in this video we're looking at the beta decay of cesium-137 and we're told there's two different
pathways for this to occur so first you could have a beta decay directly to barium 137.
notice in the periodic table here we're bouncing one space to the right in the periodic table
because a beta decay means that a neutron has turned into a proton in the nucleus
and then a high energy electron is emitted that's called the beta particle we're then told there's
a second pathway for cesium-137 to decay into barium-137 and what happens here is a lower energy
beta decay and we're told it's 0.51 mev for the electron that leaves the nucleus in an excited
state and that means we're looking at barium-137 star that's called metastable barium-137 and this
is just a higher energy state in the nucleus when that nucleus decays back down to its
ground state energy the extra energy is going to be carried off by a photon because we don't have
any particle transformations happening in that decay so this is exactly the kind of process that
creates gamma radiation now we're given a list of reference values here we have the atomic mass unit
in mev for c-squared and we have the mass of a cesium-137 atom given in atomic mass units
and the mass of a barium-137 atom given in atomic mass units
now it's just unfortunately the case that the tables you look these things up in
first of all they typically don't give these masses in mev per c-squared which would be
nice for doing nuclear physics they're given in atomic mass units so we have to do that conversion
and then a second source of confusion is that these are the masses of the atoms including their
electrons so if i'm looking at a beta decay of cesium-137 i'll just leave the neutrons out of the
notation for now because i don't need them i have an electron emitted or a beta particle emitted
it has a charge of negative one and a mass number of zero and just for completeness
there's an electron anti-neutrino emitted and its mass is negligible so a common source of
confusion if i'm comparing the mass of what went into this reaction to the mass of what comes out
it can be tempting to include the mass of that beta particle or electron but because of the way
our tables are constructed we've already counted the electron barium has one more proton in the
nucleus so it's surrounded by 56 electrons that's already been accounted for in the way this table
was constructed for the mass of the barium-137 atom including all of its electrons so don't
double count that electron it's already been included in the mass you're about to write down
for the mass of the barium atom and again i don't care about the neutrino because it's approximately
massless so then i'm asked to get the maximum energy for the electron in the first decay pathway
and this brings up another subtle issue about beta decay the amount of energy the electron runs
away with is variable it depends on the angle between the emitted electron and the emitted
electron anti-neutrino but the maximum energy of the electron is when the electron runs off with
all the energy released in the reaction so that's all we have to compute and the strategy here is to
look at the mass of what we started with that's cesium-137 that's 136.9071 atomic mass units and
i'm going to convert those to mev for c squared right now and when i run the numbers on this i get
1.27528 times 10 to the fifth mev per c squared now we're looking for a rather small effect so i'm
keeping a lot of precision next we do the barium 137 and i'm going to go ahead and add one more
digit of precision to each of these calculations because it came in so close so there was a 1
after the 8 for the cesium and my barium mass turns out to be 1.275269 times 10 to the fifth
mev per c squared now the missing mass here sometimes we use a delta m for that is 1.17 mev
per c squared and then the wonderful thing about these units is we can immediately get the energy
equivalent of that missing mass so i plug in to e equals m c squared and the mass
is 1.17 mev for c squared multiply by c squared and you've got your energy in mev
so i get 1.17 mev so that's the total energy released as we go from cesium 137 to barium 137
in the second pathway we emit an electron with an energy of 0.51 mev and it leaves some energy
left over in the excited state of the nucleus and then it decays down to its ground state and emits
a photon carrying away that extra energy i know that my reaction produces 1.17 mev
of total energy 0.51 of that was carried away by the beta particle
so how much must be carried away by the gamma and i get that the energy of this photon is 0.66
mev and we're done if you find the physics content on zack's lab helpful click on the
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