Nuclear Physics and Radioactivity Notes

Nuclear Structure

  • The atomic nucleus comprises positively charged protons and neutral neutrons.
  • Atomic mass number: Represents the total count of protons and neutrons within a nucleus.
  • Atomic number: Indicates the number of protons in the nucleus.
  • Isotopes: Nuclei with an identical number of protons but varying numbers of neutrons.
  • Conceptual Example 1: Nuclear Density
    • The density of the nucleus in a lead atom is approximately equal to that in an oxygen atom.
    • This is because nuclear density is nearly constant across different elements.

The Strong Nuclear Force and the Stability of the Nucleus

  • The strong nuclear force counteracts the mutual repulsion of protons, holding the nucleus together.
  • Larger nuclei necessitate more neutrons to maintain stability.
  • Neutrons act as a sort of nuclear "glue" without contributing to repulsive forces.

The Mass Deficit of the Nucleus and Nuclear Binding Energy

  • Deals with the concept of mass deficit and nuclear binding energy.
  • Example 3: The Binding Energy of the Helium Nucleus Revisited
    • Uses atomic mass units to calculate the binding energy of the helium nucleus.
    • Atomic mass of helium: 4.0026u
    • Atomic mass of hydrogen: 1.0078u

Radioactivity

  • A magnetic field can separate the types of particles emitted by radioactive nuclei.
  • α Decay:
    • A parent nucleus decays into a daughter nucleus by emitting an alpha particle (helium nucleus).
    • Example: Uranium-238 decays into Thorium-234.
    • Equation: {}^{238}{92}U \, \rightarrow \, {}^{234}{90}Th + {}^{4}_{2}He
  • Smoke Detectors:
    • Utilize alpha particles to create a current.
    • Radioactive material emits alpha particles, which are then detected.
  • β Decay:
    • A parent nucleus decays into a daughter nucleus by emitting a beta particle (electron).
    • Example: Thorium-234 decays into Protactinium-234.
    • Equation: {}^{234}{90}Th \, \rightarrow \, {}^{234}{91}Pa + {}^{0}_{-1}e
  • γ Decay:
    • An excited energy state transitions to a lower energy state by emitting a gamma ray.
  • Gamma Knife:
    • A medical instrument that uses gamma rays in a precise manner.

The Neutrino

  • During beta decay, energy is released, but beta particles often lack sufficient kinetic energy to account for all the released energy.
  • The additional energy is carried away by a neutrino.

Radioactive Decay and Activity

  • Half-life: The time it takes for half of the radioactive nuclei to disintegrate.
  • Table 31.2: Some Half-Lives for Radioactive Decay
    • Polonium-214: 1.64 × 10^{-4} s
    • Krypton-89: 3.16 min
    • Radon-222: 3.83 d
    • Strontium-90: 29.1 yr
    • Radium-226: 1.6 × 10^{3} yr
    • Carbon-14: 5.73 × 10^{3} yr
    • Uranium-238: 4.47 × 10^{9} yr
    • Indium-115: 4.41 × 10^{14} yr

Radioactive Dating

  • Conceptual Example 12: Dating a Bottle of Wine
    • Carbon-14 (half-life: 5730 years), Oxygen-15 (half-life: 122.2 seconds), and Tritium (half-life: 12.33 years) are considered.
    • Only Carbon-14 is useful for dating the wine due to its appropriate half-life.

Radioactive Decay Series

  • The sequential decay of one nucleus after another is called a radioactive decay series.
  • Shows a decay series starting from Uranium-238 and ending at Lead-206.
    • Includes alpha and beta decays with respective half-lives.

Radiation Detectors

  • Geiger Counter:
    • Detects radiation through ionization of gas molecules.
  • Scintillation Counter:
    • Utilizes a scintillator to produce photons when struck by a high-energy particle.
    • Photomultiplier tube amplifies the signal.