-- Verify Einstein's equilibrium equation (2) for Lyman-alpha line -- spontaneous emission A21 = 256 alpha^4 c / (6561 a0) -- induced emission B21 = c^2 / (2 h nu^3) A21 -- absorption p1 = 2 p2 = 6 B12 = p2 / p1 B21 "Coefficients for Lyman-alpha line" A21 B21 B12 "Verify Einstein equilibrium equation (2)" rho = (2 h nu^3 / c^2) / (exp(h nu / (k T)) - 1) E(n) = -alpha hbar c / (2 n^2 a0) nu = (E(2) - E(1)) / h P = B12 rho p1 exp(-E(1) / (k T)) Q = B21 rho p2 exp(-E(2) / (k T)) + A21 p2 exp(-E(2) / (k T)) check(P == Q) "ok" -- CODATA Internationally recommended 2022 values -- https://physics.nist.gov/cuu/Constants/ -- c, e, h, and k are exact values a0 = 5.29177210544 10^(-11) meter alpha = 7.2973525643 10^(-3) c = 299792458.0 meter / second e = 1.602176634 10^(-19) coulomb epsilon0 = 8.8541878188 10^(-12) farad / meter h = 6.62607015 10^(-34) joule second hbar = h / float(2 pi) k = 1.380649 10^(-23) joule / kelvin me = 9.1093837139 10^(-31) kilogram mp = 1.67262192595 10^(-27) kilogram mu0 = 1.25663706127 10^(-6) newton / ampere^2 coulomb = ampere second farad = coulomb / volt joule = kilogram meter^2 / second^2 newton = kilogram meter / second^2 tesla = kilogram / second^2 / ampere volt = joule / coulomb ampere = "ampere" kelvin = "kelvin" kilogram = "kilogram" meter = "meter" second = "second" pi = float(pi) -- use numerical value of pi mu = me mp / (me + mp) a0 = a0 me / mu -- correction for reduced electron mass a0 nu A21 B21 B12 Run