Definitions of Fundamental Physical Constants CODATA Recommended Values Maxima Package This package defines many fundamental physical quantities, using the CODATA definitions. In order to load the package, type: (C1) load("physconst.mac"); This will load the package. If you use a defined value in a calculation, you will not see the numerical value unless you specifically tell Maxima to output it. For example, if we wish to calculate E=mc^2 for a specific m: (C2) %m: 35*kg; (D2) 35 kg (C6) E: %m*%%c^2; 2 (D6) 35 %%c kg (C7) float(%); 2 3.14564312557886E+18 kg m (D7) -------------------------- 2 s Note the use of %m instead of m for mass. This avoids any confusion between the unit meters and the mass. Although in this case Maxima would have done what you expected, it is a good habit not to include names in equations that are the same as unit names, in case you make a mistake in choosing variables The Relative Standard Uncertainty (RSU) is included where relevant. To get the RSU associated with a particular variable, use the get command. For example, if you wanted the RSU for the Rydberg constant: (C8) get(%Ry, RSU); (D8) 7.6E-12 Here is a list of the defined constants: Quantity Maxima Symbol ------------------------------------------------------------------ speed of light in vacuum: %%c %c_0 magnetic constant: %u_0 %mu_0 electric constant: %e_0 %epsilon_0 characteristic impedance of vacuum: %Z_0 Newtonian constant of gravitation: %G Planck constant: %%h Planck constant in eVs: %h_eV Hbar: %h_bar Hbar: %h_bar_eV Planck mass: %P_m Planck length: %P_l Planck time: %P_t Electromagnetic Constants ------------------------------------------------------------------------ elementary charge: %%e magnetic flux quantum: %capitalphi_0 %mfq_0 conductance quantum: %G_0 Josephson constant: %K_J von Klitzing constant: %R_K Bohr magneton: %u_B Bohr magneton in eV T-1: %ueVT_B nuclear magneton: %u_N nuclear magneton in eV T-1: %ueVT_N Atomic and Nuclear Constants: General ------------------------------------------------------------------------- fine-structure constant: %alpha Rydberg constant: %Ry %Ry_INF Bohr radius: %a_0 Hartree energy: %E_h Hartree energy in eV: %Eev_h quantum of circulation h/(2me): %qcir2 quantum of circulation h/(me): %qcir Electroweak ------------------------------------------------------------------------- Fermi coupling constant: %Fcc weak mixing angled W (on-shell scheme): %wma_W Electron, e- ------------------------------------------------------------------------- electron mass: %m_e electron mass (electron relative atomic mass times u): %m_e_u electron mass - energy equivalent: %me_J electron mass - energy equivalent in MeV: %me_MeV electron-muon mass ratio: %memu electron-tau mass ratio: %metau electron-proton mass ratio: %memp electron-neutron mass ratio: %memn electron-deuteron mass ratio: %memd electron to alpha particle mass ratio: %memalpha electron charge to mass quotient: %echargeemass electron molar mass: %Molar_e Compton wavelength: %lambdaC classical electron radius: %r_e Thomson cross section: %sigma_e electron magnetic moment: %u_e electron magnetic moment to Bohr magneton ratio: %ueuB electron magnetic moment to nuclear magneton ratio: %ueuN electron magnetic moment anomaly |ue|/uB - 1: %a_e electron g-factor: %g_e electron-muon magnetic moment ratio: %ueuu electron-proton magnetic moment ratio : %ueup electron to shielded proton magnetic moment ratio (H2O, sphere, 25 C): %ueusp electron-neutron magnetic moment ratio: %ueun electron-deuteron magnetic moment ratio: %ueud electron to shielded helione magnetic moment ratio (gas, sphere, 25 C): %ueush electron gyromagnetic ratio: %gamma_e Muon, u- ------------------------------------------------------------------------- muon mass: %m_u muon mass in muon relative atomic mass times u: %mu_u energy equivalent: %muc2_J energy equivalent in MeV: %muc2_MeV muon-electron mass ratio: %mume muon-tau mass ratio: %mum muon-proton mass ratio: %mump muon-neutron mass ratio: %mumn muon molar mass: %Molar_u muon Compton wavelength: %lambda_C_u muon magnetic moment: %uu ratio of muon magnetic moment to Bohr magneton ratio: %uuuB ratio of muon magnetic moment to nuclear magneton ratio: %uuuN muon magnetic moment anomaly: %a_u muon g-factor -2(1 + au): %g_u muon-proton magnetic moment ratio: %uuup Tau, tau- ------------------------------------------------------------------------- tau mass: %m_tau tau mass (tau relative atomic mass times u): %mu_tau tau mass energy equivalent: %mtauc2_J tau mass energy equivalent in MeV: %mtauc2_MeV tau-electron mass ratio: %mtaume tau-muon mass ratio: %mtaumu tau-proton mass ratio: %mtaump tau-neutron