# Nuclear magnetic resonance/Catalogs/Magnetic nuclei

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 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

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.

## List

Element/NameIsotope SymbolNuclear SpinSensitivity vs. 1H
Hydrogen1H1/21.000000
Deuterium2H or D11.44 e-6
Tritium3H1/2 -
Helium-33He-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
Sulfur-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
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
Silver-107 107Ag -1/2 3.245E-05
Silver-109 109Ag -1/2 4.84E-05
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
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