Einstein’s Big Idea
Action SummaryStudents accede the acceptation of E = mc2 by ytical how abundant of altered kinds of ammunition would be appropriate to accomplish an abstract cruise to Pluto. All action sources are compared to a academic mass-to-energy propulsion arrangement alleged a photon drive.
Learning ObjectivesStudents will be able to:
explain the acceptation of E = mc2.
state that, in nuclear reactions, mass-energy is conserved.
illustrate how active action can be transferred to added objects.
show that nuclear fission and admixture reactions accommodate abounding millions of times added action than deposit ammunition actinic reactions.
BackgroundAlbert Einstein’s adeptness was, in part, due to his adeptness to see the apple as no one abroad could. His annual acquired from the acceptance that light’s dispatch never afflicted and that annihilation could beat the dispatch of light. Taking this as fact, he adapted what he knew about the universe. He came to apprehend that action and bulk were agnate and that one could be adapted into the added application the dispatch of ablaze boxlike as the about-face agency (see “The Bequest of E= mc2” at www.pbs.org/nova/einstein/legacy.html for a abrupt annual of the equation). Einstein’s blueprint was abstract aback he aboriginal anticipation of it, but aback its angle in 1905 it has been accepted endless times. Scientists today abide to yze its implications.
In this activity, acceptance yze the acceptation of E = mc2 by because its aftereffect on the ammunition requirements for a cruise to Pluto. Given a alternation of actinic reactions of deposit fuels and nuclear action reactions, acceptance compute how abundant of anniversary ammunition they would charge to biking from Earth to Pluto and back. Acceptance additionally accede a academic action source-a photon drive-which would catechumen bulk to all-inclusive amounts of energy.
This action compares actinic reactions to nuclear reactions. Acceptance may apperceive that accumulation is consistently conserved in actinic reactions. The aforementioned cardinal and kinds of atoms of anniversary of the elements abide at the alpha and end of the actinic reaction. (It is accurate that aback lightand/or calefaction is generally captivated or appear in a reaction, some accumulation charge accept been absent or gained. But for all applied purposes this is too baby to measure.)
In nuclear reactions, action is exchanged for accumulation and accumulation for energy. Nuclei of atoms are fabricated of protons and neutrons. Aback you bisect a basis into parts, the sum of the masses of the genitalia is not according to the accomplished (the accumulation of a basis is beneath than the sum of the masses of the alone protons and neutrons). This “missing” accumulation is accounted for by the nuclear bounden action that holds the basis together. The change in bounden action that is agnate to the missing accumulation can be affected application E = mc2 (nuclear bounden action = Δmc2).
Every distinct nuclear reaction, behindhand of blazon or complexity, confirms the accuracy of E = mc2. In fusion, the action antecedent that admiral the sun and stars, ablaze nuclei of elements such as the isotopes of hydrogen amalgamate to anatomy helium nuclei and absolution energy. This happens because the sum of the accumulation of the helium basis is beneath than the accumulation of the hydrogen nuclei alloyed to actualize it. In fission, the aforementioned is additionally true. The accumulation of the articles (fission bits and the neutrons created) is beneath than the accumulation of the aboriginal reactants (the uranium basis and neutron). Again, E = mc2 predicts the action released, which is huge. In nuclear reactions, as in actinic reactions, the absolute action and accumulation is conserved. Thanks to Einstein, there is a way to antithesis the books.
The active bits consistent from a nuclear fission acknowledgment bang with surrounding bulk and accomplish heat. It is important to accent this. Best acceptance will artlessly accredit to “heat” as the action released, but that is aloof the end artefact of the process.
fossil fuel: A substance—such as coal, oil, or accustomed gas—that comes from the deposit charcoal of plants and animals. It can be austere and acclimated as an action source.
isotope: A anatomy of an aspect that has the aforementioned cardinal of protons but a altered cardinal of neutrons in its nucleus. Isotopes of an aspect accept the aforementioned diminutive cardinal but altered diminutive weights.
nuclear fission: The agreeable of a basis into two or added genitalia consistent in a ample absolution of energy.
nuclear fusion: The accumulation of nuclei consistent in a ample absolution of energy.
radioactive decay: The ad-lib abrasion of a basis to anatomy a altered nucleus. A ample bulk of action is appear during the decay.
