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Einstein's Big Idea

Classroom Activities

Learning Objective | Materials | Background | Procedure | Activity Answer | Links & Books | Standards  Print this Teacher's Guide (PDF, 37 pages)

Activity Summary
Students consider the meaning of E = mc² 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 mass-to-energy propulsion system called a photon drive.

Learning Objectives
Students will be able to:

• explain the meaning of E = mc².

• state that, in nuclear reactions, mass-energy 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)
• hand-held 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= mc²" 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 = mc² 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 source-a photon drive-which 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 = mc² (nuclear binding energy = Δmc²).

Every single nuclear reaction, regardless of type or complexity, confirms the truth of E = mc². 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 = mc² 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.

1. 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.

2. 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.

3. 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.

4. 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.

5. 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 reactor-grade 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.

6. 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 10⁹ grams of gasoline are needed to supply the 8 x 10³² 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 10⁹ grams of gasoline x 1 gallon/2,720 grams = 8.5 x 10⁵ 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!)

7. 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 10⁷ J/kg or 3.9 x 10²⁶ 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 10²³ 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.

Student Handout Questions

1. What do all the reactants of wood and fossil fuels have in common? The reactants of wood and fossil fuels are all carbon-based. Also, each reaction requires oxygen to begin burning.

2. 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 same-water, 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.

3. 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!

4. If Pluto is 5.9 x 10⁹ 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 = mc², 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 = mc²: 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 5-8
Science Standard
Physical Science

• Transfer of energy

Mathematics Standard
Number and Operations

Grades 9-12
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.