Physics: Intro to Nuclear Physics Notes (copy) (copy)
Physics: Intro to Nuclear Physics – Cleaned and Expanded Notes
The four fundamental forces
- Gravity
- Attractive interaction between objects with mass-energy; dominates at astronomical scales because it is weakest at particle scales.
- Best described by General Relativity: mass-energy curves spacetime; objects follow geodesics.
- In nuclear contexts, gravitational effects are negligible compared to the other forces.
- Electromagnetism
- Governs interactions between electrically charged particles; holds atoms and molecules together (chemical bonds) and underlies electricity and magnetism.
- Responsible for light (electromagnetic radiation), static electricity, currents, magnetic fields, and most everyday forces (friction, cohesion).
- Carrier particle: photon.
- Strong force
- Strongest interaction; acts at sub-femtometer ranges inside nuclei.
- Fundamental level: binds quarks together into protons and neutrons via gluons (quantum chromodynamics; color charge).
- Residual strong force (nuclear force): binds protons and neutrons (nucleons) together inside nuclei, overcoming electromagnetic repulsion between protons. Often modeled via exchange of mesons (e.g., pions).
- Weak force
- Short-range interaction responsible for processes that change particle “flavor,” notably beta decay.
- Crucial in stellar fusion chains and many radioactive decays.
- Carrier particles: W+, W−, Z0 bosons.
Mass–energy equivalence
- A small amount of mass can correspond to a very large amount of energy: E = m c^2 (c ≈ 3.00 × 10^8 m/s).
- Examples:
- Approximate mass converted to energy in the WWII atomic bombings: about 0.7 grams.
- The Sun converts roughly 5 million tons of mass to energy each second.
- Estimated time until the Sun exhausts core hydrogen: about 5 billion years.
Nuclear binding energy, mass defect, and stability
- Nuclei weigh slightly less than the sum of their separate protons and neutrons; the “missing” mass (mass defect) is binding energy divided by c^2.
- Binding energy per nucleon peaks near iron/nickel; this explains:
- Fusion of very light nuclei releases energy (moving up toward the peak).
- Fission of very heavy nuclei releases energy (moving down toward the peak).
- Stable isotopes lie along the valley of stability; unstable nuclei decay toward more stable configurations.
Fission
- Definition and mechanism
- Splitting of a heavy, unstable nucleus into two (sometimes three) lighter nuclei (fission products), plus free neutrons and gamma rays.
- Often triggered by absorption of a neutron (e.g., uranium-235 + neutron → fission).
- Energy release
- Typical energy per fission event ~200 MeV; arises from increased total binding energy of the products.
- Mass decreases slightly; the mass difference becomes energy (E = m c^2).
- Chain reactions
- Fission releases additional neutrons (commonly 2–3) that can induce more fissions.
- If each fission on average produces at least one subsequent fission, a self-sustaining chain reaction occurs.
- Critical mass: minimum amount and geometry of fissile material needed to sustain a chain reaction (neutron economy must be favorable).
- Control
- Controlled: nuclear reactors use moderators (e.g., water, heavy water, graphite) to slow neutrons and control rods (e.g., boron, cadmium) to absorb excess neutrons. Safety systems include SCRAM (rapid shutdown).
- Uncontrolled: nuclear weapons achieve supercriticality rapidly to release energy explosively.
- Fuel
- Common fissile isotopes: uranium-235, plutonium-239. Uranium enrichment increases the fraction of U-235 for reactor fuel or weapons.
- Applications and history
- Electricity generation in power plants; WWII atomic bombs used fission.
Fusion
- Definition and conditions
- Combining light nuclei (e.g., hydrogen isotopes) into heavier nuclei (e.g., helium), releasing energy because the products are more tightly bound.
- Requires extreme temperature and pressure to overcome electrostatic repulsion (Coulomb barrier), creating a high-energy plasma.
- Natural fusion
- The Sun primarily uses the proton–proton chain; hotter, more massive stars can use the CNO cycle.
- Fusion in stars synthesizes elements up to iron; elements heavier than iron are primarily created in supernovae and neutron-star mergers (r-process), while some are made in asymptotic giant branch stars (s-process).
- Energy yield and feasibility
- Fusion releases more energy per unit mass than fission.