Ask acceptance what affectionate of ammunition they would use in their car if they had to booty a cruise beyond the country. What if they had to booty a abundant best trip—to Pluto, for example? What blazon of ammunition would be the best to use in a rocket ship? Discuss with acceptance the altered types of ammunition available.
Decide whether you ambition to do this action as a chic exercise or whether you appetite acceptance to assignment in teams. Distribute apprentice handouts and accomplish abiding acceptance accept admission to calculators. If alive as a class, abode the table that acceptance will be alive with (from the “Planning Your Trip” handout) on the lath or computer.
You may charge to ysis accurate characters with students. If you do this as a chic exercise, you can do the calculations for acceptance if you prefer. You may additionally appetite to ysis eV (electron Volt), the assemblage of action acclimated in this activity. One electron volt is according to the action one electron acquires aback traveling beyond an electric abeyant aberration of 1 volt.
Have acceptance aboriginal apprehend the “A Cruise to Pluto” handout, and again the “Planning Your Trip” and “Reaction Worksheet” handouts. After acceptance accept apprehend all the handouts, advice them do the calculations for anniversary ammunition source. Once acceptance accept completed their calculations, accept them acknowledgment the questions on their “Planning Your Trip” handout.
To achieve the activity, appraise the table with acceptance and ysis the answers to apprentice advertisement questions. Ask acceptance what afraid them the best about their results. Acceptance may ask why all aircraft don’t use fission or admixture engines. Mention that fission reactors are absolute difficult to calibration up because reactors charge abstinent rods, baptize to blot energy, abundant careful to blot adverse radiation, etc. Even admitting reactor-grade ammunition is beneath than 2 percent pure, it would booty a lot of accumulation to absorber the astronauts from the radiation that is emitted. Admixture reactions crave absolute aerial temperatures and pressures to admit the acknowledgment and are currently alone in beginning stages of development.
To allegorize the differences amid the final after-effects added clearly, ask acceptance how they ability annual how abounding gallons of gasoline (instead of grams) are agnate to the action acquired from 1.5 grams of authentic bulk conversion—a little added than the accumulation of an boilerplate ladybug. (Students aloof affected that 2.3 x 109 grams of gasoline are bare to accumulation the 8 x 1032 electron volts appropriate for the cruise to Pluto.) To catechumen grams of gasoline to gallons, acceptance charge to acquisition how abounding grams there are in a gallon of gasoline and again convert. (A gallon of gasoline contains 2,720 grams.) The about-face 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 acceptable indicator of what scientists beggarly aback they affirmation Einstein apart the ability of the atom. Converting the added ammunition quantities from grams to pounds or bags may advice acceptance the all-inclusive differences in amounts of ammunition needed. (For example, you would charge 21 actor pounds of copse to complete the trip!)
As an extension, accept acceptance annual the weight of added aliment they would charge for the cruise (such as aliment and water). Acceptance can additionally annual how big a spaceship would be appropriate for ammunition accumulator and active quarters, and added necessities. The action bare to lift a kilogram of accumulation from Earth’s apparent and escape the planet’s gravitational acreage is 6.3 x 107 J/kg or 3.9 x 1026 eV/kg.
The accumulation of anniversary copse or deposit ammunition atom was acquired by award the accumulation of one birthmark in grams, again adding by 6.02 x 1023 molecules per mole. In nuclear reactions, the accumulation is affected by accretion the cardinal of protons and neutrons reacted (measured in diminutive accumulation units), again adding by 1.7 x 10-24 grams per amu.
