Question

write a nuclear equation for the emission of a positron from nitrogen-13

Answer 1

¹³₇N --> ¹³₆C+ ⁺ (⁰₊₁e) + energy

In nuclear reactions LHS=RHS.

So, apply this logic for nuclear reactions. positron means +electron (charge)

Emission mechanism

Inside protons and neutrons, there are fundamental particles called quarks. The two most common types of quarks are up quarks, which have a charge of +2/3, and down quarks, with a −1/3 charge. Quarks arrange themselves in sets of three such that they make protons and neutrons. In a proton, whose charge is +1, there are two up quarks and one down quark. Neutrons, with no charge, have one up quark and two down quarks. Via the weak interaction, quarks can change flavor from down to up, resulting in electron emission. Positron emission happens when an up quark changes into a down quark.
Nuclei which decay by (beta particle or 0+1e) may also decay by electron capture. For low-energy decays, electron capture is energetically favored by 2mec2 = 1.022 MeV, since the final state has an electron removed rather than a positron added. As the energy of the decay goes up, so does the branching ratio towards positron emission. However, if the energy difference is less than 2mec2, then positron emission cannot occur and electron capture is the sole decay mode.

Energy:
A positron is ejected from the parent nucleus, and the daughter (Z-1) atom must shed an orbital electron to balance charge. The overall results is that two electrons are ejected, and the beta+ decays is energetically possible only if the mass of the parent atom exceeds the mass of the daughter atom by at least two electron masses (1.02 MeV). i.e., +energy in the reaction