in this video we're asked to compute the binding energy per nucleon for carbon 14
and express the answer in mega electron volts we're given a table of reference values below
so the first thing in the list is the atomic mass unit in mev per c-squared
and i'll post a link to the video real quick where i discuss how to get mev per c-squared
as a unit of mass if you're given kilograms next in the list we have the mass of the carbon-14 atom
and that's the entire atom including the electrons that's a really important and subtle point that
can cause problems when you're doing nuclear physics and the tables that give you these masses
they always include the mass of the electrons in this number and they express it in atomic mass
units this is why we have to have that conversion to mbvs per c squared for the atomic mass unit
the next three in my list are the mass of the proton neutron and electron and finally we get a
reminder of carbons placed in the periodic table in particular that the atomic number is six in
other words it has six protons in the nucleus so we can write down the carbon-14 nuclide in
our standard nuclide notation the six is the number of protons 14 total number of nucleons
and the eight the number of neutrons now the whole idea with binding energy is that if i look at the
mass of all the ingredients that go into an atom it turns out to be greater than the mass of the
atom itself this is called the mass defect or the missing mass and the reason we have a mass defect
is that the nuclear potential energy goes down when these nucleons get stuck together the strong
forces snapping them together potential energy is dropping and we know from the famous equation e
equals m c squared that when the energy goes down the mass goes down so this is what causes the net
mass decrease of all these nucleons when a nucleus is formed from its raw ingredients so
the plan here is to compute the total mass defect when i compare the ingredients to the entire c14
atom and then we're going to find the energy equivalent of that missing mass and then we're
going to divide by the number of nucleons in the atom and we'll have the binding energy per nucleon
so first the ingredients i have six protons i have eight neutrons and i have six electrons
and again even though we're doing nuclear physics we have to include those electrons because what
we're comparing to is the mass of an entire c14 atom including the electrons so expressing all
these masses in mev per c-squared the numbers look like this and this gives me a grand total of 13
149 mev per c-squared then i want to compare to the mass of the c14 atom but that's normally given
to us in atomic mass units so i have to do this little conversion and the atomic mass units cancel
out there and i'll be left with the right units of mev per c squared and this gives me 13 043
mev per c squared so now i can compute how much mass is missing or the mass defect and this gives
me 106 mev per c squared remember that's a unit of mass so we still need to convert to a unit
of energy here for the missing energy and that's called the total binding energy for this nucleus
and that's given by e equals m c squared in other words we take the mass and this is why these units
are so convenient the mass in mev per c squared and multiply by c squared and the c squareds
cancel and i've got my total binding energy of 106 mev and then finally i get my binding energy
per nucleon so this is just a way of comparing from one nucleus to another how tightly bound
it is you take that total binding energy and divide it up among how many nucleons there are
so in this case i'm taking 106 mev and dividing by the total number of nucleons which was 14
and i get 7.57 mev per nucleon
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