Lecture on the Atomic Nucleus

1. Lecture on the Atomic Nucleus www.assignmentpoint.com

2. The Atomic Nucleus • Two ways to rearrange nuclei and get energy: • Fission • produces energy by breaking up massive nuclei like Uranium into less massive nuclei like Barium and Krypton • A-bombs, nuclear reactors • needs Uranium 235, Plutonium 238 • Problem: no Uranium or Plutonium on the Sun • Fusion • produces energy by combining light nuclei like Hydrogen to make more massive nuclei like Helium. • H-bomb, tokamak, internal confinement fusion • Sun has lots of Hydrogen!! www.assignmentpoint.com

3. How Does Fusion Work? • Nuclear fusion: • a process by which two light nuclei combine to form a single larger nucleus. • However: nuclei are positively charged • Like charges repel • Two nuclei naturally repel each other and thus cannot fuse spontaneously • For fusion, electrical repulsion must be “overcome” • When two nuclei are very close the strong nuclear force takes over and holds them together. • How do two nuclei get close enough? www.assignmentpoint.com

4. Fusion needs fast moving nuclei Low speed High speed • Fast moving nuclei can overcome the repulsion - they get a running start. • Lots of fast moving nuclei means high temperature. • The core of the Sun has a temperature of 15 million degrees Kelvin. (ouch!) www.assignmentpoint.com

5. Fusion Power on Earth • Fusion is the source of energy for hydrogen bombs. • We are trying to harness fusion to generate electricity: • tokamak - magnetic confinement machine as envisioned for ITER shown to the right • inertial confinement fusion - Lawrence Livermore National Lab ITER reactor www.assignmentpoint.com

6. Fusion Powers the Sun • Temperatures in the cores of stars are above the approximately 8 million K needed to fuse hydrogen nuclei together. • Calculations: observed power output of the Sun consistent with fusion of hydrogen nuclei. • Observation: neutrinos from Sun produced by fusion reactions. • Hypothesis: all stars produce energy by nuclear fusion. www.assignmentpoint.com

7. proton-proton chain • fuse two hydrogen, H (1 proton) to make deuterium, 2H(1 proton, 1 neutron), neutrino and positron • fuse one deuterium and one hydrogen to make helium-3 3He(1 proton, 2 neutrons), gamma ray (energetic photon) • fuse two helium-3 to make helium 4He plus two hydrogen www.assignmentpoint.com

8. Why a complicated chain? • Fusion would be simpler if four protons would collide simultaneously to make one helium nucleus • Simpler, but less likely • rare for four objects to collide simultaneously with high enough energy • chance of this happening are very, very small • rate too slow to power the Sun • proton-proton chain: each step involves collision of two particles • chance of two particles colliding and fusing is much higher, so nature slowly builds up the helium nucleus. www.assignmentpoint.com

9. Fusion and Solar Structure • fusion only in Sun's core • only place its hot enough • heat from fusion determines Sun's structure www.assignmentpoint.com

10. Heat from Coredetermines Sun's Size • Force equilibrium • Hydrostatic equilibrium: balance between • thermal pressure from the hot core pushing outwards • gravity squeezes the star collapse to the very center • Nuclear fusion rate is very sensitive to temperature. • A slight increase/decrease in T causes fusion rate to increase/decrease by a large amount. www.assignmentpoint.com

11. Gravity and Pressure pressure from table • force equilibrium • Newton's second law: F = ma • static equilibrium: no acceleration if forces on object balance • gravity tries to pull 1/4 pounder to center of the Earth • pressure from table opposes gravity • hydrostatic equilibrium on Sun • "cloud of gas" (like 1/4 pounder) • gravity pulls cloud to the center • pressure from gas below opposes gravity • heat from fusion in the hot core increases pressure • energy output controls size of sun! weight from gravity pressure from hot gas cloud weight from gravity www.assignmentpoint.com

12. Temperature and Pressure • temperature: random motion of atoms in a gas • pressure: amount of force per unit area on piston from gas • generally pressure increases with increasing temperature www.assignmentpoint.com

13. Balancing Fusion, Gravity and Pressure If the rate of fusion increases, then: • thermal pressure increases causing the star to expand. • star expands to a new point where gravity would balance the thermal pressure. • the expansion would reduce compression of the core • the temperature in the core would drop • the nuclear fusion rate would subsequently slow down • the thermal pressure would then drop • the star would shrink • the temperature would rise again and the nuclear fusion rate would increase • Stability would be re-established between the nuclear reaction rates and the gravity compression www.assignmentpoint.com

14. Hydrostatic Equilibrium • balance between pressure, heat from fusion and gravity determines Sun's size • big stars have cooler cores, small stars have hotter cores – more compressed www.assignmentpoint.com

15. Other Particles • Helium is not the only product in the fusion of hydrogen. • Two other particles produced • Positron • Neutrino www.assignmentpoint.com

16. Gamma Ray Propagation in the Sun • Positrons quickly annihilate with electrons. • Photons produced in core of the Sun take about a million years to move to the surface. • Slow migration because they scatter off the dense gas particles • move about only a centimeter between collisions. • In each collision, they transfer some of their energy to the gas particles. • As they reach the photosphere, gamma rays have become visible photons. www.assignmentpoint.com