nuclear spin
Summary
Nuclear spin is an intrinsic angular momentum of some nuclei, such as ¹H and ¹³C, that makes them act like tiny magnets. In a magnetic field its spin states differ in energy, and NMR detects the radio-frequency energy absorbed when nuclei flip. Nuclei like ¹²C have zero spin and give no signal.
Detail
Meaning: Protons and neutrons each have spin ½. A nucleus with an odd number of protons or neutrons has nonzero spin and a magnetic moment. ¹H and ¹³C are spin-½ nuclei with two states. With no field the states have equal energy. In an external field B₀, the state aligned with the field is slightly lower in energy than the state opposed to it. A radio-frequency photon whose energy matches the gap flips the spin. This is resonance, and it is what an NMR instrument detects. Electrons around a nucleus shield it slightly, so nuclei in different environments resonate at different frequencies (chemical shift).
Equation: ΔE = hν = γhB₀/2π, where ΔE is the energy gap (J), h is Planck's constant (J·s), ν is the resonant frequency (Hz), γ is the gyromagnetic ratio of the nucleus (rad·s⁻¹·T⁻¹), and B₀ is the applied field strength (T).
On the MCAT: Questions ask which nuclei give NMR signals, or predict that a stronger field gives a larger gap and a higher resonant frequency. Others ask you to read ¹H or ¹³C spectra, including splitting by neighboring spins (n + 1 rule).
Common confusion: Spin does not mean the nucleus is physically rotating, and it is not electron spin. Nuclei with even numbers of both protons and neutrons, like ¹²C and ¹⁶O, have zero spin and are not seen. ¹³C is seen, though it is a small fraction of natural carbon.
Sources
- Organic Chemistry (Klein)
- Organic Chemistry (Wade)
- Spectrometric Identification of Organic Compounds
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.