Whilst Max Planck, Niels Bohr and many others provided these physical constants,
there remains many questions still to be answered within the universe.
We are only just now beginning to put some tiny pieces together but until we can find all the answers,
The modern physicist will still need to use many of the accepted physical constants provided by people like Max Planck and Niels Bohr.
These physical constants are often not defined from first principle techniques and
are generally used to match atomic theory to the observed atom model actual physical behaviour,
more information on the atomic model physical constants subject is available on our
defining physical constants page.
# |
Physical Constants |
Symbol |
Value |
Units |
1 |
Permeability of vacuum |
(mu_0) |
4 pi e-7 (exact) |
N A-2 |
2 |
Permittivity of vacuum |
(epsilon_0) |
8.854187817e-12 |
F m- |
3 |
Speed of light in vacuum |
(c) |
299792458 (exact) |
m s-1 |
4 |
Newtonian constant of gravitation |
(G) |
6.67259e-11 ± 8.5e-15 |
m3 kg-1s-2 |
5 |
Max Planck ( Planck constant ) |
(h) |
6.6260755e-34 ± 4.0e-40 |
J s |
6 |
Max Planck ( Planck constant in eV ) |
|
4.1356692e-15 ± 1.2e-21 |
eV s |
7 |
h-bar |
(h-bar) |
1.05457266e-34 ± 6.3e-41 |
J s |
8 |
h-bar in eV |
|
6.582122e-16 ± 2.0e-22 |
eV s |
9 |
Boltzmann constant |
(k) |
1.380658e-23 ± 1.2e-28 |
J K-1 |
10 |
Boltzmann constant in eV |
|
8.617385e-05 ± 7.3e-10 |
eV K-1 |
11 |
Boltzmann constant in Hz |
|
20836740000 ± 180000 |
K-1 s-1 |
12 |
Boltzmann constant in wavenumbers |
|
69.50387 ± 0.00059 |
m-1 K-1 |
13 |
Mass of electron |
(m_e) |
9.1093897e-31 ± 5.4e-37 |
kg |
14 |
Mass of electron in u |
|
0.000548579903 ± 1.3e-11 |
u |
15 |
Mass of electron in eV |
|
510999.06 ± 0.15 |
eV |
16 |
Atomic mass unit |
(u) |
1.6605402e-27 ± 1.0e-33 |
kg |
17 |
Standard acceleration of gravity |
(g_n) |
9.80665
| m s-2 |
18 |
Standard atmosphere |
(atm) |
101325 |
Pa |
19 |
Max Planck ( Planck mass ) |
(m_p) |
2.17671e-08 ± 1.4e-12 |
kg |
20
| Max Planck ( Planck length ) |
(l_p) |
1.61605e-35 ± 1.0e-39 |
m |
21 |
Max Planck ( Planck time ) |
(t_p) |
5.39056e-44 ± 3.4e-48 |
s |
22 |
Elementary charge |
(e) |
1.60217733e-19 ± 4.9e-26 |
C |
23 |
Magnetic flux quantum |
(Phi_0) |
2.06783461e-15 ± 6.1e-22 |
Wb |
24 |
Josephson frequency voltage quotient |
|
483597670000000 ± 1.4e+08 |
V-1 s-1 |
25 |
Quantized Hall conductance |
|
3.87404614e-05 ± 1.7e-12 |
Omega-1 |
26 |
Quantized Hall resistance |
(R_H) |
25812.8056 ± 0.0012 |
Omega |
27 |
Niels Bohr ( Bohr magneton ) |
(mu_B) |
9.2740154e-24 ± 3.1e-30 |
J T-1 |
28 |
Niels Bohr ( Bohr magneton in eV ) |
| 5.78838263e-05 ± 5.2e-12 |
eV T-1 |
29 |
