"Bohr model" E = -alpha^2 m c^2 / (2 n^2) v = alpha c / n r = n^2 hbar / (alpha m c) check(E == -1/2 m v^2) check(m v r == n hbar) alpha = e^2 / (4 pi epsilon0 hbar c) check(E == -m e^4 / (2 (4 pi epsilon0)^2 hbar^2 n^2)) check(r == 4 pi epsilon0 hbar^2 n^2 / (m e^2)) -- CODATA Internationally recommended 2022 values -- https://physics.nist.gov/cuu/Constants/ 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 -- derived units 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 -- base units ampere = "ampere" kelvin = "kelvin" kilogram = "kilogram" meter = "meter" second = "second" -- eV per joule eV = 1/e coulomb / joule "eV" E1 = -1/2 alpha^2 me c^2 eV r1 = hbar / (alpha me c) E1 r1 "Reduced electron mass" mu = me mp / (me + mp) E1 = -1/2 alpha^2 mu c^2 eV r1 = hbar / (alpha mu c) E1 r1 Run