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]. |
