CHAPTER 8 -- NUCLEAR PHYSICS
Nuclear physics studies the interactions and structure of atomic nuclei.
8.1 NUCLEAR FORCES
The Strong Interaction (Strong Force) binds quarks together to form protons and neutrons, and binds protons and neutrons together to form nuclei.
- Range: Very short (~1-3 fm).
- Strength: Roughly 137 times stronger than electromagnetism.
- It overcomes the Coulomb repulsion between protons.
The Weak Interaction is responsible for radioactive decay (like beta decay) and neutrino interactions.
- Range: Extremely short (sub-nuclear).
8.2 STABLE VS UNSTABLE NUCLEI
Plotting Neutron number (N) vs Proton number (Z) creates the "Valley of Stability."
- For light nuclei (Z < 20), stable nuclei have N approx Z.
- For heavier nuclei, more neutrons are needed to screen the proton repulsion, so N > Z.
- Nuclei outside this stability band are unstable and decay to reach a more stable configuration.
8.3 RADIOACTIVE DECAY
Unstable nuclei spontaneously transform into different nuclei, emitting radiation in the process. This is a random, probabilistic process.
Law of Radioactive Decay:
The rate of decay is proportional to the number of radioactive nuclei present.
dN / dt = -lambda * N
Solution:
N(t) = N_0 * e^(-lambda * t)
where lambda is the decay constant.
8.4 HALF-LIFE
The half-life (t_1/2) is the time required for half of a sample of radioactive nuclei to decay.
t_1/2 = ln(2) / lambda approx 0.693 / lambda
After n half-lives, the remaining fraction of the original sample is (1/2)^n.
8.5 DECAY MODES
Alpha Decay (alpha):
- Emission of a Helium-4 nucleus (2 protons, 2 neutrons).
- Occurs in heavy nuclei (e.g., Uranium).
- Parent nucleus: Z reduces by 2, A reduces by 4.
Beta Decay (beta-):
- A neutron converts into a proton, an electron, and an antineutrino.
- n -> p + e- + anti-nu_e
- Z increases by 1, A remains constant.
Beta Plus Decay (beta+):
- A proton converts into a neutron, a positron, and a neutrino.
- p -> n + e+ + nu_e
- Z decreases by 1, A remains constant.
Gamma Decay (gamma):
- An excited nucleus transitions to a lower energy state by emitting a high-energy photon (gamma ray).
- Neither Z nor A changes. It often follows alpha or beta decay.
Electron Capture:
- An inner shell electron is captured by the nucleus, combining with a proton to form a neutron and a neutrino.
- p + e- -> n + nu_e