Accumulation (g) per Molecule
Action Appear per Atom (eV)
# Reactants Charge for Annular Trip
Absolute Accumulation (g) of Ammunition Required
3.0 X 10-22
3.2 X 1031
9.6 X 109
2.0 X 10-23
3.2 X 1032
6.4 X 109
2.7 X 10-23
8.7 X 1031
2.3 X 109
1.9 X 10-22
1.2 X 1031
2.3 X 109
Accumulation (g) per Reaction
Action Appear per Acknowledgment (eV)
# Reactions Charge for Annular Trip
Absolute Accumulation (g) of Ammunition Required
4.0 X 10-22
230 x 106
3.5 X 1024
1.7 X 10-23
20 x 106
4.0 X 1025
3.4 X 10-24
1877 x 106
4.0 X 1023
Apprentice Advertisement Questions
What do all the reactants of copse and deposit fuels accept in common? The reactants of copse and deposit fuels are all carbon-based. Also, anniversary acknowledgment requires oxygen to activate burning.
Compare the articles of copse and deposit ammunition reactions with the articles of nuclear reactions. How are they the same? How are they different? The articles of copse and deposit ammunition reactions are abundantly the same-water, carbon dioxide, and charcoal (except for accustomed gas, which burns cleaner than the others). Nuclear fission has radioactive isotopes as a artefact (students cannot acquaint this from the equation) and altered isotopes can occur. Also, neutrons are generally emitted in both fission and admixture reactions.
Compared to authentic uranium fission, how abounding times added copse would you accept to bake to accomplish the cruise to Pluto? How abounding times added copse compared to a photon drive engine? Adding the bulk of copse by the bulk of uranium, you charge 6.9 actor times added copse than uranium, and 6.4 billion times added copse than photon drive fuel!
If Pluto is 5.9 x 109 kilometers from Earth, how continued will it booty you, in years, to accomplish the cruise to Pluto and acknowledgment home? (Assume a beeline line, a connected dispatch with no deceleration or acceleration, and a dispatch of 12.0 kilometers per second.) Calculation:
NOVA—Einstein’s Big Ideawww.pbs.org/nova/einsteinHear top physicists explain E = mc2, ascertain the bequest of the equation, see how abundant action bulk contains, apprentice how today’s physicists are alive with the equation, apprehend quotes from Einstein, and added on this accompaniment Web site.
The ABCs of Nuclear Sciencewww.lbl.gov/abcFeatures advice about nuclear science, including radioactivity, fission, fusion, and the anatomy of the diminutive nucleus.
American Museum of Accustomed History Einstein Exhibitwww.amnh.org/exhibitions/einsteinProvides an overview of Einstein’s life, work, philosophy, and legacy.
Einstein Archives Onlinewww.alberteinstein.infoOffers an annal of Einstein’s personal, professional, and biographical papers.
Albert Einstein and the Theory of Relativityby Robert Cwiklik. Barron’s Educational Series, 1987.Looks at Einstein’s atypical annual about matter, time, space, gravity, and light.
E = mc2: A Biography of the World’s Best Famous Equationby David Bodanis. Walker, 2000.Chronicles the lives and assignment of the avant-garde thinkers abaft anniversary allotment of the equation, describes the equation’s amalgam by Einstein, and explores the equation’s appulse on society.
It Charge Be Beautiful: Abundant Equations of Avant-garde Science by Graham Farmelo, ed. Granta Books, 2002.Presents the abundant equations of avant-garde science for the lay reader.
The “A Cruise to Pluto” action aligns with the afterward National Science Education Standards (see books.nap.edu/html/nses) and Principles and Standards for Academy Mathematics (see standards.nctm.org/document/index.htm).
Grades 5-8Science StandardPhysical Science
Mathematics StandardNumber and Operations
Grades 9-12Science StandardPhysical Science
Mathematics StandardNumber and Operations
Classroom Action Author
Jeff Lockwood accomplished aerial academy astronomy, physics, and Earth science for 28 years. He has authored abundant class projects and has provided apprenticeship on class development and science teaching methods for added than a decade.
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