INST 240 Revolutions Lecture 11 Nuclear Energy

1. INST 240RevolutionsLecture 11 Nuclear Energy

2. The spacetime momentum vector Ptime • Total length: mc • Length in time direction: γmc • Length in space direction: γmv = γ p mc γmc γmv Pspace

3. Non-relativistic limit • At low velocities (v << c): Relativistic Physics E = γmc2 p = γmv “Classical” Physics: E = ½mv2 p = mv → mc2 + ½m v2+ small corrections → mv + small corrections

4. Conserved Energy • Etotal relativistic= Ptime c = mc2 + ½m v2 • The second term is the kinetic energy! • We know that in non-relativistic processes it is (often) conserved • But here, the conserved energy has an additional term that is left even when v0 Erest= mc2

5. That’s it! • So Einstein’s famous formula Erest= mc2 turns out to be the energy of an object measured by an observer at rest with respect to the object • If the object is at rest, it does not have kinetic energy (duh!), but a moving observer will not agree

6. Agreement • All observers agree on the length of the energymomentum vector (mc) • All observers agree that the total relativistic energy is conserved Etotal relativistic= mc2 + ½m v2 = constant • Observers will disagree why it is conserved!

7. Space momentum & Energy divided by c form a vector which has Einstein’s blessing • Momentum is conserved, energy is conserved • Units of momentum are units of energy divided by c

8. Space&time and Energy&momentum diagrams Energy time Momentum space

9. Spacetime and Energymomentum diagrams Energy/c c time space Momentum

10. Should energy and momentum have bigger or smaller values in a frame moving wrt the object? • A: Both have bigger values • B: Both have smaller values • C: Energy stays the same • D: Momentum stays the same • E: energy gets bigger, momentum smaller • F: momentum gets bigger, energy gets smaller

11. Implications • “Objects have an intrinsic energy equivalent to their rest mass” • “Energy is equivalent to mass” • E = mc2 (Physicists actually don’t use this form of the equation, but it’s catchy)

12. Einstein Original Work (1906) • “Das Prinzip von der Erhaltung der Schwerpunktsenergie und die Trägheit der Energie”(Only 7 pages!) • “Schreibt man also jeglicher Energie die träge Masse E/V2 zu, so gilt (…) das Prinzip von der Erhaltung der Bewegung des Schwerpunkts auch auch für Systeme in denen electromagnetische Prozesse vorkommen.” • With träge Masse as the mass and V=c, we have m= E/c2

13. Implications • Objects have mass. • Objects that store extra energy have extra mass. • Objects that have given up all their energy have less mass.

14. Which has more mass? A hot or a cold Potatoe? • A: Same • B: Hot one • C: Cold one

15. Implications ... all the bits after the explosion A little bit heavier than...

16. Implications ... all the bits after the explosion A little bit heavier than... total mass = mass of component bits + mass due to “available energy”

17. How much heavier? Take a 1 kg block of TNT. How much heavier is it than it’s component parts?  Worksheet #5 Trinitrotoluene (TNT)

18. How much heavier? TNT releases 0.65 Calories of energy per gram. c = 3x108 m/s Trinitrotoluene (TNT) E = mc2 energy in Joules mass in kg

19. How much heavier? - Worksheet TNT releases 0.65 Calories of energy per gram. E = mc2 • 1 kg = 1000 g • 1 Calorie = 4200 Joules • 1 kg TNT releases E =2730 kJ = mc2 • m = 2,730,000 J/ (300,000,000 m/s)2 • = 2.73/9 x 10^6 x 10^-16 kg • = 3 x 10^-11 kg

20. How much heavier? 1.000000000000 kg 1.000000000050 kg Note that it has the same number of atoms! The mass comes from the bonds between the atoms

21. Why should we care? • Can understand energy production in Sun, stars • Can produce power by harvesting energy stored in mass, binding energy • Can construct powerful bombs, too, unfortunately

22. How do we know how much energy the Sun produces each second? • The Sun’s energy spreads out in all directions • We can measure how much energy we receive on Earth • At a distance of 1 A.U., each square meter receives 1400 Watts of power (the solar constant) • Multiply by surface of sphere of radius 149.6 bill. meter (=1 A.U.) to obtain total power output of the Sun

23. Energy Output of the Sun • Total power output: 4  1026 Watts • The same as • 100 billion 1 megaton nuclear bombs per second • 4 trillion trillion 100 W light bulbs • $10 quintillion (10 billion billion) worth of energy per second @ 9¢/kWh • The source of virtually all our energy (fossil fuels, wind, waterfalls, …) • Exceptions: nuclear power, geothermal

24. Where does the Energy come from? • Anaxagoras (500-428 BC): Sun a large hot rock – No, it would cool down too fast • Combustion? • No, it could last a few thousand years • 19th Century – gravitational contraction? • No! Even though the lifetime of sun would be about 100 million years, geological evidence showed that Earth was much older than this

25. What process can produce so much power? • For the longest time we did not know • Only in the 1930’s had science advanced to the point where we could answer this question • Needed to develop very advanced physics: quantum mechanics and nuclear physics • Virtually the only process that can do it is nuclear fusion

26. Nuclear Fusion • Atoms:electrons orbiting nuclei • Chemistry deals only with electron orbits (electron exchange glues atoms together to from molecules) • Nuclear power comes from the nucleus • Nuclei are very small • If electrons would orbit the statehouse on I-270, the nucleus would be a soccer ball in Gov. Kasic’s office • Nuclei: made out of protons (el. positive) and neutrons (neutral)

27. Atom:Nucleus and Electrons The Structure of Matter Nucleus: Protons and Neutrons (Nucleons) Nucleon: 3 Quarks | 10-10m | | 10-14m | |10-15m|

28. Basic Nuclear Physics • The strong force between protons and neutrons is short ranged – think velcro! • Each particle “sticks” only to its neighbors • The electrical repulsion between protons is weaker but long ranged • Each proton repels every other one • Bigger nuclei have more trouble holding together – repulsion eventually wins!

29. Nuclear fusion reaction • In essence, 4 hydrogen nuclei combine (fuse) to form a helium nucleus, plus some byproducts (actually, a total of 6 nuclei are involved) • Mass of products is less than the original mass • The missing mass is emitted in the form of energy, according to Einstein’s famous formula: E = mc2 (the speed of light is very large, so there is a lot of energy in even a tiny mass)

30. Small nuclei (like hydrogen) can “fuse” to form larger nuclei (helium, etc.), releasing energy • Basic reaction: • 4H  He + 2e+ + 2γ + 2ν • where • e+ is a positron (anti-particle of the electron) • γ is a gamma-ray photon • ν is a “neutrino” • Most of the energy released is carried by the positrons and gamma rays Nuclear Fusion 4 1H (protons) 4He

31. Hydrogen fuses to Helium Start: 4 + 2 protons End: Helium nucleus + neutrinos Hydrogen fuses to Helium

32. Why should the fuse? Why does a ball roll downhill? To minimize energy! Iron (Fe) weighs less per proton than anything else Each proton in Uranium weighs more Each proton in hydrogen weighs more