
Einstein's Big Idea


Classroom Activities

Activity Summary
Students consider the meaning of E = mc^{2} by examining how
much of different kinds of fuel would be required to make an imaginary trip to
Pluto. All energy sources are compared to a hypothetical masstoenergy
propulsion system called a photon drive.
Learning Objectives
Students will be able to:
explain the meaning of E = mc^{2}.
state that, in nuclear reactions, massenergy is conserved.
illustrate how kinetic energy can be transferred to other objects.
show that nuclear fission and fusion reactions provide many millions of
times more energy than fossil fuel chemical reactions.
 copy of the "A Trip to Pluto" student handout
(PDF or
HTML)
 copy of the "Planning Your Trip" student handout
(PDF or
HTML)
 copy of the "Reaction Worksheet" student handout
(PDF or
HTML)
 handheld or computer calculator
Background
Albert
Einstein's genius was, in part, due to his ability to see the world as no one
else could. His ideas evolved from the belief that light's speed never changed
and that nothing could exceed the speed of light. Taking this as fact, he
reshaped what he knew about the universe. He came to realize that energy and
matter were equivalent and that one could be transformed into the other using
the speed of light squared as the conversion factor (see "The Legacy of E=
mc^{2}" at
www.pbs.org/nova/einstein/legacy.html
for a brief explanation of the equation). Einstein's equation was
theoretical when he first thought of it, but since its proposal in 1905 it has
been confirmed countless times. Scientists today continue to explore its
implications.
In this activity, students explore the meaning of E = mc^{2} by
considering its effect on the fuel requirements for a trip to Pluto. Given a
series of chemical reactions of fossil fuels and nuclear energy reactions,
students compute how much of each fuel they would need to travel from Earth to
Pluto and back. Students also consider a hypothetical energy sourcea photon
drivewhich would convert matter to vast amounts of energy.
This activity compares chemical reactions to nuclear reactions. Students may
know that mass is always conserved in chemical reactions. The same number and
kinds of atoms of each of the elements exist at the beginning and end of the
chemical reaction. (It is true that since light^{ }and/or heat is often
absorbed or released in a reaction, some mass must have been lost or gained.
But for all practical purposes this is too small to measure.)
In nuclear reactions, energy is exchanged for mass and mass for energy. Nuclei
of atoms are made of protons and neutrons. When you divide a nucleus into
parts, the sum of the masses of the parts is not equal to the whole (the mass
of a nucleus is less than the sum of the masses of the individual protons and
neutrons). This "missing" mass is accounted for by the nuclear binding energy
that holds the nucleus together. The change in binding energy that is
equivalent to the missing mass can be calculated using E =
mc^{2} (nuclear binding energy = Δmc^{2}).
Every single nuclear reaction, regardless of type or complexity, confirms the
truth of E = mc^{2}. In fusion, the energy source that powers
the sun and stars, light nuclei of elements such as the isotopes of hydrogen
combine to form helium nuclei and release energy. This happens because the sum
of the mass of the helium nucleus is less than the mass of the hydrogen nuclei
fused to create it. In fission, the same is also true. The mass of the products
(fission fragments and the neutrons created) is less than the mass of the
original reactants (the uranium nucleus and neutron). Again, E =
mc^{2} predicts the energy released, which is huge. In nuclear
reactions, as in chemical reactions, the total energy and mass is conserved.
Thanks to Einstein, there is a way to balance the books.
The energetic fragments resulting from a nuclear fission reaction collide with
surrounding matter and generate heat. It is important to stress this. Most
students will simply refer to "heat" as the energy released, but that is just
the end product of the process.
Key Terms
fossil
fuel: A substance—such as coal, oil, or natural gas—that comes
from the fossil remains of plants and animals. It can be burned and used as an
energy source.
isotope: A form of an element that has the same number of protons but a
