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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 :

$^\textrm{14}_\textrm{6}\textrm{C}$ → $^\textrm{14}_\textrm{7}\textrm{N}$ + $\textrm{e}^\textrm{-}$ + $\textrm{v}^\textrm{-}_\textrm{e}$

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:

$^\textrm{23}_\textrm{12}\textrm{Mg}$ → $^\textrm{23}_\textrm{11}\textrm{Na}$ + $\textrm{e}^\textrm{+}$ + $\textrm{v}^\textrm{e}$

How can you create something with the same mass but with another proton?

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  • $\begingroup$ $n \rightarrow p + e^- + \bar{\nu}_e$ $\endgroup$ – user26143 Dec 1 '13 at 22:36
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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.

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What you missing is that the atomic mass has not changed- mass is conserved- the top number on the isotope notation 14 for both Carbon and Nitrogen in first case (in fact it goes down very slightly but they rounded it up). The Atomic number- bottom number increasing just means a neutron became a proton.

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You wrote the equations correctly. With beta decay a neutron is converted into a proton, and a beta particle is emitted from the nucleus. With positron decay a proton is converted into a neutron and a positron is emitted from the nucleus. In both types of decay the mass number (neutrons + protons) is constant.

As a side note a positron will be short lived. It will annihilate with an electron producing a pair of 511 keV gamma rays emitted in opposite directions.

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