Nuclei and Radioactivity

R = r₀ A^(1/3), where r₀ = 1.2 × 10⁻¹⁵ m (1.2 fm)

N = A − Z

Nuclear density d = 3m_p / (4π r₀³) ≈ 2.3 × 10¹⁷ kg m⁻³

Δm = [Z·mₚ + (A−Z)·mₙ] − M

BE = Δm × c² (joules) OR BE = Δm × 931.3 MeV (when Δm in u)

B = BE / A = [Z·mₚ + (A−Z)·mₙ − M] × 931.3 / A MeV per nucleon

dN/dt = −λN(t)

N(t) = N₀ exp(−λt)

T₁/₂ = 0.693 / λ (since ln 2 = 0.693)

λ = −(1/N) × dN/dt

After n half-lives: N = N₀ / 2ⁿ