"Alpha decay 3" joule = kilogram meter^2 / second^2 kilogram = "kilogram" meter = "meter" second = "second" alpha = 7.2973525643 10^(-3) c = 299792458.0 meter / second h = 6.62607015 10^(-34) joule second hbar = h / float(2 pi) -- mass of alpha particle m = 6.6446573450 * 10^(-27) kilogram C1 = sqrt(2 m) float(pi) alpha c C2 = 4 sqrt(m alpha c / hbar) A = (228,230,232,234,236,238,226,228,230,232) A = float(A) Z = (90,90,90,90,90,90,88,88,88,88) Z = float(Z) years = 365.25 24 60 60 days = 24 60 60 mins = 60 -- observed half-life in seconds tau = ( 9.1 mins, -- U228 20.23 days, -- U230 68.9 years, -- U232 2.455 10^5 years, -- U234 2.342 10^7 years, -- U236 4.463 10^9 years, -- U238 30.70 mins, -- Th226 1.9125 years, -- Th228 7.54 10^4 years, -- Th230 1.40 10^10 years) -- Th232 -- parent mass M1 = ( 228.031369, -- U228 230.0339401, -- U230 232.0371548, -- U232 234.0409503, -- U234 236.0455661, -- U236 238.0507876, -- U238 226.0249037, -- Th226 228.0287397, -- Th228 230.0331323, -- Th230 232.0380536) -- Th232 -- daughter mass M2 = ( 224.021466, -- Th224 226.0249037, -- Th226 228.0287397, -- Th228 230.0331323, -- Th230 232.0380536, -- Th232 234.0435998, -- Th234 222.0153734, -- 222Ra 224.0202104, -- 224Ra 226.0254082, -- 226Ra 228.0310686) -- 228Ra -- helium mass (electron masses cancel) M3 = 4.00260325413 -- energy of alpha particle in joules u = 1.66053906892 10^(-27) kilogram E = (M1 - M2 - M3) u c^2 -- fermi radius r0 = 1.2 10^(-15) meter r1 = r0 A^(1/3) gamma = C1 Z / sqrt(E) - C2 sqrt(Z r1) t = 2 log(2.0) r1 / sqrt(E / m) / second y = -log(tau) + log(t) + 2 gamma ybar = sum(y) / dim(y) ybar beta = exp(ybar) beta Yhat = log(t / beta) + 2 gamma Yhat "Coefficient of determination (R squared)" Y = log(tau) Ybar = sum(Y) / dim(Y) RSS = sum((Y - Yhat)^2) -- residual sum of squares TSS = sum((Y - Ybar)^2) -- total sum of squares 1 - RSS / TSS Run