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physical constants

The base system for units is SI. (That's the standard, dear physicist.)

!--------------------------------------------------!
$physical-constants                      required  !
 electron-charge                double   required  ! [C]
(elementary charge)
 electron-mass                  double   required  ! [kg]
 electron-compton-wavelength    double   required  ! [m]
 planck-constant                double   required  ! [Js]
 speed-of-light                 double   required  ! [m/s]
(exact)
 boltzmann-constant             double   required  ! [J/K]
 vacuum-permeability            double   required  ! [As/Vm]
 
fine-structure-constant        double   required  ! [-]
 classical-electron-radius      double   required  ! [m]
 avogadro-number                double   required  ! [1/mol]
 bohr-magneton                  double   required  ! [J/T] (T=Tesla)
 electron-spin-g-factor         double   required  ! [-]
 proton-mass                    double   required  ! [kg]
 neutron-mass                   double   required  ! [kg]
$end_physical-constants                  required  !
!--------------------------------------------------!

 

Syntax

 electron-charge              = -1.60217653D-19      ! [C]              ! -1.60217653(14)D-19
 electron-mass                =  9.1093826D-31       ! [kg]             !  9.1093826(16)D-31
 electron-compton-wavelength  =  2.426310238D-12     ! [m]              !  2.426310238(16)D-12
 planck-constant              =  6.6260693D-34       ! [Js]             !  6.6260693(11)D-34
 speed-of-light               =  2.99792458D+08      ! [m/s]            ! 
(exact)
 boltzmann-constant           =  1.3806505D-23       ! [J/K]            !  1.3806505(24)D-23
 vacuum-permeability          =  8.854187817D-12     ! [As/Vm]
 fine-structure-constant      =  7.297352568D-03     ! [-]              !  7.297352568(24)D-03
 classical-electron-radius    =  2.817940325D-15     ! [m]              !  2.817940325(28)D-15
 avogadro-number              =  6.0221415D+23       ! [1/mol]          !  6.0221415(10)D+23
 bohr-magneton                = -9.27400949D-24      ! [J/T] (T=Tesla)  ! -9.27400949(80)D-24
 electron-spin-g-factor       =  2.0023193043718D+00 ! [-]              !  2.0023193043718(75)D+00
(negative?)
 proton-mass                  =  1.67262171D-27      ! [kg]             !  1.67262171(29)D-27
 neutron-mass                 =  1.67492728D-27      ! [kg]             !  1.67492728(29)D-27

Source: http://physics.nist.gov/cuu (2004-11-19)

 

Further constants

  • reduced_planck_constant is calculated internally inside the program: planck-constant/(2pi)
    reduced_planck_constant      =  1.05457168D-34   ! [Js]
                                    1.054571682D-34  !
    (calculated by nextnano³ from other constants)
  • bohr_radius is calculated internally inside the program:
    4 * pi * vacuum_permeability * reduced_planck_constant^2 / (electron_mass * electron_charge^2)
    bohr_radius                  =  5.291772108D-11  ! [m]              !  5.291772108(18)D-11
                                    5.291772081D-11  !
    (calculated by nextnano³ from other constants)
  • hydrogen_ionization_energy_J is calculated internally inside the program:
    electron_mass * electron_charge^4 / (32 * pi^2 * reduced_planck_constant^2 * vacuum_permeability^2)
    hydrogen_ionization_energy_J =  2.17987209D-18   ! [J]              !  2.17987209(37)D-18
                                    2.179872088D-18  !
    (calculated by nextnano³ from other constants)
  • hydrogen_ionization_energy_eV is calculated internally inside the program:
    hydrogen_ionization_energy_J / electron-charge
    NIST:     13.6056923(12) eV
    nextnano³: 13.60569231 eV
    hydrogen_ionization_energy_eV = 13.6056923(12)   ! [eV]
    corresponds to hydrogen_ionization_energy_J
                                    13.60569231      !
    (calculated by nextnano³ from other constants)
  • Hartree_eV is calculated internally inside the program:
    2 * hydrogen_ionization_energy_eV
    NIST:     27.2113845(23) eV
    nextnano³: 27.21138461 eV
  • From the Boltzmann constant kB, one obtains kBT at room temperature (T = 300 K) in units of [eV]:
    kBT = 0.02585202955132541 eV

Derived constants

[h_bar^2/(2*m0)]

  • h2b2m_Jm2   = reduced_planck_constant^2 / (2*electron_mass) =
                = 6.10426...d-39 [J  m^2]
  • h2b2m_evAA2 = h2b2m_Jm2 / ABS(electron_charge) * (1d10)^2 =
                = 3.80998...     [eV AA^2]      ! AA = Angstrom

 

Physical constants are stored in MODULE mod_physical_constants.

!*********************************************!
MODULE mod_physical_constants                 !
!*********************************************!
!---------------------------------------------! SI-units (That's the standard, dear physicist.)
 REAL(8) :: electron_charge                   ! [C]
 REAL(8) :: electron_mass                     ! [kg]
 REAL(8) :: electron_compton_wavelength       ! [m]
 REAL(8) :: planck_constant                   ! [Js]
 REAL(8) :: speed_of_light                    ! [m/s]
 REAL(8) :: boltzmann_constant                ! [J/K]
 REAL(8) :: vacuum_permeability               ! [As/Vm]
 REAL(8) :: fine_structure_constant           ! [-]
 REAL(8) :: classical_electron_radius         ! [m]
 REAL(8) :: avogadro_number                   ! [-]
 REAL(8) :: bohr_magneton                     ! [J/T] (T=Tesla)
 REAL(8) :: electron_spin_g_factor            ! [-]
 REAL(8) :: proton_mass                       ! [kg]
 REAL(8) :: neutron_mass                      ! [kg]

 REAL(8) :: reduced_planck_constant           ! [Js]

 REAL(8) :: bohr_radius                       ! [m]
 REAL(8) :: hydrogen_ionization_energy_J      ! [J]
 REAL(8) :: hydrogen_ionization_energy_eV     ! [eV]
 REAL(8) :: Hartree_eV                        ! [eV]

!---------------------------------------------!
!*********************************************!
END MODULE mod_physical_constants             !

!*********************************************!

 

Mathematical constants are stored in MODULE math_constants.
Here, the variable pi is defined:

REAL(8),PARAMETER :: pi = 3.1415926535897932385d0

 

 

Conversion factors

  • µm <=> eV: h * c / e * 106 = 1.239841906

    Example: 1.23984 / 8.4 µm    = 0.1476 eV
          
     1.23984 / 0.1476 eV = 8.4 µm
  • µm <=> THz: c * 10-6  = 299.792458

    Example: 299.79 / 8.4 µm    = 35.69 THz
          
     299.79 / 35.69 THz = 8.4 µm
  • 1018 cm-3 <=> M: 602.21415

    Example: 30.11   / 602.2 = 0.050 M
          
     0.050 M * 602.2 = 30.11
  • 1018 cm-3 <=> mM: 0.60221415

    Example: 30.11 / 0.6022 = 50 mM
          
     50 mM * 0.6022 = 30.11
   
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