How are nuclear reactions balanced?

This is similar to the description of a chemical reaction in that, like any equation, a nuclear reaction needs to have the same elements on the left as it does on the right. The only difference is that in a nuclear reaction, new elements can be created.

Energy, on the other hand, is not always conserved in a nuclear reaction. Some of the mass can be converted to energy, usually in the form of kinetic energy and photons. If you have some mass and energy to start, you can be sure that you need to account for all of that at the end of the experiment. Energy is neither created nor destroyed. You will have as much energy at the beginning as you have at the end.

The most fundamental nuclear reactions are those in which atoms are split, neutrons are released, protons are released, electrons are released, or nucleons are absorbed.

Mercury-197 atoms have the ability to spontaneously absorb electrons, changing one of their protons into a neutron and transforming the atom into Gold-197 and a photon.

To be more exact, you'll need to calculate the recoil energy of the gold. The energy of the resulting gamma can be calculated as the difference between the rest mass energy of the items on the left size and the rest mass energy of the gold.

In addition, charge conservation and the conservation of unusual quantities like Lepton Family Number (though possibly not always) must be taken into account.

Nuclear reactions are balanced by ensuring that the total number of protons and neutrons (mass number) on both sides of the reaction equation remains the same. Additionally, the total electric charge (atomic number) must also be conserved. Balancing nuclear reactions involves adjusting the coefficients of the reactants and products to satisfy these conservation principles.