Physics - Atomic and Nuclear Physics (Radioactivity and Half-life)

Atomic Structure: An atom consists of a nucleus containing protons and neutrons, surrounded by electrons. It is represented as $^{A}_{Z}X$, where $A$ is the nucleon (mass) number and $Z$ is the proton (atomic) number.

Isotopes: Atoms of the same element with the same number of protons ($Z$) but different numbers of neutrons, resulting in a different mass number ($A$).

Radioactive Decay: A random and spontaneous process where unstable nuclei emit radiation to become more stable. The three main types are Alpha ($\alpha$), Beta ($\beta$), and Gamma ($\gamma$).

Alpha Decay: Emission of a helium nucleus $^{4}_{2}He$. The parent nucleus loses 2 protons and 2 neutrons, decreasing $A$ by 4 and $Z$ by 2.

Beta Decay ($\beta^-$): A neutron decays into a proton and an electron ($^{0}_{-1}e$). $A$ remains the same, but $Z$ increases by 1.

Gamma Radiation: High-energy electromagnetic waves with no mass or charge. It often follows $\alpha$ or $\beta$ decay to release excess energy.

Half-life ($T_{1/2}$): The time taken for half the radioactive nuclei in a sample to decay, or for the activity (measured in Becquerels, $Bq$) to fall to half its initial value.

Background Radiation: Low-level ionizing radiation that is constantly present in the environment from natural sources (radon gas, cosmic rays) and artificial sources (medical X-rays, nuclear fallout).