A bromine-80 nucleus can decay by gamma emission, positron emission, or electron capture. What is the product nucleus in each case?

Here's how the would look for type of decay.

• Gamma emission

A gamma particle is just a photon, which in turn is a particle that has no mass and no charge. As a result, the nuleus that emits the gamma particle will remain unchanged.

In your case, the nuclear equation will look like this

##""_35^80"Br" -> ""_35^80"Br" + ""_0^0gamma##

• Positron emission

takes place when a proton inside the nucleus is converted into a neutron; at the same time, a positron and a neutrino are emitted.

A positron is the antiparticle of an electron, i.e. same mass, but a positive charge. Since a proton is converted into a neutron, the will decrease by 1, but the will remain unchanged.

##""_35^80"Br" -> ""_34^80"Se" + ""_1^0e + ""_0^0nu##

Notice that Br-80 decays into Se-80.

takes place when an electron falls into the nucleus. As a result, a proton is converted into a neutron and a neutrino is emitted.

Once again, the conversion of a proton into a neutron will decrease the by 1, but keep the unchanged.

##""_35^80"Br" + ""_text(-1)^0e -> ""_34^80"Se" + ""_0^0nu##

Once again, Br-80 will decay into Se-80.