Write the balanced nuclear equation for the beta-minus decay of carbon-14, explaining why atomic number increases even though no protons are directly 'added' from outside the nucleus.

Beta-minus decay occurs when a neutron inside the nucleus converts into a proton, an electron (the emitted beta particle, ⁰₋₁e), and an antineutrino (often omitted in introductory equations) — since a neutron becomes a proton, atomic number increases by 1 even though no particle is added from outside, and mass number stays the same because a neutron (mass number contribution of 1) is simply replaced by a proton (also mass number contribution of 1) within the nucleus. For carbon-14: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e, with nitrogen (atomic number 7) as the daughter. Writing the daughter as having the SAME atomic number as carbon (6) misses that beta decay specifically changes a neutron into a proton, increasing atomic number. Writing the mass number as decreasing to 13 misunderstands that beta decay conserves mass number, since a neutron converting to a proton doesn't remove a nucleon from the nucleus, only changes its type. Describing beta-minus decay as the loss of a proton from the nucleus (rather than the gain of one, via neutron-to-proton conversion) reverses the actual particle-level mechanism.