different number of neutrons in its nucleus. Isotopes of an element have the
same atomic number but different atomic weights.
nuclear fission: The splitting of a nucleus into two or more parts
resulting in a large release of energy.
nuclear fusion: The combining of nuclei resulting in a large release of
energy.
radioactive decay: The spontaneous disintegration of a nucleus to form a
different nucleus. A large amount of energy is released during the decay.
Ask students what kind of fuel they would use in their car if they had to take
a trip across the country. What if they had to take a much longer trip—to
Pluto, for example? What type of fuel would be the best to use in a rocket
ship? Discuss with students the different types of fuel available.
Decide whether you wish to do this activity as a class exercise or whether
you want students to work in teams. Distribute student handouts and make sure
students have access to calculators. If working as a class, place the table
that students will be working with (from the "Planning Your Trip" handout) on
the board or computer.
You may need to review scientific notation with students. If you do this as
a class exercise, you can do the calculations for students if you prefer. You
may also want to review eV (electron Volt), the unit of energy used in this
activity. One electron volt is equal to the energy one electron acquires when
traveling across an electric potential difference of 1 volt.
Have students first read the "A Trip to Pluto" handout, and then the
"Planning Your Trip" and "Reaction Worksheet" handouts. After students have
read all the handouts, help them do the calculations for each fuel source. Once
students have completed their calculations, have them answer the questions on
their "Planning Your Trip" handout.
To conclude the activity, examine the table with students and review
the answers to student handout questions. Ask students what surprised them the
most about their results. Students may ask why all spacecraft don't use fission
or fusion engines. Mention that fission reactors are very difficult to scale up
because reactors need moderating rods, water to absorb energy, heavy shielding
to absorb harmful radiation, etc. Even though reactorgrade fuel is less than 2
percent pure, it would take a lot of mass to shield the astronauts from the
radiation that is emitted. Fusion reactions require very high temperatures and
pressures to initiate the reaction and are currently only in experimental
stages of development.
To illustrate the differences between the final results more clearly, ask
students how they might calculate how many gallons of gasoline (instead of
grams) are equivalent to the energy derived from 1.5 grams of pure matter
conversion—a little more than the mass of an average ladybug. (Students
just calculated that 2.3 x 10^{9} grams of gasoline are needed to
supply the 8 x 10^{32} electron volts required for the trip to Pluto.)
To convert grams of gasoline to gallons, students need to find how many grams
there are in a gallon of gasoline and then convert. (A gallon of gasoline
contains 2,720 grams.) The conversion is: 2.3 x 10^{9} grams of
gasoline x 1 gallon/2,720 grams = 8.5 x 10^{5} gallons (850,000
gallons).That is a good indicator of what scientists mean when they claim
Einstein unlocked the power of the atom. Converting the other fuel quantities
from grams to pounds or tons may help students grasp the vast differences in
amounts of fuel needed. (For example, you would need 21 million pounds of wood
to complete the trip!)
As
an extension, have students calculate the weight of other supplies they would
need for the trip (such as food and water). Students can also calculate how big
a spaceship would be required for fuel storage and living quarters, and other
necessities.
The
energy needed to lift a kilogram of mass from Earth's surface and escape the
planet's gravitational field is 6.3 x 10^{7} J/kg or 3.9 x
10^{26} eV/kg.
The
mass of each wood or fossil fuel molecule was obtained by finding the mass of
one mole in grams, then dividing by 6.02 x 10^{23} molecules per mole.
In nuclear reactions, the mass is calculated by summing the number of protons
and neutrons reacted (measured in atomic mass units), then multiplying by 1.7 x
10^{24} grams per amu.
Fuel Type

