Nuclear magnetic resonance/Catalogs/Magnetic nuclei

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Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) spectroscopy both exploit magnetically active atomic nuclei. That is, compounds containing elements with non-zero nuclear spin (I ) can be studied by these techniques. The elements with non-vanishing nuclear spin are said to be magnetic nuclei. We refer to the articles on NMR spectroscopy and MRI for the use of the NMR-type spectroscopies in chemistry and medical diagnostics.

Nuclei with non-vanishing nuclear spin possess a magnetic moment and hence can be studied by magnetic resonance techniques. The prediction whether a nucleus has spin belongs to the realm of nuclear physics. This fact is usually taken for granted by the practitioners of NMR and MRI. Below an empirical list of nuclei with non-zero spin is given, together with their sensitivity (which basically is the probability of a spin transition).

Nuclear spin

Although nuclear spin I is listed as a single variable in the table below, it is the vector sum of the individual angular momenta of all protons and neutrons (nucleons). A nucleon has an angular momentum j = l + s, where the strong (in comparison to electromagnetic) nuclear forces couple the nucleon spin s to the nucleon orbit l. Depending on j the magnetic moment of the nucleon may be positive (parallel to j) or negative (antiparallel).^[1] The angular momenta j of the individual nucleons are coupled to total nuclear spin I.^[2]

In general, all atoms whose numbers of protons and numbers of neutrons are not both even will be magnetically active because the spins of the individual nucleons do not cancel each other out completely, that is total I ≠ 0. When placed in a very strong magnet the degenerate 2I+1 nuclear states will split into 2I+1 energy states whose energy differences are dependent on the strength of the magnetic field. In the simplest case where the nuclear spin I = 1/2, the spin can be aligned with or against the field. By exciting the nuclei with energy, typically in the radio frequency range of the electromagnetic spectrum, the lowest energy state is excited to a higher energy state. A signal, called the free induction decay (FID) is then measured as the excited state relaxes back to the lower energy state.

The table below lists the isotope(s) of elements that have non-zero nuclear spin and therefore may be used in NMR or MRI spectroscopy. Only three chemical elements with atomic numbers less than bismuth (Z=83) do not have magnetically active isotopes: argon, caesium and promethium.

NOTE: All nuclear spins I are positive. Negative spin values shown below indicate that the gyromagnetic ratio has a negative value, which means that the atomic magnetic moment and the nuclear spin are aligned antiparallel to each other. For nuclear magnetic resonance spectroscopists designing complex excitation schemes, it is convenient to think of such atoms as having negative nuclear spins because, compared to atoms with positive gyromagnetic ratios, the nuclei align in the opposite direction and therefore also precess (rotate) about the magnetic field in the opposite direction. (No matter what sign the spin value has they respond to a strong magnetic field one in the direction Z and the other in the direction −Z. Important is to note they respond likewise only the direction differs by 180˚in the direction of the applied magnetic field.)

Reference and note

↑ L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 2nd ed., Pergamon Press, Oxford, (1965), p. 452
↑ It is common to refer to I as nuclear spin, although it contains also orbit contributions of the nucleons.

