How do nuclei in the higher energy state return to the lower state?

Through spin-lattice and spin-spin relaxation processes, nuclei in the higher energy state return to the lower state.

Spin-Lattice Flexibility

In an NMR experiment, the lattice sample contains the nuclei.

The lattice field is a complex magnetic field created by the rotating and vibrating nuclei in the lattice.

A portion of the lattice field's constituents will possess identical phases and frequencies to the target nuclei's Larmor frequency.

These elements have the ability to interact with higher energy nuclei, causing them to deplete and revert to their lower state.

The temperature of the sample rises slightly as a result of the energy that a nucleus loses, increasing the lattice's vibration and rotation.

Spin-Spin Decompression

The exchange of energy between neighboring nuclei with the same precessional frequency but different energy levels is known as spin-spin relaxation.

Energy will be gained by one nucleus and lost by the other.

The average lifetime of a nucleus in the excited state decreases, but there is no net change in the number of nuclei in each state, which results in line broadening.

Nuclei in higher energy states return to lower energy states by emitting electromagnetic radiation, typically in the form of gamma rays. This process is called gamma decay.