Hi. It's Mr. Andersen and this is AP Physics essentials video 12. It is on E=mc2. This
is maybe the most famous equation in all of physics. It was developed by Albert Einstein
in 1905. And what it really shows is energy-mass equivalence. In others that energy can be
converted into mass. And mass can be converted back into energy. And this equation tells
us how much energy is going to be released in that process. And so there are a couple
of conservation rules that you are probably familiar with. Number 1 is the conservation
of mass. And so if I take a piece of wood for example and chop it in half, the mass
of those 2 pieces is equal to the mass of the original piece of wood. But if I burn
that wood, I am going to create a lot of things like water. I am going to create carbon dioxide.
But the mass of that all of that is going to be equal to the wood itself as well. So
we can not create or destroy matter. There is also a rule of conservation of energy.
So the energy in that wood used to be energy inside a tree, used to be energy in the sun
that was delivered to the tree through photosynthesis. But we do not create energy. We do not destroy
it. But what we learned in the last century is that mass can be converted into energy
and energy can be converted back into mass. And so we have kind of adjusted that conservation
rule. And it is the conservation of mass-energy. And we refer to those as the same thing. Mass
is energy. Energy is mass. They are essentially the same thing. And this equation allows us
to see how we can convert between the two. And so the three things in this equation are
energy, mass and then the speed of light. So if I want to figure out how much energy
is in matter, I can just multiply it times the speed of light squared. And so what is
the speed of light? Well it is a really large number. And if I square a really large number
I get an even larger number. And so there is a huge amount of energy locked in a small
amount of matter. And so Einstein realized this and it lead to things like atomic bombs
and nuclear energy. And so let me give you a couple of examples of this conversion of
mass to energy. And so let's start with carbon 12. And that is what we base our atomic mass
unit on. In other words how do we define an atomic mass unit? It is essentially 1/12 the
mass of carbon 12. And so the mass of carbon 12 is 12.000 atomic mass units. It is the
standard. But let's say I deconstruct, I take all those protons, neutrons and electrons
apart. And then we mass them individually. Well you would think conservation of mass
is going to be the same thing. But let's do that. Let's break apart those electrons. They
have a mass of 0.00548 atomic mass units. If I multiple that times the 6 electrons this
is the total mass of electrons. I can do the same thing for the protons and the neutrons
that I have. And then if I add all of these up I get a number that is larger than the
number I had before. In other words if you break apart an atom, if you break it into
its constituent parts it actually has more mass divided then it did when it was all together.
And so where did the mass come from? And where will the mass go when we convert it back into
that atom? Well it is used in binding energy of the atom itself. And so when we convert
that back into carbon 12 again, that mass is gone, but it has been converted into energy
that is holding that atom together. Another place we could see that would be in a particle
accelerator. And so the large Hadron collider is really large. It is 17 miles around. And
so what they are doing is accelerating protons. And they are going much faster than this.
And so this proton takes 1 second to move around. In the large Hadron collider it is
going to go around, in 1 second, 11,000 times. And so it is approaching the speed of light.
It is like 3 meters per second less than the speed of light. But it will never get to the
speed of light. Why is that? Well as the proton is moving, if we want to accelerate it we
have to put energy into it. And a lot of that energy ends up being converted into mass.
And so the proton gets heavier and heavier and heavier. And eventually it would move
towards infinite mass. And we would require infinite energy to speed it to the speed of
light. And so that is kind of a universal speed limit. And so again in this case we
are converting energy into mass. They are convertible. And so we could use this equation
to figure out how much energy it is going to take. And the math is very, very simple.
Let's say I had a certain amount of uranium. So we have 5 kilograms of uranium 235. And
I want to see how much energy is in that. Well we are going to be able to solve for
energy in Joules, just using the mass of that uranium times the speed of light squared.
Now it would be the same amount of energy in 5 kilograms of you. It doesn't matter what
the matter is, there is going to be energy inside it. And so I set up the equation like
this and then I just plug in my values. And so we are putting 5 kilograms in here. The
speed of light is 3.0 times 10 to the 8 meters per second. Again I have to square that. And
so I get an incredibly large number of joules. We could convert that into watts if we wanted
to figure out how long we could light a light bulb for. And what you find is this small
amount uranium would be able to light a light bulb for millions and millions of years. And
so there is a huge amount of energy locked in that matter. Now obviously we would lose
energy. There would be energy lost along the way but it is a really really large number.
And so did you learn why the theory of conservation of mass was replaced by the theory of conservation
of mass energy? It is because mass can be converted into energy and vice versa. And
I hope that was helpful.