Niels Bohr ( Bohr magneton in Hz ) |
| 13996241800 ± 4200 |
T-1 s-1 |
30 |
Niels Bohr ( Bohr magneton in wave numbers ) |
|
46.686437 ± 1.4e-05 |
m-1 T-1 |
31 |
Niels Bohr ( Bohr magneton in kelvins ) |
|
0.6717099 ± 5.7e-06 |
K T-1 |
32 |
Nuclear magneton |
(mu_N) |
5.0507866e-27 ± 1.7e-33 |
J T-1 |
33 |
Nuclear magneton in eV |
|
3.15245166e-08 ± 2.8e-15 |
eV T-1 |
34 |
Nuclear magneton in Hz |
|
7622591.4 ± 2.3 |
T-1 s-1 |
35 |
Nuclear magneton in wavenumbers |
|
0.0254262281 ± 7.7e-09 |
m-1 T-1 |
36 |
Nuclear magneton in kelvins |
|
0.0003658246 ± 3.1e-09 |
K T-1 |
37 |
Fine structure constant |
(alpha) |
0.00729735308 ± 3.3e-10 |
|
38 |
Inverse fine structure constant |
|
137.0359895 ± 6.1e-06 |
|
39 |
Rydberg constant |
(Ry) |
10973731.534 ± 0.013 |
m-1 |
40 |
Rydberg constant in Hz |
|
3.2898419499e+15 ± 3.9e+06 |
s-1 |
41 |
Rydberg constant in joules |
|
2.1798741e-18 ± 1.3e-24 |
J |
42 |
Rydberg constant in eV |
|
13.6056981 ± 4.0e-06 |
eV |
43 |
Niels Bohr ( Bohr radius ) |
(a_0) |
5.29177249e-11 ± 2.4e-18 |
m |
44 |
Hartree energy |
(E_h) |
4.3597482e-18 ± 2.6e-24
| J |
45 |
Hartree energy in eV |
| 27.2113961 ± 8.1e-06 |
eV |
46 |
Quantum of circulation |
|
0.000363694807 ± 3.3e-11 |
m2 s-1 |
47 |
Electron charge |
(eV) |
1.60217733e-19 ± 4.9e-26 |
J |
48 |
Electron muon mass ratio |
|
0.00483633218 ± 7.1e-10 |
|
49 |
Mass electron proton ratio 1/1836.1527 |
|
0.000544617013 ± 1.1e-11 |
|
50 |
Electron deuteron mass ratio |
|
0.000272443707 ± 6e-12 |
|
51 |
Electron alpha-particle mass ratio |
|
0.000137093354 ± 3e-12 |
|
52 |
Electron specific charge |
|
-175881962000 ± -53000 |
C kg-1 |
53 |
Electron molar mass |
|
5.48579903e-07 ± 1.3e-14 |
kg mol-1 |
54 |
Electron Compton wavelength |
(lambda_C) |
2.42631058e-12 ± 2.2e-19 |
m |
55 |
Electron Compton wavelength over 2 pi |
(lambda-bar_C) |
3.86159323e-13 ± 3.5e-20 |
m |
56 |
Electron classical radius |
(r_e) |
2.81794092e-15 ± 3.8e-22 |
m |
57 |
Electron Thomson cross section |
(sigma_e) |
6.6524616e-29 ± 1.8e-35 |
m2 |
58 |
Electron magnetic moment |
|
9.2847701e-24 ± 3.1e-30 |
J T-1 |
59 |
Electron magnetic moment in Bohr magnetons |
|
1.001159652193 ± 1.0e-11 |
|
60 |
Electron magnetic moment in nuclear magnetons |
|
1838.282 ± 3.7e-05 |
|
61 |
Electron magnetic moment anomaly |
(a_e) |
0.001159652193 ± 1.0e-11 |
|
62 |
Electron g-factor |
(g_e) |
2.002319304386 ± 2.0e-11 |
|
63 |
Electron muon magnetic moment ratio |
|
206.766967 ± 3.0e-05 |
|
64 |
Electron proton magnetic moment ratio |
|
658.2106881 ± 6.6e-06 |
|
65
| Muon mass |
|
1.8835327e-28 ± 1.1e-34 |
kg |
66 |
Muon mass in u |
|
0.113428913 ± 1.7e-08 |
u |
67 |
Muon mass in eV |