- Controlled, sustained fusion on Earth remains challenging; research focuses on magnetic confinement (tokamaks, stellarators) and inertial confinement (laser-driven capsules). Lawson criterion outlines conditions for net energy gain.
- Fusion weapons
- Thermonuclear (hydrogen) bombs use a fission primary to initiate fusion in a secondary stage (distinct from WWII fission bombs).
Radioactivity and the weak force
- Weak interaction processes
- Beta-minus decay: neutron → proton + electron + antineutrino (driven by the weak force; a down quark converts to an up quark).
- Beta-plus decay: proton → neutron + positron + neutrino.
- Electron capture: a proton captures an inner electron → neutron + neutrino.
- Role in stars
- Enables key steps in the proton–proton chain (e.g., conversion of protons to deuterium via positron and neutrino emission).
- Earth’s internal heat
- Heat from radioactive decay (alpha, beta, gamma) of isotopes such as U-238, Th-232, K-40 contributes to mantle convection and plate tectonics. Beta decays specifically involve the weak force.
- Radiation types and detection
- Alpha (helium nuclei): strongly ionizing, low penetration; beta (electrons/positrons): moderate penetration; gamma (photons): high penetration.
- Detectors include Geiger–Müller tubes, scintillators, semiconductor detectors, cloud and bubble chambers.
- Shielding: paper/skin stops alpha; aluminum or plastic reduces beta; dense materials (lead, concrete) attenuate gamma.
- Half-life and decay law
- Half-life is the time for half the nuclei in a sample to decay. Activity decays exponentially with time.
- Different isotopes have characteristic half-lives; these underpin dating methods and reactor fuel cycles.
Carbon-14 dating (radiocarbon dating)
- Production and uptake
- Cosmic rays convert atmospheric nitrogen-14 into carbon-14; CO2 with C-14 is taken up by living organisms, maintaining a nearly constant C-14/C-12 ratio while alive.
- After death
- Intake stops; C-14 decays to N-14 by beta-minus decay (half-life ~5,730 years).
- Dating range and calibration
- Effective up to roughly 60,000 years; older samples have too little C-14 to measure reliably.
- Calibration curves account for past variations in atmospheric C-14 (including the “bomb pulse” from >2,000 nuclear tests, many atmospheric before 1963).
- Applications
- Archaeology, geology, paleoclimatology, forensics.
Wave–particle duality and quantum ideas
- Light as wave and particle
- Exhibits diffraction, interference, and polarization (wave behavior).
- Interacts in discrete quanta called photons (particle behavior). Photon energy is proportional to frequency (E = h f, where h is Planck’s constant).
- Young’s double-slit experiment
- Light through two slits forms an interference pattern, demonstrating wave behavior; single-photon experiments show individual impacts that build the pattern, revealing quantized particle-like detection.
- Matter waves
- All matter has wave-like properties: de Broglie wavelength equals h divided by momentum; electron diffraction confirms this.
- Additional quantum effects
- Compton scattering shows photon–electron collisions change photon wavelength (particle aspect of light).
- Uncertainty principle limits simultaneous knowledge of conjugate quantities (e.g., position and momentum).
Spectroscopy
- Atomic energy levels
- Electrons occupy discrete energy levels; higher levels mean higher energy and typically larger average distance from the nucleus.
- Absorption: electron gains exact energy difference to jump up a level. Emission: electron drops to a lower level, emitting a photon whose color (wavelength) matches the energy gap.
- Spectral fingerprints
- Each element and molecule has unique sets of lines (emission and absorption spectra), allowing identification of substances in labs and astronomical objects.
- Types of spectra
- Continuous spectrum: unbroken range of colors/wavelengths (e.g., hot dense objects like stellar photospheres or incandescent filaments approximate blackbody radiation).
- Emission line spectrum: bright lines at distinct wavelengths from excited low-density gas.
- Absorption line spectrum: dark lines superimposed on a continuous background when cooler gas absorbs specific wavelengths.
- Visible spectrum
- Order by increasing energy (and frequency, decreasing wavelength): red, orange, yellow, green, blue, indigo, violet. Red has lowest photon energy; violet has highest in visible range.
- Tools and applications
- Spectrometers disperse light via prisms or diffraction gratings.
- Rydberg series describe hydrogen’s spectral lines (e.g., Balmer lines in visible).
