Hi. It’s Mr. Andersen. And this is AP Physics
essentials video 89. It is on mass-energy
equivalence. Remember one of the greatest
laws in physics is the law of conservation
of energy. So the energy stays the same in
a system or within an object. But remember
the matter, the mass inside that system also
has energy. Einstein showed us that using
the equation E=mc2. So when we see certain
interactions, let’s look at the fission
of uranium 235, we are releasing energy. And
so uranium 235 is relatively unstable. If
we hit it with a neutron it becomes uranium
236, which is highly unstable. And it will
quickly break apart into krypton 92, barium
141 and then 3 other neutrons are given off.
If another neutron hits another uranium 235
that happens again and that could happen again
and again. So we get this chain reaction.
And so those neutrons flying around have a
huge amount of energy. It came from the matter
itself. And so we could tap that energy. So
in a nuclear reactor we could heat up the
water surrounding the uranium. It then makes
steam which makes electricity in a generator.
We cool down that water and then we recycle
it over and over again. And so the conservation
of energy always occurs in an object or a
system over time. The energy stays the same.
But remember any object or system is going
to have matter which has mass. And that can
be converted into energy and back again using
E=mc2. So in this video I am going to show
you how to calculate the amount of energy
that comes from mass in an interaction like
that. And the example we will give is fission.
And so to talk about E=mc2 let me give you
an example of that. This is carbon 12. Remember
carbon 12 is the standard. It is the standard
upon which we figure out an atomic mass unit
is. It has exactly 12 atomic mass units inside
it. 6 protons. 6 neutrons. 6 electrons. But
if I were to take that and deconstruct that
carbon 12 into its 6 electrons, protons, neutrons
we know what the atomic mass of each of those
is. So it would be 6 times the atomic mass
unit of the electron. 6 times that of the
proton. 6 times that of the neutron. If I
add up all of the individual masses of those
subatomic particles what I get is a larger
number atom then when it is all put together.
And so what happens when we break it apart
to that energy, it becomes mass. And as we
build it back again it becomes energy. So
where did it go? The energy is in the binding
energy. It is the energy that is holding that
nucleus together with all those protons inside
it. And so as we convert matter into energy
and back again, energy is going to be conserved.
And so let’s go through that energy of fission
again. We get the arrival of a neutron and
then it breaks it down into barium, krypton.
And so what I am going to do is show you how
much energy is released in this one reaction.
And so what you want to try to do is calculate
it. You could pause the video right now and
calculate it, try it on your own. You will
have to know a few things. You have to know
the atomic mass units of the uranium 235.
Atomic mass units of the neutrons, the barium
and the krypton. But all I am going to do
is figure out the mass change and then I am
going to use E=mc2 to figure out the amount
of energy. If you are totally lost, let me
show you how I would do that. So before the
reaction we had two things. We had the uranium
235 and the neutron. So I am going to figure
out the mass of each of those together. So
I am simply going to add those up and this
is going to be the mass before. I then figure
out the mass after. So what do we get after?
We get the barium, the krypton and the three
neutrons. And so I am going to add those up,
the mass of all of those. And you can see
that we have a lower mass after. Now where
did that mass go? It became the energy. And
so how much energy? It is going to be 0.189
units. So that is the mass change. And if
we want to figure out the amount of energy
then we are going to have to use Einstein’s
equation, E=mc2. Remember the units are going
to be important. So energy is going to be
measured in joules, mass in kilograms and
then the speed of light is going to be C.
And so I set up my equation like this. You
can see one problem right away and that is
that my units are in atomic mass units, but
I have to use kilograms right here. And so
we have got a conversion, one atomic mass
unit equals 1.66605x10-27 kilograms. And so
I am going to have to use that to figure out
my mass. So I have converted it to kilograms
right here. And then I just simply solve that.
And this is going to be the amount of joules
of energy that are produced when we lose the
mass in that fission reaction. Now it does
not seem like much energy, but think how many
atoms are going to be found in, for example,
a kilogram of uranium. There is a huge amount
of joules of energy that are being released
when we have this fission reaction. And so
did you learn to apply the conservation of
mass and conservation of energy to solve a
simple problem? 
I hope so. And I hope that was helpful.