|
105658389 ± 34 |
eV |
68 |
Muon electron mass ratio |
|
206.768262 ± 3.0e-05 |
|
69 |
Muon molar mass |
|
0.000113428913 ± 1.7e-11 |
kg mol-1 |
70 |
Muon magnetic moment |
|
4.4904514e-26 ± 1.5e-32 |
J T-1 |
71 |
Muon magnetic moment in Bohr magnetons |
|
0.00484197097 ± 7.1e-10 |
|
72 |
Muon magnetic moment in nuclear magnetons |
|
8.8905981 ± 1.3e-06 |
|
73 |
Muon magnetic moment anomaly |
(a_mu) |
0.001165923 ± 8.4e-09 |
|
74 |
Muon g factor |
(g_mu) |
2.002331846 ± 1.7e-08 |
|
75 |
Muon proton magnetic moment ratio |
|
3.18334547 ± 4.7e-07 |
|
76 |
Mass proton |
(m_p) |
1.6726231e-27 ± 1.0e-33 |
kg |
77 |
Mass proton in u |
|
1.00727647 ± 1.2e-08 |
u |
78 |
Mass proton in eV |
|
938272310 ± 280 |
eV |
79 |
Proton electron mass ratio |
|
1836.152701 ± 3.7e-05 |
|
80 |
Proton muon mass ratio |
|
8.8802444 ± 1.3e-06 |
|
81 |
Proton specific charge |
|
95788309 ± 29 |
C kg-1 |
82 |
Proton molar mass |
|
0.00100727647 ± 1.2e-11 |
kg mol-1 |
83 |
Proton Compton wavelength< |
(lambda_C,p) |
1.32141002e-15 ± 1.2e-22 |
m |
84 |
Proton magnetic moment |
|
1.41060761e-26 ± 4.7e-33 |
J T-1 |
85 |
Proton magnetic moment in Bohr magnetons |
|
0.001521032202 ± 1.5e-11 |
|
86 |
Proton magnetic moment in nuclear magnetons |
|
2.792847386 ± 6.3e-08 |
|
87 |
Diamagnetic shielding correction for protons (H_2 O,spherical sample, 298.15 K) |
(sigma_H2O) |
2.5689e-05 ± 1.5e-08 |
|
88 |
Shielded proton moment (H_2 O, spherical sample, 298.15 K) |
(mu_p') |
1.41057138e-26 ± 4.7e-33 |
J T-1 |
89 |
Shielded proton moment in Bohr magnetons |
|
0.001520993129 ± 1.7e-11 |
|
90 |
Shielded proton moment in nuclear magnetons |
|
2.792775642 ± 6.4e-08 |
|
91 |
Proton gyromagnetic ratio |
(gamma_p) |
267522128 ± 81 |
T-1 s-1 |
92 |
|
(gamma_p) |
42577469 ± 13 |
T-1 s-1 |
93 |
Proton gyromagnetic ratio, uncorrected (H_2 O, spherical sample, 298.15 K) |
(gamma_p') |
267515255 ± 81 |
T-1 s-1 |
94 |
|
(gamma_p'/2pi) |
42576375 ± 13 |
T-1 s-1 |
95 |
Mass of a neutron |
(m_n) |
1.6749286e-27 ± 1.0e-33 |
kg |
96 |
Mass of a neutron in u |
|
1.008664904 ± 1.4e-08 |
u |
97 |
Mass of a neutron in eV |
|
939565630 ± 280 |
eV |
98 |
Neutron-electron mass ratio |
|
1838.683662 ± 4.0e-05 |
|
99 |
Proton neutron mass ratio |
|
1.001378404 ± 9e-09 |
|
100 |
Neutron molar mass |
|
0.001008664904 ± 1.4e-11 |
kg mol-1 |
101 |
Neutron Compton wavelength |
(lambda_C,n) |
1.3195911e-15 ± 1.2e-22 |
m |
102 |
Neutron magnetic moment |
|
9.6623707e-27 ± 4.0e-33 |
J T-1 |
103 |
Neutron magnetic moment in Bohr magnetons |
|
0.00104187563 ± 2.5e-10 |
|
104 |
Neutron magnetic moment in nuclear magnetons |
|
1.91304275 ± 4.5e-07 |
|
| 105 |
