Nuclear spin

Nuclear spin, denoted by the symbol I, is the total spin angular momentum of the nucleus of an atom.

The nucleus, with the exception of the hydrogen nucleus, is composed of protons and neutrons. Like the electron, a proton has an intrinsic angular momentum called spin, with a value of ½. Another similarity between protons and electrons is that protons may pair up with anti-parallel spins, which results in a net proton spin of zero for each proton pair. The ½ spin and pairing up characteristics are also inherent in neutrons.

Simplistically, we can regard nuclear spin I as the collective spins of protons and neutrons in the nucleus. Even though there isn’t a formula to predict the number of proton pairs and neutron pairs in an atom, we can generalise the following:

No. of protons No. of neutrons I
even even 0
odd odd 1 or 2 or 3 or…
even odd ½ or 3/2 or 5/2 or…
odd even ½ or 3/2 or 5/2 or…

For example, 17O has 8 protons and 9 neutrons. According to the table above, we would expect I_{^{17}O} = 1/2 or 3/2 or 5/2…. If 17O has 4 anti-parallel pairs of protons and 4 anti-parallel pairs of neutrons, its nuclear spin will be 1/2. However, experimental results show that I_{^{17}O} = 5/2, which means that 17O has a total of 6 pairs of protons and neutrons.

Other examples are: I_{^1H} = 1/2 (one proton) and I_{^{12}C} = 0 (6 protons and 6 neutrons). The difference in nuclear spins for 1H and 12C (and other isotopes – see table below) is exploited in an important analytical technique in chemistry called nuclear magnetic resonance.




12C, 16O


1H, 13C, 15N, 19F, 29Si, 31P


2H, 14N


11B, 23Na, 35Cl, 37Cl


17O, 27Al



Just as the electron spin quantum number s is associated with the electron spin magnetic number ms, where ms =  –s, –s + 1 …0 … s – 1, s, the nuclear spin number I is related to the nuclear spin magnetic number mI, where mI = –I, –I + 1 …0 … I – 1, I. For 1H, mI = –1/2 or mI = +1/2, i.e. 2 possible spin orientations.

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