does nucleus in an atom spin?
Not quite. Isotopes with even number of nucleons may also have non-zero spin, but only isotopes with even number of nucleons may have zero spin.Best answer to your question: some do, some don't- only isotopes with an odd number of nucleons have non-zero spin.
Are you sure about that? What happens when you send those isotopes through a Stern-Gerlach aparatus?(But isotopes with an odd number of BOTH neutrons and protons are in a spin superposition, and we've fallen down the rabbit hole into Quantum Mechanics, sorry!).
To answer this question properly, we need to know how OP is thinking about it - there are several possibilities.does nucleus in an atom spin?