One of the main nucleus property would by its charge – Z (and of course it depends on the number of protons). Second property would be its mass,that would give us the answer how many neutrons do we have in it (if we already know Z). Radius wouldn’t be significant,because if we know the mass,we can calculate its radius. Another property would be its radioactive tendencies. Whether its radioactive or not depends on its composition ( If we have too many protons,compared to neutrons it would be B+ radioactive, and if too many neutrons – B-,but there are cases where we have alpha particle emitted).