Explain nuclear spin

A proton behaves as a tiny magnet

A ¹H nucleus has spin quantum number I = 1/2 and an associated magnetic moment.

Without an applied field its orientations have equal energy; field B₀ splits them into lower-energy aligned and higher-energy opposed states.

Treat the arrows as labels for two quantum states, not as pictures of tiny nuclei physically pointing like compass needles. The experiment distinguishes allowed spin states through their energies in a magnetic field.

Nuclear spin states

Nuclear spin is intrinsic angular momentum of a nucleus; non-zero spin gives magnetic behaviour relevant to NMR.

For ¹H in B₀ there are two allowed spin states, conventionally α lower and β higher.

For a proton, the spin quantum number is 1/2, so two orientations are available in an applied field. The aligned α state is slightly lower in energy than the opposed β state.

Population difference creates a signal

At thermal equilibrium slightly more protons occupy the lower α state than β. The energy separation grows with field strength.

NMR observes transitions between nuclear-spin states, not electron promotion between molecular orbitals.

Without an applied field, the two states have the same energy. Applying B₀ separates them and creates a small excess population in α; that population difference is what makes net absorption measurable.

A stronger field increases the separation and the population difference. It does not create extra spin states or change a proton into a different isotope.

Place ¹H states in a field

At B₀ = 0, draw one degenerate line. At B₀>0, draw α below β and label ΔE.

Show a slightly larger α population; do not calculate ΔE quantitatively.

A complete diagram therefore shows one coincident level at B₀ = 0, two separated levels at B₀ > 0, α below β, and slightly more nuclei in α.

Choose an NMR-active nucleus

Supplied data: ¹H has I = 1/2; a second isotope has I = 0.

Use the supplied spin quantum numbers; do not infer activity only from atomic number.

When reading a diagram, check the field condition first. Then identify level order and population; do not infer either from arrow length or page position alone.

Separate nuclear from electron spin

A student writes: “¹H NMR works because B₀ promotes an electron from the HOMO to the LUMO.”

Identify which particle's spin the experiment probes and what B₀ splits.

Explain the change in a stronger B₀ in words before considering radiation absorption.

Spin is not literal orbital motion

Intrinsic spin is a quantum property; the nucleus is not modelled as a classical ball physically rotating on an axis.

The useful consequence is its magnetic moment and quantised orientations in B₀.

The α and β labels describe nuclear-spin energy states. They are not molecular orbitals, electron-spin boxes or two different kinds of hydrogen atom.

From spin to resonance

After the check questions, explain the ¹³C case without notes. Return later for a different ¹⁹F question.

Try this next: explain energy absorption.

In an exam explanation, include four links: applied field → two proton spin energies → α slightly more populated → a possible net radiofrequency absorption.