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Chapters 43 & 44. Nuclear Physics, Particles, and Cosmology. Chapter 43. Nuclear Physics. Just how dense is the nucleus of an atom?. Looking at the nucleus of an atom only, most are similar in density . Thus Approximate Nuclear Radius: R = R 0 A 1/3 , A = # protons + # neutrons
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Chapters 43 & 44 Nuclear Physics, Particles, and Cosmology
Chapter 43 Nuclear Physics
Just how dense is the nucleus of an atom? Looking at the nucleus of an atom only, most are similar in density. Thus Approximate Nuclear Radius: R = R0A1/3, A = # protons + # neutrons (where R0 = 1.2 x 10-15 m = 1.2 fm) This comes from Rutherford, scattering alpha particles off thin gold foil and proving the positive charges in matter were concentrated in the tiny balls we now call the nucleus of an atom. Electrons with a negative charge were found to be ‘orbiting’ this nucleus.
Representing the Content of the Nucleus : In nuclear chemistry, mass is important. Protons and neutrons (baryons) are nearly identical at ~1.67 × 10−27 kg. Electrons are far lighter, ~ 1/1800 mass of proton. The number of protons + neutrons = A, the atomic mass or baryonic number. The number of protons = Z, the atomic number. • We label the nucleus with the element symbol, say X and the notation:ZA X .
Basis of Nuclear Reactions • ZA X (A = #n’s + #p’s) (Z = #p’s) • In a nuclear reaction the sum of the top and bottom numbers on either side of the equation are identical. This expresses: 1) Conservation of nuclear charge, 2) conservation of baryon number. • Atoms with the same Z, but different A (different no. of neutrons) are called isotopes. Example 1H (normal hydrogen), 2H (D, deuterium, slowly decays to H) , and 1H (tritium, rapidly decays).
Three Types of Nuclear Decay • 1. Alpha Decay: a nucleus gives off a 24He or 24α, a helium 4 nucleus. • 2. Beta Decay: a neutron in a nucleus (or free) morphs into a proton, giving off an electron. Energized free electrons are called beta radiation. 01n 11p + -10e + νe (with a bar on top--electron anti-neutrino). • 3. Gamma Decay: an excited nucleus gives off high energy light (gamma rays), keeping the same number of neutrons and the same number of protons. We indicate the excited nucleus by a *, like U*.
Isotopes and the average atomic mass • Neutral elements must have a balanced number of protons and electrons. • The number of neutrons in the nucleus varies. It’s often greater than the number of protons. • A good example is carbon. Carbon has three isotopes, carbon-12, carbon-13, and carbon-14. When each isotope is multiplied by the natural abundance, carbon-12 dominates but the contribution of the heavier isotopes is apparent when the average is found on the periodic table to be 12.011 amu.
Rate of Nuclear Decay: • Nuclear decay happens exponentially: R = R0e-λ t, where R0 is the initial rate of decay, R is the current rate, and λ is the decay constant, so a log-log plot will be roughly linear and give λ as the slope. • The half life of an isotope or particle is T1/2 = ln2/λ. • It is the time for half the parent to change into the daughter. Half life of Carbon 14 is roughly 6,000 years.
Nuclear binding • If one were to add up the rest mass of six electrons, six protons, and six neutrons that build carbon-12, one would find the mass of the assembled atom to be slightly less than the mass of the combined parts. • This mass difference is called the mass defect. • The mass defect (or portions thereof), converted to energy in joules by E = mc2, would be the source of the energy that’s released when, say, one atom of uranium is split into one atom of krypton and one atom of barium.
Nuclear binding energy versus amu • The figure below allows us to calculate the energy “freed” when a transformation takes place (either by splitting a big isotope into smaller ones or by adding smaller isotopes into a larger one).
A plot of #N versus #P • If the count were 1N per 1P as is the case in very light atoms, the plot would be linear. • Instead we see a curved “island of stability” where #N outnumber #P.
Alpha decay • The Radon 226 isotope loses 4 amu and +2 charge. Algebra reveals what remains.
Elements follow a natural decay pathway • The Segre chart on the right shows sequential decay fromU-238 to lighter and smaller isotopes until finally reachingPb-206.
Radioactive decay rates • All radioactive decay follows first-order kinetics. • The half-life (T½)will be used in this situation often. It is the time for half of a radioactive sample to decay to another element. • No is the original number of isotope in the sample, N(t) represents how many still exists after time, t.
Biological effects of radiation • The different forms of radiation cause damage differently. • A dose standard is the grey = 1 J/kg. Because a grey is large, doses are often measured in hundredths of a gray … the rad (J/kg/100). • Thinking just one step farther, damage depends on what type of tissue is injured. The effect will be to translate rad into rem (radiation equivalent man).
Sources of exposure and beneficial uses • There are a number of ways to accumulate radiation exposure. See figure below.
