in this video we're looking at the beta decay of c14 and we're trying to compute the total energy
released in this beta decay we're given a table of reference values so we're given the atomic
mass unit in mev per c-squared and i'll post a link real quick to a video where i showed how to
convert kilograms into mev per c-squared if you're curious and then we have the mass of the c-14 atom
and we need to note really carefully here that we're talking about the entire atom
including the electrons so this could be inconvenient for doing nuclear physics but
that's how these tables are normally arranged so i have the mass of that nucleus plus its electrons
i'm also given the mass of the n14 atom including all of its electrons finally i clipped out a
section of the periodic table involving these two elements and i can see that this beta decay
transforms that carbon nucleus into a nitrogen nucleus and the process there is that a neutron
will turn into a proton and in the process it's going to emit an electron that's called beta
radiation to get into a little more detail of the reaction this is what it looks like
i have carbon with its atomic number of 6 meaning 6 protons carbon 14 has 14 total nucleons which
means it has eight neutrons when it goes through this beta decay one of the neutrons turns into a
proton giving me seven protons that's why i end up with nitrogen i still have 14 total nucleons which
means seven neutrons in addition an electron is going to fly out and i could write that as a beta
for this high energy electron and it has a charge of negative one
and then just to throw in some detail that we're not even going to use but just for completeness
an electron antineutrino is also emitted and it has negligible mass
now depending on the angle between that neutrino and the beta particle the electron may take all
the energy of this decay or just a fraction of it but in this problem we're just trying to get
the total energy released in the reaction so the basic strategy here is to look at the mass of the
thing we started with and then look at the mass of what flies out of this reaction and there should
be some missing mass and if we convert that to energy we find out how much energy was released
in the reaction now a really common mistake for a beta decay is to include the mass of that electron
and this is really just an issue with the way the tables are designed here so again
back here in the references the mass of the c14 the mass of the n14 that includes their electrons
in other words when i put in the mass of this n14 on the right hand side of the equation it's going
to include seven electrons when i put in the mass of this carbon on the left side of the equation
it's going to include the mass of six electrons so just because the way these tables are designed
i've already accounted for the mass of the beta particle on the right hand side and if i were
to add in another electron mass i'd be double counting so now let's just write down what the
initial mass was and that's 14.003241 atomic mass units but i want to get into mev per c
squared so i'm just going to replace that atomic mass unit with 931.494 and this gives me 1344
mev per c squared and then i look at the mass of everything that comes out
of this reaction and again the mass of this nitrogen the way the tables are designed
includes the extra electron already and the mass of the neutrino is negligible
and this is where i realized i should have kept more precision in the mass of the c14
the difference is so small i'm going to have to go back and fix that in just a moment
so for the n14 that's 13 043.78 and when i go back and fix the precision on the c14 that was 1343.93
finally i take the difference and i find the missing mass here
and when i run the numbers on this i get 0.15
mev per c squared of missing mass now i still need to convert that to an energy
and maybe you can get casual enough where you just say it's going to be 0.151 mav
but just to look under the hood for a second what we're using is e equals m c squared
and we love these units for mass of mev per c squared because they're so quick
in this sort of calculation so i have 0.151 mev per c squared for the mass times c squared and c
squared's cancel and i find out that the energy released in this reaction is 0.151 mev
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