Initial Physical Constants
Physical Constants in the ScientificConstants package
The CODATA 1998 Adjustment
The following table lists the commonly used fundamental physical constants in the ScientificConstants package:
Name
Symbol
Universal
speed_of_light_in_vacuum
c
permeability_of_vacuum
mu[0]
permittivity_of_vacuum
epsilon[0]
characteristic_impedance_of_vacuum
Z[0]
Newtonian_constant_of_gravitation
G
Planck_constant
h
Planck_constant_over_2pi
hbar
Planck_mass
m[P]
Planck_length
l[P]
Planck_time
t[P]
Electromagnetic
elementary_charge
e
magnetic_flux_quantum
Phi[0]
conductance_quantum
G[0]
Josephson_constant
K[J]
von_Klitzing_constant
R[K]
Bohr_magneton
mu[B]
nuclear_magneton
mu[N]
Atomic and Nuclear
fine_structure_constant
alpha
Rydberg_constant
R[infinity]
Bohr_radius
a[0]
Hartree_energy
E[h]
electron_mass
m[e]
Compton_wavelength
lambda[C]
classical_electron_radius
r[e]
Thomson_cross_section
sigma[e]
electron_magnetic_moment
mu[e]
electron_magnetic_moment_anomaly
a[e]
electron_g_factor
g[e]
electron_gyromagnetic_ratio
gamma[e]
muon_mass
m[mu]
muon_Compton_wavelength
lambda[C,mu]
muon_magnetic_moment
mu[mu]
muon_magnetic_moment_anomaly
a[mu]
muon_g_factor
g[mu]
tau_mass
m[tau]
tau_Compton_wavelength
lambda[C,tau]
proton_mass
m[p]
proton_Compton_wavelength
lambda[C,p]
proton_magnetic_moment
mu[p]
proton_g_factor
g[p]
shielded_proton_magnetic_moment
mu_prime[p]
proton_magnetic_shielding_correction
sigma_prime[p]
proton_gyromagnetic_ratio
gamma[p]
shielded_proton_gyromagnetic_ratio
gamma_prime[p]
neutron_mass
m[n]
neutron_Compton_wavelength
lambda[C,n]
neutron_magnetic_moment
mu[n]
neutron_g_factor
g[n]
neutron_gyromagnetic_ratio
gamma[n]
deuteron_mass
m[d]
deuteron_magnetic_moment
mu[d]
helion_mass
m[h]
shielded_helion_magnetic_moment
mu_prime[h]
shielded_helion_gyromagnetic_ratio
gamma_prime[h]
alpha_particle_mass
m[alpha]
Physicochemical
Avogadro_constant
N[A]
atomic_mass_constant
m[u]
Faraday_constant
F
molar_gas_constant
R
Boltzmann_constant
k
molar_volume_of_ideal_gas
V[m]
Loschmidt_constant
n[0]
Stefan_Boltzmann_constant
sigma
first_radiation_constant
c[1]
first_radiation_constant_for_spectral_radiance
c[1,L]
second_radiation_constant
c[2]
Wien_displacement_law_constant
b
Many of the above physical constants are derived constants. To see the definition of a constant, use the ScientificConstants[GetConstant] command. For an explanation of the derivations, see the following section.
The constants c (speed_of_light_in_vacuum), mu[0] (permeability_of_vacuum), epsilon[0] (permittivity_of_vacuum), and Z[0] (characteristic_impedance_of_vacuum) are exact by definition (that is, they are assigned an uncertainty of zero). See the CODATA 1998 Adjustment for details.
The uncertainty assigned to G (Newtonian_constant_of_gravitation) is approximately 12 times larger than its previous value from the 1986 adjustment. This is due to the re-evaluation of previous results and some newer work. See the CODATA 1998 Adjustment for details.
The following table lists applied physical constants in the ScientificConstants package.
standard_acceleration_of_gravity
g
mass_of_Sun
M[Sun]
mass_of_Earth
M[Earth]
radius_of_Earth
R[Earth]
The constant g (standard_acceleration_of_gravity) is exact by definition (that is, it is assigned an uncertainty of zero). See the CODATA 1998 Adjustment for details.
The following table lists less commonly used fundamental physical constants in the ScientificConstants package.
electron_relative_atomic_mass
`A[r](e)`
proton_relative_atomic_mass
`A[r](p)`
neutron_relative_atomic_mass
`A[r](n)`
deuteron_relative_atomic_mass
`A[r](d)`
helion_relative_atomic_mass
`A[r](h)`
alpha_particle_relative_atomic_mass
`A[r](alpha)`
electron_proton_magnetic_moment_ratio
`mu[e]/mu[p]`
deuteron_electron_magnetic_moment_ratio
`mu[d]/mu[e]`
electron_to_shielded_proton_magnetic_moment_ratio
`mu[e]/mu_prime[p]`
shielded_helion_to_shielded_proton_magnetic_moment_ratio
`mu_prime[h]/mu_prime[p]`
neutron_to_shielded_proton_magnetic_moment_ratio
`mu[n]/mu_prime[p]`
electron_muon_mass_ratio
`m[e]/m[mu]`
molar_mass_constant
M[u]
tau_mass_times_c_squared
`m[tau]c^2`
The constant M[u] (molar_mass_constant) is exact by definition (that is, it is assigned an uncertainty of zero). See the CODATA 1998 Adjustment for details.
The values and uncertainties of the fundamental physical constants are determined experimentally. As expected, there is much multiplicity and interdependence of results.
Occasionally, the CODATA Task Group on Fundamental Constants reviews the available experimental results and theoretical constraints, and uses a statistical treatment to obtain a self-consistent set of values and uncertainties for the fundamental physical constants. This set is intended to represent our current knowledge of the values of the fundamental constants.
In the CODATA 1998 Adjustment, the result of a least-squares fitting algorithm is a set of 57 adjusted constants with associated uncertainties and correlations (that is, a covariance matrix). Most of the commonly used fundamental physical constants are derived from a subset of the adjusted constants and some other independent or exact constants. The values and uncertainties of the derived constants are determined by a usual calculation of error analysis, using the covariance matrix.
In ScientificConstants, the 1998 CODATA results are closely reflected by defining 16 nonderived constants with the values and uncertainties of 16 of the CODATA adjusted constants. Another two nonderived constants are defined as two physical constants that are closely related to two other CODATA adjusted constants.
The following table lists the 16 CODATA adjusted constants defined in ScientificConstants.
The following table lists the two other physical constants defined in ScientificConstants that are closely related to CODATA adjusted constants.
The above two constants are closely related to the CODATA adjusted constants additive correction to theoretical a[e] and additive correction to theoretical a[mu].
Furthermore, in the ScientificErrorAnalysis package, the correlations between pairs of the above 18 constants are defined.
Similar to the CODATA 1998 Adjustment, most of the commonly used fundamental physical constants are defined in ScientificConstants as derived constants in terms of the above 18 constants and some other independent or exact constants.
The derived constants of ScientificConstants are treated as quantities-with-error with functional dependence by the ScientificErrorAnalysis package.
For a discussion of the connections between the ScientificErrorAnalysis and ScientificConstants packages, see ScientificErrorAnalysis and ScientificConstants.
See Also
Details of Commands for Physical Constants
ScientificConstants
ScientificConstants References
ScientificConstants[Constant]
ScientificConstants[GetConstant]
ScientificConstants[GetConstants]
ScientificConstants[ModifyConstant]
ScientificErrorAnalysis
ScientificErrorAnalysis and ScientificConstants
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