Beta Decay Question so this is bothering me a tad but why during calculations, do we subtract the masses of all electrons from both the original atom and the "new atom" and then subtract the mass for the emitted electron?
Let's say we have the beta decay:
$$\rm ^{14}_{6}C \to {}^{14}_{7}N + \beta^- + anti-neutrino$$
We neglect the mass for the anti-neutrino, so in the solution we have then the masses of both the C and N atoms and the electron emitted, and we subtract N and e^- from the C mass, but they also subtract all electron masses involved for both atoms,that is 6 electrons for C and 7 for N, why?
And if so why doesn't the formula for beta decays show this too?
 A: The full equation is as follows 
$$\rm ^{14}_{6}C \to {}^{14}_{7}N^+ + {}^{\;\;0}_{-1}\beta^- + {}^{0}_{0}\bar \nu$$
Now $\rm {}^{14}_{7}N^+ + {}^{\;\;0}_{-1}\beta^-$ is the same as $\rm {}^{14}_{7}N^+ + {}^{\;\;0}_{-1}e^-$ which is the same as $\rm {}^{14}_{7}N$ except for the binding energy of the electron in the $\rm {}^{14}_{7}N$ atom.
The tables are for atomic masses and the assumption which is made is that the binding energy of the electrons orbiting the nucleus is very much smaller than the binding energy of the nucleons within the nucleus.
There is thus no need to do any subtraction of electrons.
If you do your counting of particle this decay is equivalent to 
$$\rm ^{1}_{0}n \to {}^{1}_{1}p^+ + {}^{\;\;0}_{-1}\beta^- + {}^{0}_{0}\bar \nu$$
ie a neutron decaying into a proton etc
A: The notation
$$\rm ^{14}_{6}C \to {}^{14}_{7}N^+ + {}^{\;\;0}_{-1}\beta^- + {}^{0}_{0}\bar \nu$$
is not about masses but rather (relevant) particles. You start with one $\rm{C}$ atom that brings an appropriate number of electrons with it and end up with a $\rm{N}$ atom with the proper number of electrons attached plus the emitted electron and neutrino.
The masses don't even add up:


*

*Carbon-14: $14.003241 \rm{~u}$

*Nitrogen-14: $14.0030740048(6) \rm{~u}$

*(source: wikipedia)


And they shouldn't, because the "missing" is converted to energy (excitation of the nitrogen atom and kinetic energy of the electron and maybe the neutrino).
