Derived constants and units (derived.ini)

The table below lists the contents of the derived.ini file. It contains constants and units that are derived from the base physical constants.

The definitions depend on the following items:

  • Mathematical constants: pi
  • Base constants: R_inf, c, k_J, R_K, k_F, R, and k_Aprime
Symbol Expression Prefixable Name & notes
—— Derived physical constants and intermediate units ——
Phi_0 1/k_J   magnetic flux quantum
G_0 2/R_K   conductance quantum
e Phi_0*G_0   elementary charge (aka Hartree unit of charge)
h 2*e*Phi_0   Planck constant
N_A k_F/e   Avogadro constant
k_B R/N_A   Boltzmann constant
cyc k_Aprime*c/R_K False cycle (aka circle, revolution, turn) (a unit—not a constant—but useful below)
c_1 2*pi*h*c**2/cyc**3   first radiation constant
c_2 h*c/k_B   second radiation constant
c_3_f 2.821439372122079*c/c_2   Wien frequency displacement constant (the number is x, where exp(x)*(3 - x) = 3)
c_3_lambda c_2/4.965114231744276   Wien wavelength displacement constant (the number is x, where exp(x)*(5 - x) = 5)
sigma c_1/15*(pi/c_2)**4   Stefan-Boltzmann constant (aka Stefan’s constant)
Ry h*c*R_inf   Rydberg energy
Ha 2*Ry   Hartree energy (aka hartree)
T_H Ha/k_B   Hartree temperature

Since angle is explicit, it appears in several of the constants:

  • Phi_0 ≈ 2.068×10-15 Wb [1]
  • G_0 ≈ 7.748×10-5 S cyc [2]
  • h ≈ 6.626×10-34 J Hz-1 [1]
  • c_1 ≈ 3.742×10-16 W m2 cyc-4 [2]
  • c_2 ≈ 1.438×10-2 m K cyc-1 [2]
  • c_3_f ≈ 5.879×1010 Hz K-1 [1]
  • c_3_lambda ≈ 2.898×10-3 K m cyc-1 [2]

The definition of the Planck constant implies that h*cyc ≈ 6.626×10-34 J (the traditional expression of h) and h*rad ≈ 1.05457×10-34 J (the traditional expression of ħ). Note that the cycle (cyc) is not an abbreviation for cycles per second as it became in the MKS system of units. It is a unit of angle.

References

[NIST2014]National Institute of Science and Technology, “Fundamental Physical Constants: Complete Listing,” http://physics.nist.gov/constants, accessed 2014.

Footnotes

[1](1, 2, 3) See the BIPM units regarding the weber (Wb) and the hertz (Hz).
[2](1, 2, 3, 4) Traditionally, angle is dropped [NIST2014].