Mass (g) per Molecule

Energy Released per Molecule (eV)

# Reactants Need for Round Trip

Total Mass (g) of Fuel Required

Wood

3.0 X 10^{22}

25

3.2 X 10^{31}

9.6 X 10^{9}

Coal

2.0 X 10^{23}

2.5

3.2 X 10^{32}

6.4 X 10^{9}

Natural Gas

2.7 X 10^{23}

9.2

8.7 X 10^{31}

2.3 X 10^{9}

Gasoline

1.9 X 10^{22}

66

1.2 X 10^{31}

2.3 X 10^{9}

Fuel Process

Mass (g) per Reaction

Energy Released per Reaction (eV)

# Reactions Need for Round Trip

Total Mass (g) of Fuel Required

Fission

4.0 X 10^{22}

230 x 10^{6}

3.5 X 10^{24}

1400

Fusion

1.7 X 10^{23}

20 x 10^{6}

4.0 X 10^{25}

680

Photon drive

3.4 X 10^{24}

1877 x 10^{6}

4.0 X 10^{23}

1.5

Student Handout Questions
What do all the reactants of wood and fossil fuels have in common? The
reactants of wood and fossil fuels are all carbonbased. Also, each reaction
requires oxygen to begin burning.
Compare the products of wood and fossil fuel reactions with the products of
nuclear reactions. How are they the same? How are they different? The
products of wood and fossil fuel reactions are largely the samewater, carbon
dioxide, and soot (except for natural gas, which burns cleaner than the
others). Nuclear fission has radioactive isotopes as a product (students cannot
tell this from the equation) and different isotopes can occur. Also, neutrons
are often emitted in both fission and fusion reactions.
Compared
to pure uranium fission, how many times more wood would you have to burn to
make the trip to Pluto? How many times more wood compared to a photon drive
engine? Dividing the amount of wood by the amount of uranium, you need 6.9
million times more wood than uranium, and 6.4 billion times more wood than
photon drive fuel!
If Pluto is 5.9 x 10^{9} kilometers from Earth, how long will it
take you, in years, to make the trip to Pluto and return home?
(Assume
a straight line, a constant velocity with no deceleration or acceleration, and
a speed of 12.0 kilometers per second.) Calculation:
Web Sites
NOVA—Einstein's Big Idea
www.pbs.org/nova/einstein
Hear top physicists explain E = mc^{2}, discover the legacy of
the equation, see how much energy matter contains, learn how today's physicists
are working with the equation, read quotes from Einstein, and more on this
companion Web site.
The ABCs of Nuclear Science
www.lbl.gov/abc
Features information about nuclear science, including radioactivity, fission,
fusion, and the structure of the atomic nucleus.
American Museum of Natural History Einstein Exhibit
www.amnh.org/exhibitions/einstein
Provides an overview of Einstein's life, work, philosophy, and legacy.
Einstein Archives Online
www.alberteinstein.info
Offers an archive of Einstein's personal, professional, and biographical papers.
Books
Albert
Einstein and the Theory of Relativity
by Robert Cwiklik. Barron's Educational Series, 1987.
Looks at Einstein's novel ideas about matter, time, space, gravity, and
light.
E = mc^{2}: A Biography of the World's Most Famous Equation
by David Bodanis. Walker, 2000.
Chronicles the lives and work of the innovative thinkers behind each part of
the equation, describes the equation's synthesis by Einstein, and explores the
equation's impact on society.
It Must Be Beautiful: Great Equations of Modern Science
by Graham Farmelo, ed. Granta Books, 2002.
Presents the great equations of modern science for the lay reader.
The "A Trip to Pluto" activity aligns with the following National Science
Education Standards (see books.nap.edu/html/nses)
and Principles and Standards for School Mathematics (see
standards.nctm.org/document/index.htm).
Grades 58
Science Standard
Physical Science
Mathematics Standard
Number and Operations
Grades 912
Science Standard
Physical Science
 Structure of atoms
 Chemical reactions
 Conservation of energy and the increase in disorder
Mathematics Standard
Number and Operations
Classroom Activity Author
Jeff
Lockwood taught high school astronomy, physics, and Earth science for 28 years.
He has authored numerous curriculum projects and has provided instruction on
curriculum development and science teaching methods for more than a decade.

Getting to Pluto (and Back)
The
figure used in this activity as the energy needed to make a round trip to
Pluto—8 x 10^{32} eV—attempts to consider the escape
velocity, deceleration, and acceleration needed to make the trip. It does not
take into account other, more complex aspects (such as variability in speed and
trajectory) that occur during actual space travel. There are many options for
calculating trip energy to Pluto and back. The trip energy used for this
activity is based
on
needing an estimated 955 million joules per kilogram of mass, or 6.0 x
10^{27} electron volts per kilogram, to complete the journey. Assuming
a spacecraft with a mass of 135,000 kilograms brings the total energy for the
trip to 8 x 10^{32} eV.

