Gyromagnetic Ratio

The magnetogyric ratios of nuclides and nucleons.

The gyromagnetic ratio γ (also - and more precisely: magnetogyric ratio) is defined as the ratio of the angular momentum to the magnetic dipole moment of a particle or a system. For the nucleons e.g. B. the gyromagnetic ratio results from the magnetic moment and the spin.

Gyromagnetic Ratio of Atomic Nuclei

For atomic nuclei with a magnetic dipole moment, the magnetogyric ratio is a constant characteristic of a single isotope. In NMR spectroscopy in particular, the gyromagnetic ratio γ of the NMR-active nuclei in conjunction with the natural isotopic abundance is used as a measure of detection sensitivity.

The following table shows a list of the gyromagnetic properties [10⁷ rad T^-1 s^-1] of the individual nuclides including nuclear spin and the natural proportion of the isotope to the corresponding element in percent [%]. Further nuclear magnetic and other properties can be accessed via the linked data sheets.

A	Nuclide	Symbol	Spin	Gyromagnetic ratio γ [10⁷ rad T^-1 s^-1]	Isotopic Abundance
1	Hydrogen-1	11H	1/2+	26.675222	99.99 %
1	Hydrogen-2	21H	1+	4.1066	0.01 %
1	Hydrogen-3	31H	1/2+	28.535
2	Helium-3	32He	1/2+	-20.38	0.0002(2) %
3	Lithium-6	63Li	1+	3.9371	4.85 %
3	Lithium-7	73Li	3/2-	10.3976	95.15 %
4	Beryllium-9	94Be	3/2-	- 3.9575	100 %
5	Boron-10	105B	3+	2.875	19.65 %
5	Boron-11	115B	3/2-	8.584	80.35 %
6	Carbon-13	136C	1/2-	6.7283	1.06 %
7	Nitrogen-14	147N	1+	1.9338	99.6205 %
7	Nitrogen-15	157N	1/2-	- 2.712	0.3795 %
8	Oxygen-17	178O	5/2+	- 3.6279	0.0383 %
9	Fluorine-19	199F	1/2+	25.181	100 %
10	Neon-21	2110Ne	3/2+	- 2.113	0.27(1) %
11	Sodium-23	2311Na	3/2+	7.0801	100 %
12	Magnesium-25	2512Mg	5/2+	- 1.639	10.011 %
13	Aluminium-27	2713Al	5/2+	6.976	100 %
14	Silicon-29	2914Si	1/2+	- 5.3188	4.673 %
15	Phosphorus-31	3115P	1/2+	10.841	100 %
16	Sulfur-33	3316S	3/2+	2.055	0.7 %
17	Chlorine-35	3517Cl	3/2+	2.624	75.8 %
17	Chlorine-37	3717Cl	3/2+	2.1842	24.2 %
18	Argon-39	3918Ar	7/2-	1.78
19	Potassium-39	3919K	3/2+	1.2498	93.2581(44) %
19	Potassium-41	4119K	3/2+	0.686	6.7302(44) %
20	Calcium-43	4320Ca	7/2-	- 1.8025	0.135(10) %
21	Scandium-45	4521Sc	7/2-	6.5081	100 %
22	Titanium-47	4722Ti	5/2-	- 1.5105	7.44(2) %
22	Titanium-49	4922Ti	7/2-	- 1.5109	5.41(2) %
23	Vanadium-50	5023V	6+	2.6717	0.0250(10) %
23	Vanadium-51	5123V	7/2-	7.0453	99.750(10) %
24	Chromium-53	5324Cr	3/2-	- 1.512	9.501(17) %
25	Manganese-55	5525Mn	5/2-	6.608	100 %
26	Iron-57	5726Fe	1/2-	0.8661	2.119(29) %
27	Cobalt-59	5927Co	7/2-	6.317	100 %
28	Nickel-61	6128Ni	3/2-	- 2.394	1.1399(13) %
29	Copper-63	6329Cu	3/2-	7.1088	69.15(15) %
29	Copper-65	6529Cu	3/2-	7.6104	30.85(15) %
30	Zinc-67	6730Zn	5/2-	1.6778	4.04(16) %
31	Gallium-69	6931Ga	3/2-	6.4389	60.108(50) %
31	Gallium-71	7131Ga	3/2-	8.1812	39.892(50) %
32	Germanium-73	7332Ge	9/2+	0.93660	7.76(8) %
33	Arsenic-75	7533As	3/2-	4.5961	100 %
34	Selenium-77	7734Se	1/2-	5.1214	7.60(7) %
35	Bromine-79	7935Br	3/2-	6.7256	50.65 %
35	Bromine-81	8135Br	3/2-	7.2498	49.35 %
36	Krypton-83	8336Kr	9/2+	1.0331	11.500(19) %
37	Rubidium-85	8537Rb	5/2-	2.5923	72.17(2) %
37	Rubidium-87	8737Rb	3/2-	8.7851	27.83(2) %
38	Strontium-87	8738Sr	9/2+	- 1.1639376	7.04 %
39	Yttrium-89	8939Y	1/2-	- 1.3155	100 %
40	Zirconium-91	9140Zr	5/2+	2.4975	11.22(5) %
41	Niobium-93	9341Nb	9/2+	6.5674	100 %
