[puzzledobserver]

While we hear a lot about isotopes (nuclei with same proton count but different neutron count), we don't hear as much about nuclear isomers (nuclei with the same proton count and same neutron count, but somehow having different configurations).

1. Are nuclear isomers a thing?

2. Corollary: Could it be the case that some nuclei are stable and others are unstable, even though they have the same numbers of protons and neutrons?

[Denvercoder9]

The answer to both your questions is yes. Wikipedia has a pretty extensive article about it: https://en.wikipedia.org/wiki/Nuclear_isomer