Energy-Mass Equivalence
Principle
By Albert Einstein
E = mc2
E = total energy of a system
M = total mass of the system
C = speed of light
If an object is not moving then:
Eo = moc2
Eo is the rest energy and mo is the rest
mass
Example: I put my sister’s 200g pet gerbil into a
thermonuclear flux capacitor which converts the
gerbil into pure energy. How much energy do I
get out?
Eo = moc2
Eo = 0.200(3.0x108 )2
Eo = 1.8x1016 J
One gerbil is enough energy to power the entire
country for a little while
Relativistic Considerations
If the object is moving at relativistic
speeds, then mass dilates:
m =γmo
So:
E = mc2 becomes
E = γmoc2
Relativisitic Considerations
Total E is the rest E plus Ek:
E = Eo + Ek
mc2 = moc2 + Ek
Ek = mc2 - moc2
Ek = γmoc2 - moc2
Ek = moc2 (γ – 1)
Newton’s formula for Ek works well:
Ek = ½ mv2
But it breaks down at very high speeds. In
that case, use Einstein’s version.
Einstein’s formula is the same as Newton’s
formula but it is harder to work with.
Sample Problem
A 400kg car is traveling at 30m/s. Find the
kinetic energy of the car using Newton’s
formula and Einstein’s formula.
Newton:
Ek = ½ mv2
Ek = ½ (400)(30)2
Ek = 1.80x105 J
Einstein:
Ek = moc2 (γ – 1)
At v = 30m/s, γ = 1.000000000000005
Ek = 400(3.0x108)2 (5x10-15)
Ek = 1.80x105 J
Same as Newton, but a lot more tricky.
Nuclear Fusion
Helium-3 is made of 2 protons
and 1 neutron.
proton mass = 1.0072764668 amu
= 1.6726 x 10-27 kg
neutron mass = 1.0086649156
amu = 1.6749 x 10-27 kg
electron mass = 0.0005446623
amu = 9.1093 × 10-31 kg
Total mass = 3.0243071738 amu
Nuclear Fusion
Sum of parts of He-3 is 3.0243071738 amu
Actual mass of He-3 is 3.0160293191 amu
The Helium has less mass than its component
parts! Where does the extra mass go?
Nuclear Fusion
All elements are made of protons and
neutrons etc that are bound together.
Once they are bound together, they lose
mass – really they lose energy. The
energy lost is called the “binding energy”.
To split the atoms apart, you’ll need to
inject this energy back into the atom.
The binding energy of He-3 is:
3.0243071738 amu - 3.0160293191 amu
= 0.0082778547 amu
This energy is given off as a gamma ray.
2P + 1N  He3 + γ
The fusion of hydrogen to make helium
produces energy. This is the process that
makes the sun hot and bright.
Nuclear Fission
Fission is the reverse process of fusion.
Splitting Helium takes energy, so it is not a
useful process.
As elements get heavier, it takes more and
more energy to keep them together.
Some elements are too massive to stay in
one piece, so they naturally fall apart.
These are radioactive elements.
Uranium is one of these heavy elements.
It has 235 nucleons (protons and
neutrons) and readily falls apart.
Unlike Helium, Uranium takes energy to
keep it together.
When uranium 235 fissions, it splits into
Krypton, Barium and 3 neutrons. It also
releases mass in the form of a gamma ray.
U  Kr + Ba + 3n + γ
This process is called nuclear fission.