42	Molybdenum-95	9542Mo	5/2+	- 1.7514	15.873(30) %
42	Molybdenum-97	9742Mo	5/2+	- 1.7884	9.582(15) %
44	Ruthenium-99	9944Ru	5/2+	- 1.2286	12.76(14) %
44	Ruthenium-101	10144Ru	5/2+	- 1.3773	17.06(2) %
45	Rhodium-103	10345Rh	1/2-	- 0.8468	100 %
46	Palladium-105	10546Pd	5/2+	- 1.2305	22.33(8) %
47	Silver-107	10747Ag	1/2-	1.0878	51.839(8) %
47	Silver-109	10947Ag	1/2-	1.2519	48.161(8) %
48	Cadmium-111	11148Cd	1/2+	5.7046	12.795(12) %
48	Cadmium-113	11348Cd	1/2+	5.9609	12.227(7) %
49	Indium-113	11349In	9/2+	5.8845	4.281(52) %
49	Indium-115	11549In	9/2+	5.8971	95.719(52) %
50	Tin-111	11150Sn	7/2+	18(9)
50	Tin-115	11550Sn	1/2+	8.8014	0.34(1) %
50	Tin-117	11750Sn	1/2+	9.589	7.68(7) %
50	Tin-119	11950Sn	1/2+	10.0318	8.59(4) %
51	Antimony-121	12151Sb	5/2+	6.4442	57.21(5) %
51	Antimony-123	12351Sb	7/2+	3.4904	42.79(5) %
52	Tellurium-123	12352Te	1/2+	7.0576	0.89(3) %
52	Tellurium-125	12552Te	1/2+	8.5087	7.07(15) %
53	Iodine-127	12753I	5/2+	5.3817	100 %
54	Xenon-129	12954Xe	1/2+	7.4521	26.401(138) %
54	Xenon-131	13154Xe	3/2+	2.2091	21.232(51) %
55	Cesium-133	13355Cs	7/2+	3.5339	100 %
56	Barium-135	13556Ba	3/2+	2.6755	6.59(10) %
56	Barium-137	13756Ba	3/2+	3.5575	11.23(23) %
57	Lanthanum-138	13857La	5+	3.5575	0.08881(71) %
57	Lanthanum-139	13957La	7/2+	3.801	99.91119(71) %
59	Praseodymium-141	14159Pr	5/2+	7.765	100 %
60	Neodymium-143	14360Nd	7/2-	1.474	12.173(26) %
60	Neodymium-145	14560Nd	7/2-	0.913	8.293(12) %
61	Promethium-147	14761Pm	7/2+	3.613
62	Samarium-147	14762Sm	7/2-	1.1124	15.00(14) %
62	Samarium-149	14962Sm	7/2-	0.9175	13.82(10) %
63	Europium-151	15163Eu	5/2+	6.5477	47.81(6) %
63	Europium-153	15363Eu	5/2+	2.9371	52.19(6) %
64	Gadolinium-155	15564Gd	3/2-	0.8273	14.80(9) %
64	Gadolinium-157	15764Gd	3/2-	1.0792	15.65(4) %
65	Terbium-159	15965Tb	3/2+	6.4306	100 %
66	Dysprosium-161	16166Dy	5/2+	0.9206	18.889(42) %
66	Dysprosium-163	16366Dy	5/2-	1.275	24.896(42) %
67	Holmium-165	16567Ho	7/2-	5.710	100 %
68	Erbium-167	16768Er	7/2+	- 0.7752	22.869(9) %
69	Thulium-169	16969Tm	1/2+	- 2.1376	100 %
70	Ytterbium-171	17170Yb	1/2-	4.7348	14.216(7) %
70	Ytterbium-173	17370Yb	5/2-	- 1.3025	16.098(9) %
71	Lutetium-175	17571Lu	7/2+	3.0589	97.401(13) %
71	Lutetium-176	17671Lu	7-	4.7348	2.599(13) %
72	Hafnium-177	17772Hf	7/2-	1.086	18.60(16) %
72	Hafnium-179	17972Hf	9/2+	0.6821	13.62(11) %
73	Tantalum-181	18173Ta	7/2+	3.2445	99.98799(32) %
74	Tungsten-183	18374W	1/2-	1.1283	14.31(4) %
75	Rhenium-185	18575Re	5/2+	6.1057	37.40(5) %
75	Rhenium-187	18775Re	5/2+	6.1682	62.60(5) %
77	Iridium-191	19177Ir	3/2+	0.4665	37.3(2) %
77	Iridium-193	19377Ir	3/2+	0.508	62.7(2) %
78	Platinum-195	19578Pt	1/2-	5.8383	33.775(240) %
79	Gold-197	19779Au	3/2+	0.4692	100 %
80	Mercury-199	19980Hg	1/2-	4.8458	16.94(12) %
80	Mercury-201	20180Hg	3/2-	- 1.7888	13.17(9) %
81	Thallium-203	20381Tl	1/2+	15.5394	29.52(1) %
81	Thallium-205	20581Tl	1/2+	15.6922	70.48(1) %
82	Lead-207	20782Pb	1/2-	5.6264	22.1(50) %
83	Bismuth-209	20983Bi	9/2-	4.3752	100 %
84	Polonium-201	20184Po	3/2-	+10(10)
84	Polonium-209	20984Po	1/2-	7.4	trace
89	Actinium-227	22789Ac	3/2-	3.5	100 %
90	Thorium-229	22990Th	5/2+	0.40
91	Protactinium-231	23191Pa	3/2-	0.40	100 %
92	Uranium-235	23592U	7/2-	0.4926	0.7204(6) %
93	Neptunium-237	23793Np	5/2+	3.1	100 %
94	Plutonium-239	23994Pu	1/2+	0.972
95	Americium-241	24195Am	5/2-	1.04
95	Americium-243	24395Am	5/2-	1.54	100 %

