Question

what particle is emitted from the nucleus during a proton and neutron decay?

Answer 1

http://en.wikipedia.org/wiki/Beta_decay

http://en.wikipedia.org/wiki/Proton_decay

Answer 2

Hmmmm, the question sounds as if one believes proton decay actually exists.
http://en.wikipedia.org/wiki/Proton_decay

neutron decay: Now in the nucleus, neutrons do not decay, and again, your question baffles me. Free neutrons decay with "beta decay", the neutron emits an electron and an electron anti-neutrino, and leaving a proton.
http://en.wikipedia.org/wiki/Neutron