Nuclear Stability and Transformations
Nuclear stability is determined by the balance between protons and neutrons within an atomic nucleus. The stability diagram (N,Z) illustrates the relationship between these particles and helps predict nuclear behavior.
Definition: Noyau stable et instable (Stable and unstable nuclei) are classified based on their position in the stability diagram. Stable nuclei lie within the "valley of stability," while unstable nuclei have an excess of protons, neutrons, or nucleons.
Lors d'une transformation nucléaire, un noyau se transforme spontanément into a more stable configuration by emitting particles or energy. The three main types of nuclear transformations are:
- Alpha decay: Emission of a helium nucleus (²He)
- Beta decay: Emission of an electron (β⁻) or positron (β⁺)
- Gamma decay: Emission of high-energy electromagnetic radiation
Highlight: Conservation laws play a crucial role in nuclear transformations. The total number of nucleons and the electric charge must be conserved in all nuclear reactions.
Radioactive Decay and Half-Life
Radioactive decay follows an exponential law, described by the equation N(t) = N₀e⁻λt, where N(t) is the number of radioactive nuclei at time t, N₀ is the initial number of nuclei, and λ is the decay constant.
Definition: The demi-vie radioactive (half-life) is the time required for half of the radioactive nuclei in a sample to decay. It is related to the decay constant by the formula T₁/₂ = ln(2)/λ.
The activity of a radioactive sample, A(t), represents the rate of decay and is given by A(t) = λN(t) = A₀e⁻λt, where A₀ is the initial activity.
Example: Calcul demi-vie exercice: To calculate the half-life of a radioactive isotope, measure the time it takes for the activity to decrease by half. For instance, if the activity of a sample decreases from 1000 Bq to 500 Bq in 5730 years, the half-life of the isotope is 5730 years (commonly associated with carbon-14).
