Rucete ✏ AP Physics 2 In a Nutshell
8. Quantum, Atomic, and Nuclear Physics
This chapter explores the quantum nature of light and matter, atomic models, nuclear structure, and nuclear reactions. It covers key concepts like the photoelectric effect, matter waves, spectral lines, special relativity, radioactive decay, and nuclear energy transformations.
Photoelectric Effect
• Light can eject electrons from certain metals if the frequency is above a threshold value.
• Photon energy: E = hf (h = Planck’s constant)
• Maximum kinetic energy of emitted electrons: KEmax = hf – ϕ (ϕ = work function of metal)
• Intensity affects the number of emitted electrons, but frequency determines whether electrons are emitted at all.
• Stopping potential measures the maximum kinetic energy.
Photon Momentum and Compton Effect
• Photon momentum: p = h/λ
• Compton scattering shows photons collide with electrons and change wavelength, confirming particle behavior of light.
Matter Waves and de Broglie Hypothesis
• All particles have wave-like properties: λ = h/p = h/(mv)
• Observable mainly for tiny particles like electrons.
• Basis for electron diffraction experiments and the Heisenberg uncertainty principle.
Spectral Lines and Bohr Model
• Excited atoms emit light at specific discrete wavelengths.
• Hydrogen spectrum (Balmer series) shows visible lines corresponding to electron transitions to the n=2 level.
• Bohr’s model: electrons orbit nucleus in quantized energy levels without radiating energy until they jump between levels.
• Energy of emitted photon: E = Efinal – Einitial
Special Relativity
• Time dilation: moving clocks run slower.
Δt = Δt₀ / √(1 – v²/c²)
• Length contraction: moving objects are shorter along the direction of motion.
L = L₀√(1 – v²/c²)
• Mass increases with speed: m = m₀ / √(1 – v²/c²)
• Effects become significant at speeds close to the speed of light.
Mass-Energy Equivalence
• Famous equation: E = mc²
• Mass can be converted into enormous amounts of energy (basis for nuclear energy).
• Mass defect: mass difference between separated nucleons and nucleus corresponds to binding energy.
Atomic and Nuclear Structure
• Nucleus composed of protons and neutrons (nucleons).
• Atomic number (Z): number of protons; Mass number (A): protons + neutrons.
• Isotopes: same Z, different A (different number of neutrons).
Binding Energy
• Binding energy holds the nucleus together.
• Greater binding energy per nucleon → more stable nucleus.
• Iron-56 has one of the highest binding energies per nucleon (most stable).
Radioactive Decay
• Alpha decay: emits helium nucleus (α particle).
• Beta decay: neutron converts into proton (β⁻ decay) or proton into neutron (β⁺ decay).
• Gamma decay: emits high-energy photon without changing nuclear composition.
• Half-life: time required for half the nuclei in a sample to decay.
• Decay follows exponential law: N = N₀e^(–λt)
Fission and Fusion
Fission
• Heavy nuclei split into smaller nuclei, releasing energy (e.g., nuclear reactors, atomic bombs).
Fusion
• Light nuclei combine to form heavier nuclei, releasing even more energy (e.g., sun, hydrogen bombs).
• Fusion requires extremely high temperatures to overcome electrostatic repulsion.
In a Nutshell
Quantum, atomic, and nuclear physics reveal the particle-wave duality of matter and the quantization of energy. Light’s behavior as photons, electron transitions in atoms, special relativity, and nuclear reactions all reshape classical views of nature, leading to powerful technologies like lasers, nuclear reactors, and medical imaging.