γ as a natural constant

The gyromagnetic conditions for free protons, neutrons, electrons and others are natural constants with the unit s^-1 T^-1 = A s kg^-1 [T: magnetic flux density Tesla; A: Ampere] = C kg^-1 [coulomb per kilogram]:

Current values: CODATA 2018 [1].

Electron

Gyromagnetic ratio of the electron
Symbol:	γ_e
Value:	1,760 859 630 23 x 10¹¹	s^-1 T ^-1
Standard uncertainty:	0,000 000 000 53 x 10¹¹	s^-1 T ^-1
Relative standard uncertainty::	3,0 x 10^-10
Concise form:	1,76085963023(53) x 10¹¹	s^-1 T ^-1

Gyromagnetic ratio of the electron in MHz/T
Symbol:	γ_e
Value:	28 024,951 4242	MHz T ^-1
Standard uncertainty:	0,000 0085	MHz T ^-1
Relative standard uncertainty:	3,0 x 10^-10
Concise form:	28024,9514242(85)	MHz T ^-1

Neutron

Gyromagnetic ratio of the neutron
Symbol:	γ_n
Value:	1,832 471 71 x 10⁸	s^-1 T ^-1
Standard uncertainty:	0,000 000 43 x 10⁸	s^-1 T ^-1
Relative standard uncertainty:	2,4 x 10^-7
Concise form:	1,83247171(43) x 10⁸	s^-1 T ^-1

Gyromagnetic ratio of the neutron in MHz/T
Symbol:	γ_n
Value:	29,164 6931	MHz T ^-1
Standard uncertainty:	0.000 0069	MHz T ^-1
Relative standard uncertainty:	2,4 x 10^-7
Concise form:	29,1646931(69)	MHz T ^-1

Proton

Gyromagnetic ratio of the proton
Symbol:	γ_p
Value:	2,675 221 8744 x 10⁸	s^-1 T ^-1
Standard uncertainty:	0,000 000 0011 x 10⁸	s^-1 T ^-1
Relative standard uncertainty:	4,2 x 10^-10
Concise form:	2,6752218744(11) x 10⁸	s^-1 T ^-1

Gyromagnetic ratio of the proton in MHz/T
Symbol:	γ_p
Value:	42,577 478 518	MHz T ^-1
Standard uncertainty:	0,000 000 018	MHz T ^-1
Relative standard uncertainty:	4,2 x 10^-10
Concise form:	42,577478518(18)	MHz T ^-1

Gyromagnetic ratio of the shielded proton
Symbol:	γ´_p
Value:	2,675 153 151 x 10⁸	s^-1 T ^-1
Standard uncertainty:	0,000 000 029 x 10⁸	s^-1 T ^-1
Relative standard uncertainty:	1,1 x 10^-8
Concise form:	2,675153151(29) x 10⁸	s^-1 T ^-1

Gyromagnetic ratio of the shielded proton in MHz/T
Symbol:	γ_p´
Value:	42,576 384 74	MHz T ^-1
Standard uncertainty:	0,000 000 46	MHz T ^-1
Relative standard uncertainty:	1,1 x 10^-8
Concise form:	42,57638474(46)	MHz T ^-1

Helion

Helion ³He²⁺ is the doubly positively charged atomic nucleus of the helium isotope with the mass 3: Helium-3.

Gyromagnetic ratio of the shielded Helion
Symbol:	γ´_h
Value:	2,037 894 569 x 10⁸	s^-1 T ^-1
Standard uncertainty:	0,000 000 024 x 10⁸	s^-1 T ^-1
Relative standard uncertainty:	1,2 x 10^-8
Concise form:	2,037894569(24) x 10⁸	s^-1 T ^-1

Gyromagnetic ratio of the shielded Helion in MHz/T
Symbol:	γ´_h
Value:	32,434 099 42	MHz T ^-1
Standard uncertainty:	0,000 000 38	MHz T ^-1
Relative standard uncertainty:	1,2 x 10^-8
Concise form:	32,43409942(38)	MHz T ^-1

References:

[1] - Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor:
CODATA recommended values of the fundamental physical constants: 2018.
In: Rev. Mod. Phys. 93, 025010, (2021), DOI 10.1103/RevModPhys.93.025010.

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Last update: 2023-11-10

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