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, ^{17}O has 8 protons and 9 neutrons. According to the table above, we would expect = 1/2 or 3/2 or 5/2…. If ^{17}O 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 = 5/2, which means that ^{17}O has a total of 6 pairs of protons and neutrons.
Other examples are: = 1/2 (one proton) and = 0 (6 protons and 6 neutrons). The difference in nuclear spins for ^{1}H and ^{12}C (and other isotopes – see table below) is exploited in an important analytical technique in chemistry called nuclear magnetic resonance.
I |
Isotopes |
0 |
^{12}C, ^{16}O |
1/2 |
^{1}H, ^{13}C, ^{15}N, ^{19}F, ^{29}Si, ^{31}P |
1 |
^{2}H, ^{14}N |
3/2 |
^{11}B, ^{23}Na, ^{35}Cl, ^{37}Cl |
5/2 |
^{17}O, ^{27}Al |
3 |
^{10}B |
Just as the electron spin quantum number s is associated with the electron spin magnetic number m_{s}, where m_{s} = –s, –s + 1 …0 … s – 1, s, the nuclear spin number I is related to the nuclear spin magnetic number m_{I}, where m_{I }= –I, –I + 1 …0 … I – 1, I. For ^{1}H, m_{I }= –1/2 or m_{I }= +1/2, i.e. 2 possible spin orientations.