Nuclear & Astrophysics

Radioactivity

Unstable nuclei emit radiation:

Alpha (α): a helium nucleus; highly ionising, stopped by paper.
Beta (β⁻): a fast electron (a neutron → proton); stopped by aluminium.
Gamma (γ): an EM wave; very penetrating, reduced by lead.

Decay is random and spontaneous. Activity $A = \lambda N$, and: $$N = N_0 e^{-\lambda t}, \quad t_{1/2} = \frac{\ln 2}{\lambda}$$ The half-life is the time for half the nuclei (or activity) to remain.