Neutron-electron magnetic moment ratio |
|
0.00104066882 ± 2.5e-10 |
|
106 |
Neutron-proton magnetic moment ratio |
|
0.68497934 ± 1.6e-07 |
|
107 |
Deuteron mass |
(m_d) |
3.343586e-27 ± 2.0e-33 |
kg |
108 |
Deuteron mass in u |
|
2.013553214 ± 2.4e-08 |
u |
109 |
Deuteron mass in eV |
|
1875613390 ± 570 |
eV |
110 |
Deuteron electron mass ratio |
|
3670.483014 ± 7.5e-05 |
|
111 |
Deuteron proton mass ratio |
|
1.999007496 ± 6e-09 |
|
112 |
Deuteron molar mass |
|
0.002013553214 ± 2.4e-11 |
kg mol-1 |
113 |
Deuteron magnetic moment |
(mu_d) |
4.3307375e-27 ± 1.5e-33 |
J T-1 |
114 |
Deuteron magnetic moment in Bohr magnetons |
|
0.0004669754479 ± 9.1e-12 |
|
115 |
Deuteron magnetic moment in nuclear magnetons |
|
0.85743823 ± 2.4e-08 |
|
116 |
Deuteron electron magnetic moment ratio |
| 0.000466434546 ± 9.1e-12 |
|
117 |
Deuteron proton magnetic moment ratio |
|
0.3070122035 ± 5.1e-09 |
|
118 |
Avagadro constant |
(N_A) |
6.0221367e+23 ± 3.6e+17 |
mol-1 |
119 |
Atomic mass constant |
(m_u) |
1.6605402e-27 ± 1.0e-33 |
kg |
120 |
Atomic mass constant in eV |
|
931494320 ± 280 |
eV |
121 |
Faraday constant |
(F) |
96485.309 ± 0.029 |
C mol-1 |
122 |
Max Planck ( Molar Planck constant ) |
|
3.99031323e-10 ± 3.6e-17 |
J s mol-1 |
123 |
|
(N_A hc) |
0.11962658 ± 1.1e-07
| J m mol-1 |
124 |
Molar gas constant |
(R) |
8.31451 ± 7.0e-05 |
J mol-1 K-1 |
125 |
Molar volume (ideal gas), STP |
(V_m) |
0.0224141 ± 1.9e-07 |
m3 mol-1 |
126 |
Loschmidt constant |
(n_0) |
2.686763e+25 ± 2.3e+20 |
m-3 |
127 |
Stefan-Boltzmann constant |
(sigma) |
5.67051e-08 ± 1.9e-12
| W m-2 K-4 |
128 |
First radiation constant |
(c_1) |
3.7417749e-16 ± 2.2e-22 |
W m2 |
129 |
Second radiation constant |
(c_2) |
0.01438769 ± 1.2e-07 |
m K |
130 |
Wien displacement law constant |
(b) |
0.002897756 ± 2.4e-08 |
m K |
131 |
BIPM maintained ohm, Omega_69-B1 as of 1 Jan 85 |
(Omega_B185) |
1-1.563e-6 ±; 5.0e-08 |
Omega |
132 |
Drift rate of Omega 69-B1 |
(dOmega_69-B1/dt) |
-0.0566 ±; -0.0015 |
muOmega/yr |
133 |
BIPM maintained volt 483 694 GHz(h/2e) |
(V_76-B1) |
1-7.59e-6 ±; 3.0e-07 |
V |
134 |
BIPM maintained ampere A_BIPM |
(A_B185) |
1-6.03e-6 ±; 3.0e-07
| A |
135 |
Cu x-unit: (xu(CuKalpha1)) |
|
1.00207789e-13 ±; 7.0e-20 |
m |
136 |
Mo x-unit: (xu(MoKalpha1)) |
|
1.00209938e-13 ±; 4.5e-20 |
m |
137 |
AA *: (AAngstrom-star) |
|
1.00001481e-10 ±; 9.2e-17 |
m |
138 |
Lattice spacing of Si (in vacuum, 295.65 K) |
(a) |
5.4310196e-10 ±; 1.1e-16 |
m |
139 |
Lattice spacing Si (220) plane |
(d_220) |
1.9201554e-10 ±; 4.0e-17 |
m |
140 |
Molar volume of Si |
(V_m(Si)) |
1.20588179e-05 ±; 8.9e-12 |
m3 mol-1 |
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