Why is #CDCl_3# a triplet in #C^13 NMR#?

The deuterium in the CDCl₃ splits the #""^13"C"# signal into a triplet.

Whenever you run a #""^13"C"# spectrum in CDCl₃, you always get a triplet solvent peak at 77.5 ppm.

For example, here's a spectrum of t-butyl chloride.

You see the characteristic CDCl₃ triplet at 77.5 ppm.

The reason is that #""^2"H"# has a spin quantum number #I# = 1.

A nucleus with #I = 1# has #2I + 1 = 3# possible orientations.

These orientations have the same energy in the absence of a magnetic field.

In the presence of a magnetic field, these energy levels split. Each level is labelled with a magnetic quantum number #m# = +1, 0, -1.

So a #""^13"C"# nucleus will be split into three different energy levels depending on the +1, 0, or -1 orientation of the deuterium atom.

Each orientation has the same probability, so the signal is a 1:1:1 triplet.