5/26/2011
One other misconception
E = mc2
Probably the most famous scientific
equation of all time, first derived by
Einstein is the relationship E = mc2.
This tells us the energy corresponding to a mass, m,
at rest. What this means is that when mass disappears,
for example in a nuclear fission process, this amount of
energy must appear in some other form. It also tells us
the total energy of a particle of mass m sitting at rest.
What E = mc2 doesn’t mean:
Many people think that E = mc2 means matter,
when traveling at the speed of light
transforms into pure energy.
THIS IS NOT TRUE
1. Matter can’t travel at the speed of light.
2. The speed of light squared is not a velocity.
All E = mc2 means is that mass and energy are
two sides of the same coin. They are the
same thing.
E = mc2
"It followed from the special theory
of relativity that mass and energy are
both but different manifestations of the
same thing -- a somewhat unfamiliar
conception for the average mind.
Furthermore, the equation E is equal to
m c-squared, in which energy is put equal to mass,
multiplied by the square of the velocity of light, showed that
very small amounts of mass may be converted into a very
large amount of energy and vice versa. The mass and
energy were in fact equivalent, according to the formula
mentioned above. This was demonstrated by Cockcroft and
Walton in 1932, experimentally."
Energy
• Rest energy - The energy a particle has by simply being
a particle (having mass). Also called mass-energy
Erest = mc2
• Kinetic Energy - Energy due to the movement of the
2
particle
KE =
mc
− mc 2
1− (v 2 /c 2 )
• Total Energy - The total energy a particle has due to
the fact it is a particle (rest energy) and the fact that it
is moving (kinetic energy)
E total = E rest + KE =
mc 2
1− (v 2 /c 2 )
Example: How much work is required to
accelerate an electron from rest to a
speed of 0.900c? (melectron = 9.11x10-31kg)
W = ΔKE = KEf – KEi
W = KE f =
W = KE f =
mc 2
− mc 2
v2
1− 2
c
(9.11x10−31 )(3.0 x108 )2
1−
0.9002 c 2
c2
− (9.11x10−31 )(3.0 x108 ) 2
W = 1.06 x10−13 J
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5/26/2011
Example: A nickel has a mass of 5.00 g. If this mass
could be converted to electric energy, how long
would it keep a 100. W light bulb lit? (remember 1 W
E = mc 2 = 1 J/sec)
rest
Erest = (0.005kg )(3.0 x108 m / s ) 2
Erest = 4.5 x1014 J
1sec
4.5 x1014 J ×
= 4.5 x1012 sec
100 J
1 year
= 143, 000 years !
4.5 x1012 sec×
3.14 x107 sec
Fusion & Fission processes take advantage of a
particle’s rest energy (E = mc2) & change mass into
energy.
Fusion processes in stars fuse hydrogen atoms
together to form helium atoms according to the
following (simplified) process:
41H -> 4He + energy
• If one mole of 1H = 1.007824 g
• & one mole of 4He= 4.002603 g,
A. how much mass is lost in this process?
B) Where did this mass go/what did it turn in to?
Energy, specifically light & heat
C) How much energy was created when 2.8793x10-5
kg of mass turned into energy?
E = mc 2
E = (2.8793×10 −5 kg)(3.0 ×10 8 m / s) 2
Example: A 10 kg piece of thorium at rest
suddenly decays into an 8 kg sample of
radon that is traveling very quickly.
A) Can energy just appear out of nowhere? If
not, where did the radon’s kinetic energy come
from?
The sample lost 2.0 kg of mass and
gained KE. The mass must have turned
into KE.
E = 2.59137 ×1012 J
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5/26/2011
B) How much kinetic energy
did the radon sample gain?
E = mc2
E = (2.0kg)(3.0x108m/s)2
E = 1.8x1017 J
C) What is the new
velocity of the radon
sample?
(remember: mass/energy is always conserved)
mic
2
2
Ei = E f
1− (vi / c 2 )
=
m f c2
2
1− (v f /c 2 )
(10.0kg)c 2
(8.0kg)c 2
=
2
1− (0 2 / c 2 )
1− (v f c 2 / c 2 )
3