A nuclear clock synchronized to 229Th

What do you mean? The half-life is ~8000y so its not like you'll run out. Do you mean the isomeric state is different because the nucleus is unstable long-term, I'm not sure that this matters.

From the article: “Nuclear transitions, by contrast, usually occur at energies far above typical electronic transitions, leaving most nuclear resonances beyond direct coherent access with conventional optical spectroscopy. The 229Th isomer is a singular exception. Its transition energy lies in the vacuum-ultraviolet (VUV) range, making it the only known nuclear transition that can be addressed directly with current laser technology.”

Interesting question. A bit above my level, so I had to read a few Wikipedia articles an make a few guesses.

> Does using an unstable isotope introduce any wobble?

I understand more about the transitions in electrons, but they are quite similar. When an electron jump from an orbital to another an emit light, the width of line is proportional to 1 / mean life time of the estate.

In this case they are using 229Th and 229mTh in https://en.wikipedia.org/wiki/Isotopes_of_thorium They use crystals of CaF2 where some Ca(2+) are replaced by 229Th(4+). This isotope of Th is super unusual because the energy of the transition is so low that is comparable with the energy of the electrons, so the ionized version 229mTh+ has a longer half life than the neutral version 229mTh. I guess you must use the 229mTh+ as the expected time to calculate the width of the lines, i.e. 30 min.

I think your actual question is related to the final estate that is 229Th (no m there) that is also radioactive, but the half life is 8000 years that is 1.5E8 times longer. This should increase the with of the line, but IIRC like 1/1.5E8 more that is too tiny to be important.

I guess yes, but only a tiiiiiny additional part.

> Could this method work with a stable element?

The protons and neutrons have inside the nuclei a structure that is similar to the electrons in the atom. There is a lot of structure, and there are equivalent of noble gas where an additional proton or neutron will cause a huge change https://en.wikipedia.org/wiki/Magic_number_(physics) I only took a course that has like a week (2 classes) about this, so I'm guessing more than what I'd like.

IIUC one of the neutrons switch the direction of the spin, so the total spin of the nuclei goes from 3/2 to 5/2. I'm not sure why in this case the change in energy is so small. Probably the 90 protons are paired and they don't care too much about the switch, and the neutro that switch is unpaired and don't fuss too much the others.

I guess it's important that the atom has a lot of protons and electron to have enough "orbitals" to accommodate the non switched and switched versions without too much problem. But I don't know enough to be sure about the details.

Anyway this doesn't look related to the

So, probably in a parallel universe it is possible that a stable atom can do this, but in this universe the only atom that has a so low level is sadly radioactive.