

Hydrogen energy levels (E_n = −13.6 eV/n²)

Bohr-model formula giving the energy of the nth hydrogen level; negative values indicate the electron is bound.

Ground state

The lowest-energy state of an atom; for hydrogen in the Bohr model, n = 1.

Excited state

Any atomic state with higher energy than the ground state (for hydrogen, any n > 1).

Ionization

Removing an electron completely from an atom (reaching E = 0 in the Bohr-model energy convention).

Ionization energy

The energy required to ionize an atom from a given level (raise the electron from E_n to 0).

Emission spectrum

Bright lines at specific wavelengths produced when excited atoms drop to lower energy levels and emit photons.

Absorption spectrum

Dark lines at specific wavelengths formed when atoms absorb photons that raise electrons to higher energy levels.

Energy transition (ΔE)

The change in atomic energy between initial and final levels (ΔE = Efinal − Einitial); photon energy equals |ΔE|.

Energy level diagram

A visual representation of allowed energies as horizontal lines; downward arrows indicate emission, upward arrows indicate absorption.

Nuclear notation (^{A}_{Z}X)

Symbolic form for a nuclide: X is the element, Z is the atomic number (protons), and A is the mass number (protons + neutrons).

Atomic number (Z)

The number of protons in the nucleus; it determines the element’s identity.

Mass number (A)

The total number of nucleons (protons + neutrons) in a nucleus.

Neutron number (N = A − Z)

The number of neutrons in a nucleus, found by subtracting atomic number from mass number.

Isotope

Atoms of the same element (same Z) with different numbers of neutrons (different A), often with different nuclear stability.

Strong nuclear force

A very strong, short-range attractive force between nucleons that holds nuclei together despite proton-proton electric repulsion.

Mass defect (Δm)

The difference between the sum of the free nucleon masses and the actual mass of the bound nucleus; the “missing” mass corresponds to binding energy.

Binding energy (E_b = Δmc²)

The energy required to separate a nucleus into individual protons and neutrons; equal to mass defect times c².

Q-value

The energy released or required in a nuclear reaction: Q = (minitial − mfinal)c² (positive means energy released).

Radioactive decay

A spontaneous nuclear change that emits particles and/or radiation; random for a single nucleus but predictable statistically for many nuclei.

Half-life (T_1/2)

The time required for half the undecayed nuclei in a sample to decay; decay is multiplicative (halving each half-life).

Activity (becquerel, Bq)

Decay rate (decays per second); proportional to the number of undecayed nuclei (A = λN).

Alpha decay

Decay that emits an alpha particle (^{4}_{2}He); mass number A decreases by 4 and atomic number Z decreases by 2.

Beta minus decay

Decay that emits an electron; a neutron converts to a proton, so A stays the same while Z increases by 1.

Gamma emission

Emission of a high-energy photon when a nucleus drops from an excited state to a lower nuclear state; A and Z do not change.

Nuclear fission

A heavy nucleus splits into smaller nuclei (often after absorbing a neutron), potentially releasing energy due to increased binding energy per nucleon of products.

Nuclear fusion

Light nuclei combine to form a heavier nucleus; can release energy for light elements but requires overcoming electrostatic repulsion (very high temperatures/confinement).