List

Element/Name	Isotope Symbol	Nuclear Spin	Sensitivity vs. ¹H
Hydrogen	¹H	1/2	1.000000
Deuterium	²H or D	1	1.44 e-6
Tritium	³H	1/2	-
Helium-3	³He	-1/2	-
Lithium-6	⁶Li	1	0.000628
Lithium-7	⁷Li	3/2	0.270175
Beryllium-9	⁹Be	-3/2	0.013825
Boron-10	¹⁰B	3	0.00386
Boron-11	¹¹B	3/2	0.132281
Carbon-13	¹³C	1/2	0.000175
Nitrogen-14	¹⁴N	1	0.000998
Nitrogen-15	¹⁵N	-1/2	3.84E-06
Oxygen-17	¹⁷O	-5/2	1.07E-05
Fluorine-19	¹⁹F	1/2	0.829825
Neon-21	²¹Ne	-3/2	6.3E-06
Sodium-23	²³Na	3/2	0.092105
Magnesium-25	²⁵Mg	-5/2	0.00027
Aluminium-27	²⁷Al	5/2	0.205263
Silicon-29	²⁹Si	-1/2	0.000367
Phosphorus-31	³¹P	1/2	0.06614
Sulphur-33	³³S	3/2	1.71E-05
Chlorine-33	³³Cl	3/2	0.003544
Chlorine-37	³⁷Cl	3/2	0.000661
Potassium-39	³⁹K	3/2	0.000472
Potassium-41	⁴¹K	3/2	5.75E-06
Calcium-43	⁴³K	-7/2	9.25E-06
Scandium-45	⁴⁵Sc	7/2	0.3
Titanium-47	⁴⁷Ti	-5/2	0.00015
Titanium-49	⁴⁹Ti	-7/2	0.00021
Vanadium-50	⁵⁰V	6	0.00013
Vanadium-51	⁵¹V	7/2	0.37895
Chromium-53	⁵³Cr	-3/2	8.6E-05
Manganese-55	⁵⁵Mn	5/2	0.174386
Iron-57	⁵⁷Fe	1/2	7.37E-07
Cobolt-59	⁵⁹Co	7/2	0.275439
Nickel-61	⁶¹Ni	-3/2	4.21E-05
Copper-63	⁶³Cu	3/2	0.064035
Copper-65	⁶⁵Cu	3/2	0.035263
Zinc-67	⁶⁷Zn	5/2	0.000117
Gallium-69	⁶⁹Ga	3/2	0.041579
Gallium-71	⁷¹Ga	3/2	0.055965
Germanium-73	⁷³Ge	-9/2	0.000108
Arsenic-75	⁷⁵As	3/2	0.025088
Selenium-77	⁷⁷Se	1/2	0.000523
Bromine-79	⁷⁹Br	3/2	0.039649
Bromine-81	⁸¹Br	3/2	0.048596
Krypton-83	⁸³Kr	-9/2	0.000216
Rubidium-85	⁸⁵Rb	5/2	0.007544
Rubidium-87	⁸⁷Rb	3/2	0.048596
Strontium-87	⁸⁷Sr	-9/2	0.000188
Yttrium-89	⁸⁹Y	-1/2	0.00012
Zirconium-91	⁹¹Zr	-5/2	0.00106
Niobium-93	⁹³Nb	9/2	0.4807
Molybdenum-95	⁹⁵Mo	5/2	0.00051
Molybdenum-97	⁹⁷Mo	-5/2	0.00032
Technetium-99	⁹⁹Tc	9/2	0.374386
Ruthenium-99	⁹⁹Ru	-5/2	0.000146
Ruthenium-101	¹⁰¹Ru	-5/2	0.000274
Rhodium-103	¹⁰³Rh	-1/2	3.11E-05
Paladium-105	¹⁰⁵Pd	-5/2	0.000247
Silver-107	¹⁰⁷Ag	-1/2	3.245E-05
Silver-109	¹⁰⁹Ag	-1/2	4.84E-05
Cadmium-111	¹¹¹Cd	-1/2	0.001216
Cadmium-113	¹¹³Cd	-1/2	0.001313
Indium-113	¹¹³In	9/2	0.014702
Indium-115	¹¹³In	9/2	0.331579
Tin-117	¹¹⁷Sn	-1/2	0.003428
Tin-119	¹¹⁹Sn	-1/2	0.004421
Antimony-121	¹²¹Sb	5/2	0.091228
Antimony-123	¹²³Sb	7/2	0.019474
Tellurium-123	¹²³Te	-1/2	0.000156
Tellurium-125	¹²⁵Te	5/2	0.002193
Iodine-127	¹²⁷I	5/2	0.092982
Xenon-129	¹²⁹Xe	-1/2	0.005579
Xenon-131	¹³¹Xe	3/2	0.000581
Caesium-133	¹³³Cs	7/2	0.047193
Barium-135	¹³⁵Ba	3/2	0.000316
Barium-137	¹³⁷Ba	3/2	0.000774
Lanthinum-139	¹³⁹La	7/2	0.05895
Praseodymium-141	¹⁴¹Pr	5/2	0.29825
Neodymium-143	¹⁴³Nd	-7/2	0.0004
Neodymium-145	¹⁴⁵Nd	-7/2	6.5E-05
Samarium-147	¹⁴⁷Sm	-7/2	2.21E-05
Samarium-149	¹⁴⁷Sm	-7/2	0.000104
Europium-151	¹⁵¹Eu	5/2	0.084211
Europium-153	¹⁵³Eu	5/2	0.007895
Gadolidium-155	¹⁵⁵Gd	-3/2	0.03.51E-05
Gadolidium-157	¹⁵⁷Gd	-3/2	8.42E-05
Terbium-159	¹⁵⁹Tb	3/2	0.057895
Dysprosium-161	¹⁶¹Dy	-5/2	7.95E-05
Dysprosium-163	¹⁶³Dy	5/2	0.000281
Holmium-165	¹⁶⁵Ho	7/2	0.175439
Erbiumm-167	¹⁶⁷Er	-7/2	0.000116
Thulium-169	¹⁶⁹Tm	-1/2	0.000561
Ytterbium-171	¹⁷¹Yb	1/2	0.000711
Ytterbium-173	¹⁷³Yb	-5/2	0.0002
Lutetium-175	¹⁷⁵Lu	7/2	0.027386
Lutetium-176	¹⁷⁶Lu	7	0.000902
Halfnium-177	¹⁷⁷Hf	7/2	0.00015
Halfnium-179	¹⁷⁹Hf	-9/2	4.7E-05
Tantalum-181	¹⁸¹Ta	7/2	0.03579
Tungsten-183	¹⁸³W	1/2	1E-05
Rhenium-185	¹⁸⁵Re	5/2	0.049123
Rhenium-187	¹⁸⁷Re	5/2	0.085965
Osmium-187	¹⁸⁷Os	1/2	2E-07
Osmium-189	¹⁸⁹Os	3/2	0.000374
Iridium-191	¹⁹¹Ir	3/2	4E-06
Iridium-193	¹⁹³Ir	3/2	8.77E-06
Platinum-195	¹⁹⁵Pt	1/2	0.003351
Gold-197	¹⁹⁷Au	3/2	1.05E-05
Mercury-199	¹⁹⁹Hg	1/2	0.000951
Mercury-201	²⁰¹Hg	-3/2	0.000189
Titanium-203	²⁰³Ti	1/2	0.050702
Titanium-205	²⁰⁵Ti	1/2	0.134912
Lead-207	²⁰⁷Pb	1/2	0.00207
Bismuth-209	²⁰⁹Bi	9/2	0.136316
Uranium-235	²³⁵Ur	-7/2	-
Plutonium-239	²³⁹Pu	1/2	-
Americium-243	²⁴³Am	5/2	-

[1] L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 2nd ed., Pergamon Press, Oxford, (1965), p. 452

[2] It is common to refer to I as nuclear spin, although it contains also orbit contributions of the nucleons.

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