mass ratio: %mtaumn tau molar mass: %Molar_tau tau Compton wavelength: %lambda_C_tau Proton, p ------------------------------------------------------------------------- proton mass: %m_p proton mass (proton relative atomic mass times u): %mu_p energy equivalent: %mpc2_J energy equivalent in MeV: %mpc2_MeV proton-electron mass ratio: %mpme proton-muon mass ratio: %mpmu proton-tau mass ratio: %mpmtau proton-neutron mass ratio: %mpmn proton charge to mass quotient: %emp proton molar mass: %Molar_p proton Compton wavelength h/mpc: %lambda_C_p proton magnetic moment: %up proton magnetic moment to Bohr magneton ratio: %upuB proton magnetic moment to nuclear magneton ratio: %upuN proton g-factor 2up/uN: %g_p proton-neutron magnetic moment ratio: %upun shielded proton magnetic moment (H2O, sphere, 25 C): %usp shielded proton magnetic moment to Bohr magneton ratio: %uspuB shielded proton magnetic moment to nuclear magneton ratio: %uspuN proton magnetic shielding correction (H2O, sphere, 25 C): %spc proton gyromagnetic ratio: %gamma_p shielded proton gyromagnetic ratio (H2O, sphere, 25 C): %gamma_sp Neutron, n ------------------------------------------------------------------------- neutron mass: %m_n neutron mass (neutron relative atomic mass times u): %mu_n neutron mass energy equivalent: %mnc2_J neutron mass energy equivalent in MeV: %mnc2_MeV neutron-electron mass ratio: %mnme neutron-muon mass ratio: %mnmu neutron-tau mass ratio: %mnm neutron-proton mass ratio: %mnmp neutron molar mass: %Molar_n neutron Compton wavelength: %lambda_C_n neutron magnetic moment: %un neutron magnetic moment to Bohr magneton ratio: %unuB neutron magnetic moment to nuclear magneton ratio: %unuN neutron g-factor: %g_n neutron-electron magnetic moment ratio: %unue neutron-proton magnetic moment ratio: %unup neutron to shielded proton magnetic moment ratio (H2O, sphere, 25 C): %unusp neutron gyromagnetic ratio: %gamma_n Deuteron, d ------------------------------------------------------------------------- deuteron mass: %m_d deuteron mass (deuteron relative atomic mass times u): %mu_d deuteron mass energy equivalent: %mdc2_J deuteron mass energy equivalent in MeV: %mdc2_eV deuteron-electron mass ratio: %mdme deuteron-proton mass ratio: %mdmp deuteron molar mass: %Molar_d deuteron magnetic moment: %ud deuteron magnetic moment to Bohr magneton ratio: %uduB deuteron magnetic moment to nuclear magneton ratio: %uduN deuteron-electron magnetic moment ratio: %udue deuteron-proton magnetic moment ratio: %udup deuteron-neutron magnetic moment ratio: %udun Helion, h ------------------------------------------------------------------------- helion mass: %m_h helion mass (helion relative atomic mass times u): %mu_h helion mass energy equivalent: %mhc2_J helion mass energy equivalent in MeV: %mhc2_MeV helion-electron mass ratio: %mhme helion-proton mass ratio: %mhmp helion molar mass: %Molar_h shielded helion magnetic moment (gas, sphere, 25 C): %ush shielded helion magnetic moment to Bohr magneton ratio: %ushuB shielded helion magnetic moment to nuclear magneton ratio: %ushuN shielded helion to proton magnetic moment ratio (gas, sphere, 25 C): %ushup shielded helion to shielded proton magnetic moment ratio (gas/H2O, spheres, 25 C): %ushusp shielded helion gyromagnetic (gas, sphere, 25 C): %gamma_h Alpha particle, ------------------------------------------------------------------------- alpha particle mass: %m_alpha alpha particle mass (alpha particle relative atomic mass times u): %mu_alpha alpha particle mass energy equivalent: %malphac2_J alpha particle mass energy equivalent in MeV: %malphac2_MeV alpha particle to electron mass ratio: %malphame alpha particle to proton mass ratio: %malphamp alpha particle molar mass: %Molar_alpha PHYSICO-CHEMICAL ------------------------------------------------------------------------- Avogadro constant: %N_A %L atomic mass constant mu = 112m(12C) = 1 u = 10E-3 kg mol-1/NA: %m_u energy equivalent of the atomic mass constant: %muc2_J energy equivalent of the atomic mass constant in MeV: %muc2_MeV Faraday constant: %%F molar Planck constant: %N_Ah molar gas constant: %%R Boltzmann constant: %k_J Boltzmann constant in eV: %k_eV Loschmidt constant NA/Vm: %n_0 molar volume of ideal gas RT/p T = 273.15 K, p = 101.325 kPa: %Vm_1 molar volume of ideal gas RT/p T = 273.15 K, p = 100 kPa: %Vm_2 Sackur-Tetrode constant (absolute entropy constant): T1 = 1 K, p0 = 100 kPa: %S_0R_1 T1 = 1 K, p0 = 101.325 kPa: %S_0R_2 Stefan-Boltzmann constant: %sigma first radiation constant: %c_1 first radiation constant for spectral radiance: %c_1L second radiation constant: %c_2 Wien displacement law constant: %b