in this video we're looking at the alpha decay of polonium-210 and we're told a little bit of
background information about polonium-210 it's part of the uranium-238 decay series it's one of
the daughter nuclei in that decay series and it has a half-life of about 138 days and what we're
trying to do here is write down the reaction for the alpha decay of polonium-210 and then
in the second part of the question we're going to compute the energy released in this reaction in
mega electron volts or mev we're given a reference table that includes the atomic mass unit written
in mev per c-squared and then the mass of our original nuclide polonium-210 in atomic mass units
and we're given a big hint here about what results from the alpha decay of polonium-210 it's lead 206
and we're given the mass for that in atomic mass units and finally we're given the mass of helium-4
in other words an alpha particle in atomic mass units note that all these masses actually include
the mass of the electrons that would ordinarily be attached to their atom so imagine that we
didn't know what the decay product was we didn't know it was lead 206 all you have to do is look
at our original nuclide polonium-210 and when an alpha particle is emitted that's two protons and
two neutrons in the nucleus so you just knock down the atomic number by 2 and we get from an atomic
number of 84 to an atomic number of 82 and then you realize you're looking at lead as the decay
products so as we start to look at the reaction we're going to look at polonium-210 in its proper
nuclide notation and the atomic number goes on the lower left that's 84 84 protons is what that means
polonium 210 means 210 total nucleons so then we can get the number of neutrons by just taking 210
minus 84 and this gives us 126 total neutrons now again alpha decay means we emit a helium nucleus
and that has two protons two neutrons four total nucleons and then to figure out the daughter
nucleus again we've lost two protons which gives us lead so we have 82 protons so we'll go ahead
and write lead that's pb with 82 protons the alpha particle carried away four total nucleons so we
subtract 4 from the 210 giving us 206 so we have lead 206 and then the number of neutrons remaining
well we lost two of those as well so we have 124 now to get the energy released in this reaction
what we need to do is look at how much mass has disappeared in the reaction then we'll get the
energy equivalent of that mass so we start with our mass of polonium-210 and we subtract from
that the mass of all the decay products there's lead 206 and there's an alpha particle we could
call it a helium 4. now remember all the values in this table include the mass of the electrons that
are ordinarily attached to those atoms but with 84 electrons on that polonium-210 82 electrons
attached to that lead 206 and two electrons attached to that the electron masses cancel
out of this calculation so it doesn't matter plugging in the numbers in atomic mass units
we end up with point zero zero
atomic mass units missing this is the mass that's been converted to energy
in the reaction we want to convert this to the convenient units of mev per c-squared and we
were given the atomic mass unit in those units 931.494 mbv per c squared and i'll post a link
to the video where that was first derived and when we run the numbers on this we get 5.405
mev per c squared now that number is the amount of missing mass remember those units of mev per
c-squared are mass units to figure out the energy equivalent well it's going to be the same number
but to be extra thorough here what we're doing is applying e equals m c squared and the mass
is 5.405 mev per c squared when you multiply that by c squared those cancel out and i get my final
energy release for this reaction of 5.405 mev and we're done if you enjoyed this video or at
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