1.4 Units and scales in nuclear physics

Nuclear physics deals with tiny particles and massive energies. We need special units to make sense of it all. From electron volts measuring energy to femtometers sizing up nuclei, these units help us grasp the atomic world.

Understanding these units is key to grasping nuclear concepts. They let us compare particle masses, measure radioactivity, and assess radiation risks. Mastering these units opens the door to exploring the fascinating realm of nuclear physics.

Energy and Mass Units

Electron Volt and Atomic Mass Unit

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• Electron volt (eV) serves as fundamental energy unit in nuclear physics
  • Defined as energy gained by an electron accelerated through 1 volt potential difference
  • Equivalent to approximately $1.602 × 10^{-19}$ joules
  • Commonly used multiples include keV ($10^3$ eV), MeV ($10^6$ eV), and GeV ($10^9$ eV)
• eV applications extend to particle physics and atomic interactions
  • Measures binding energies of electrons in atoms (typically few eV)
  • Quantifies nuclear reaction energies (often in MeV range)
• Atomic mass unit (amu) represents standard unit for measuring atomic and nuclear masses
  • Defined as 1/12 of the mass of a carbon-12 atom
  • Approximately equal to $1.66054 × 10^{-27}$ kg
  • Facilitates convenient expression of particle masses (proton mass ≈ 1.007276 amu)
• Relationship between mass and energy established through Einstein's famous equation
  • $E = mc^2$ connects mass (m) to energy (E) via speed of light (c)
  • Allows conversion between amu and eV (1 amu ≈ 931.5 MeV)

Length and Area Units

Nuclear Scale Measurements

• Femtometer (fm) functions as primary unit for measuring nuclear dimensions
  • Also known as fermi, named after physicist Enrico Fermi
  • Equals $10^{-15}$ meters, appropriate for subatomic scales
  • Typical nuclear radius ranges from 1 to 10 fm
• Proton charge radius measured at approximately 0.8768 fm
  • Demonstrates scale of individual nucleons
  • Highlights precision of modern experimental techniques
• Barn serves as unit of area in nuclear and particle physics
  • Defined as $10^{-28}$ square meters
  • Name originates from phrase "as big as a barn" in context of nuclear cross-sections
  • Commonly used to express probability of nuclear interactions (cross-sections)

Applications in Nuclear Physics

• Femtometer enables precise description of nuclear structure
  • Nuclear shell model utilizes fm to define potential wells
  • Helps explain magic numbers in nuclear stability
• Barn proves crucial in quantifying reaction probabilities
  • Cross-sections for neutron capture often measured in barns
  • Fission cross-sections vary widely (0.001 to 1000 barns)
• Combination of fm and barn provides comprehensive framework
  • Describes both nuclear sizes and interaction probabilities
  • Facilitates calculations in nuclear reactor design and particle accelerator experiments

Radioactivity and Radiation Dose Units

Activity Measurement Units

• Curie (Ci) represents historical unit of radioactivity
  • Originally defined as activity of 1 gram of radium-226
  • Equivalent to $3.7 × 10^{10}$ disintegrations per second
  • Still used in some applications despite being replaced by SI unit
• Becquerel (Bq) functions as SI unit for radioactivity
  • Defined as one nuclear disintegration per second
  • Named after physicist Henri Becquerel, discoverer of radioactivity
  • Relates directly to number of unstable nuclei in a sample
• Conversion between Ci and Bq illustrates vast scale differences
  • 1 Ci = $3.7 × 10^{10}$ Bq
  • Demonstrates why Bq often uses prefixes (kBq, MBq, GBq)

Radiation Dose and Health Effects

• Sievert (Sv) measures biological effects of ionizing radiation
  • SI unit for equivalent dose and effective dose
  • Takes into account different types of radiation and tissue sensitivities
  • Typical annual background radiation dose ≈ 2-3 mSv
• Radiation weighting factors adjust absorbed dose to equivalent dose
  • Gamma rays and beta particles have factor of 1
  • Neutrons range from 5 to 20 depending on energy
  • Alpha particles assigned factor of 20 due to high ionization density
• Effective dose calculation incorporates tissue weighting factors
  • Accounts for varying radiosensitivity of different organs
  • Allows comparison of different exposure scenarios
• Occupational and medical exposures often expressed in Sv
  • Annual limit for radiation workers typically 20 mSv
  • CT scan of abdomen delivers approximately 10 mSv