- Astronomers measure redshift, composition, temperature, and magnetic fields; chemists analyze elements and bonds (atomic and molecular spectra).
The photoelectric effect
- Phenomenon
- Light shining on a material (often a metal) can eject electrons if the light’s frequency is above a threshold characteristic of the material.
- Key observations
- Existence of a threshold frequency: no electrons emitted below it, regardless of light intensity.
- Above threshold, increasing frequency increases the kinetic energy of emitted electrons.
- Intensity above threshold increases the number of emitted electrons (current), not their individual energies.
- Emission is essentially instantaneous with illumination, contradicting classical wave predictions.
- Explanation
- Einstein proposed that light comes in quanta (photons) with energy E = h f.
- A photon transfers its energy to a single electron. If E exceeds the work function (material-dependent binding energy), the electron is emitted; excess energy becomes kinetic energy (Kmax = h f − work function).
- Einstein received the 1921 Nobel Prize in Physics for explaining the photoelectric effect.
- Measurements and uses
- Stopping potential in a photoelectric setup measures the maximum kinetic energy of emitted electrons.
- Applications include solar cells, photomultiplier tubes, photodiodes, and light sensors.
Nuclear reactors and safety (context for fission energy)
- Reactor types
- Light-water reactors (pressurized and boiling water), heavy-water reactors, gas-cooled graphite reactors, fast breeder reactors (use fast neutrons, breed more fissile fuel from fertile isotopes like U-238 → Pu-239).
- Core components
- Fuel (UO2 pellets), moderator (water, heavy water, graphite) to slow neutrons, control rods (boron, cadmium) to absorb neutrons, coolant to remove heat.
- Neutron economy
- Prompt neutrons are emitted immediately in fission; delayed neutrons (from decay of fission products) enable controllability—critical to reactor control.
- Safety layers
- Multiple physical barriers: fuel cladding, reactor vessel, containment building.
- Passive and active systems for heat removal; emergency shutdown (SCRAM) rapidly inserts control rods.
- Waste and lifecycles
- Spent fuel contains fission products and transuranics; management involves cooling pools, dry cask storage, and potential reprocessing. Radiotoxicity decreases over time depending on half-lives.
Astrophysical nucleosynthesis (context for element formation)
- Stellar burning stages
- Hydrogen → helium (pp chain, CNO cycle), helium → carbon/oxygen (triple-alpha), advanced burning in massive stars up to iron.
- Beyond iron
- Rapid neutron capture (r-process) in supernovae and neutron star mergers creates many heavy elements.
- Slow neutron capture (s-process) in evolved stars contributes to elements heavier than iron with longer timescales.
- Observations
- Spectroscopy of stars and remnants reveals elemental abundances, confirming nucleosynthesis pathways.
Electromagnetism in atomic and nuclear contexts
- Chemical bonds
- Ionic, covalent, metallic, and hydrogen bonds arise from electromagnetic interactions between electrons and nuclei.
- Atomic structure
- Coulomb attraction binds electrons to nuclei; quantization yields discrete energy levels and spectra.
- Magnetism
- Moving charges and intrinsic electron spin create magnetic fields; magnetism couples to electron configurations and materials (diamagnetism, paramagnetism, ferromagnetism).
Additional numerical anchors and facts
- Fission energy scale: about 200 MeV per fission of U-235; roughly 3×10^10 J released by converting 1 gram of mass via E = m c^2.
- Fusion DT reaction (deuterium + tritium) is the most accessible on Earth: yields a helium-4 nucleus, a 14.1 MeV neutron, and significant energy; main challenges are confinement, materials, and breeding tritium.
- Nuclear tests
- More than 2,000 nuclear tests have occurred globally; early atmospheric tests altered atmospheric isotope ratios (e.g., C-14 “bomb pulse”).
Key takeaways and connections
- Nuclear energy (fission or fusion) originates from differences in nuclear binding energy; mass defects convert to energy.
- The strong force binds nuclei; the weak force enables changes in nuclear composition (beta processes); electromagnetism binds atoms and produces light; gravity shapes cosmic-scale structures.
- Wave–particle duality and quantization are essential for understanding atomic spectra, photoelectric effect, and the behavior of both light and matter at small scales.
- Spectroscopy links atomic structure to observed light, enabling identification of elements from laboratories to distant galaxies.