In nuclear chemistry, how does a neutron split to form a proton and an electron? I'm studying radioisotopes at the moment and balancing nuclear reactions isn't making sense in that more matter is coming out of the equation in negative β⁻ decay equations:

$$\ce{_6^{14}C -&gt; _7^{14}N + e- + \bar{\nu_e}}$$

Notice how the original element has decayed into a new element with an unchanged mass number but an atomic number that has increased by one.

In positive β⁺ decay equations, it makes sense: 

$$\ce{_{12}^{23}Mg -&gt; _{11}^{23}Na + e+ + \nu_e}$$

How can you create something with the same mass but with another proton?
One neutron has changed into a proton, that's what has happened. Our convention in chemistry is to identify nuclear species by the proton number (or the "atomic number") and that is why a new nuclide with an increased atomic number is formed. Both the $\beta^+$ and $\beta^-$ decay follow identical paths: in $\beta^-$ decay, a neutron changes into a proton (thus giving no change in mass number and increase in atomic number), whereas in $\beta^+$ decay, a proton decays into a neutron giving no change in the mass number and a decrease in the atomic number.