Geochemistry — IUPAC-VII applied chemistry at the rock/mineral/fluid grain. Foundations: radiometric decay N(t) = N_0·exp(−λt), half-life t_{1/2} = ln 2 / λ (Rutherford 1900, Holmes 1913) underwrites all isotope geochronology. U-Pb…
geochemistry
N(t) = N₀·exp(−λt); t_{1/2} = ln 2 / λ (universal isotope clock)
Radiometric decay (Rutherford 1900; Holmes 1913 applied it to zircon for the first radiometric geochronology). The number of un-decayed…
K_D = C_s / C_l; 2-phase mass-bal: C_l = X_tot/(F·K_D + 1−F)
Nernst partition coefficient: equilibrium solid/liquid distribution of a trace element between a mineral and its coexisting melt (or…
k = A·exp(−Ea/RT); ln(k₂/k₁) = (Ea/R)·(T₂−T₁)/(T₁T₂)
Arrhenius rate law (Arrhenius 1889): the temperature-dependence of a first-order rate constant k(T) = A·exp(−E_a/RT) where A is the…
N(t_{1/2})/N₀ = 1/2; with λ=ln 2, t=1 ⇒ ratio = 1/2 exactly
Sympy-exact witness of the half-life defining identity. Setup: N(t) = N₀·exp(−λt); at t = ln 2 / λ the exponent is −ln 2 exactly, giving…
R/R₀ = f^{α−1}: at f=1 ⇒ 1; at α=1 ⇒ 1 (no-fractionation limits)
Sympy-exact witness of the Rayleigh fractionation law at the two no-fractionation limits. Setup: R/R₀ = f^{α−1}, where R is the…
C_l = X_tot/(F·K_D + 1−F); at F=0 ⇒ X_tot; at F=1 ⇒ X_tot/K_D
Sympy-exact witness of the two-phase Nernst mass-balance formula at its all-liquid and all-solid limits. Setup: C_l(F, K_D) = X_tot /…