Fission, Fusion, & Nuclear Reactions Nuclear fission: breaking apart of nuclei further down the periodic table than iron. Nuclear fusion: fusing together of lighter nuclei than iron. Why do some nuclei break up and some fuse? Binding energy/baryon goes up to iron, then down as you go further down the periodic table. Nuclear Binding Energy: EB = (ZMH + Nmn –AZM)c2. AZM is the mass of the neutral atom, c2 = 931.5 MeV/u (u = closely the mass of the p and n); there are Z protons and N neutrons. What is obeyed in a nuclear reaction? conservation of charge, energy, momentum, angular momentum, and nucleon number.
Nuclear fission I • A large nucleotide splits or is split into smaller nucleotides. • Follow the “droplet model” across the bottom of the slide.
Nuclear fission II • Nuclear fission reactions require enough material to sustain a cascade. This effect is called a “chain reaction,” and the amount of material is called “the critical mass.”
Nuclear fission—III • Controlled fission requires thermal control (with circulating water) and moderation of neutrons (with graphite).
Meltdown? • A nuclear fission power plant uses a little less than enough to explode as an atom bomb, a little less than critical mass. However, if the control rods are left up, the nuclear material gets very hot and undergoes a meltdown. It also leaves behind a dangerous residue, which must be disposed of way underground. • Fukishima? UGH!!!
Nuclear fusion • Lighter isotopes are added together to make a heavier one. • The energy released is immense. This is the reaction that powers a star.
Fusion Power Plant • A nuclear fusion power plant fuses hydrogen into helium and gives off totally clean energy, with almost no dangerous radioactive residue. When we break even (producing more energy output than input), we could use the energy for electricity, break apart hydrogen and power our cars, producing only water—NO GREENHOUSE GASES! Hybrids still produce over 70% of the greenhouse gases compared to normal cars. Our current cars can easily and inexpensively be converted to hydrogen power. Nuclear fusion puts out roughly 6,000 times more energy than is inputted (IF no energy is wasted).
Chapter 44 Particle Physics and Cosmology
Introduction • Where did the universe originate? What was the “big bang”? Can we learn anything by studying the trends from the smallest known nuclear particles (quarks) to the largest (galaxies)? • Does all this sound like Star Trek? Perhaps it does but there are things we can know. Let’s glean some insights about where we might study further (after all, there is next semester’s registration coming).
Basic Types of Particles • The Standard Theory of Elementary Particles says that there are two major families of particles: quarks and leptons (see next 2 slides). However, there are mesons exchanged by them. Each has its own antiparticle. • Mesons: the force between nucleons is mediated by mesons, creating potential energy U(r) = -f2e-r/ro/r (nuclear potential energy). • Mesons: Photons mediate the electromagnetic force & Gluons, mediating the strong force between Quarks in n’s and p’s, & between them.
Quarks • Quarks have 1/3 multiples of protonic charge—three of them make up a neutron or a proton. There are six standard quarks. Three quarks with -1/3 +2/3 +2/3 units charge = 1 unit charge for a proton. Three quarks with -1/3 -1/3 +2/3 make up a neutron. • Quarks are tightly bound in baryons (neutrons or protons) by the strong nuclear force, a contact force which holds protons and neutrons together in the nucleus. Gluons mediate that force.
Leptons • Leptons are electron-like particles and their associated neutrinos: • Electron (e) and associated electron neutrino (νe), • Muon (μ, more mass than e) and associated muon neutrino (νμ) , • Tauon (Greek letter tau, more mass than μ) and associated tauon neutrino (ντ).
Positrons and electrons • It sounds like we’ve gone off into science fiction already, but even though the interactions of positrons and electrons sound like “matter and antimatter,” they are well studied & provide clues. • Positron? • Opposite charge, but same mass as electron
Particles as force mediators • Attraction and repulsion inmacroscopic world are often a matter of correctly applying Coulomb’s law. In the microscopic world, in quantum mechanics, force exchange can be imagined as two electrons playing catch with medicine ball while wearing roller skates. Yukawa potential represents spread-out charge—more accurate than Coulomb.
Linear and circular accelerators • It’s not important what motion accelerates the particles, it’s important that they collide at near light-speed. Figure 44.6 reveals the mechanical action within a cyclotron.
Forces and particles • There are four known forces. There are many particles that interact under the influence of the four forces. Dr. Stephen Hawking has written extensively about the concept of a “unified field theory” that seeks to weave a common thread through all four. His book, A Brief History of Time, attempts to write on this topic so that any of us might read and understand.
Leptons—fundamental particles • From collisions of protons, electrons, and atomic ions, clues have been gathered about smaller fundamental particles.
Superstring and M Theories • The superstring theory claims that quarks and leptons are variations on the same thing: a vibrating loop of string in multidimensions (now 10). • M Theory (membrane theory) says straight strings connect to membranes in 11 dimensions. This unifies 5 possibilities for superstring theory into one. • The above two theories are called Theories of Everything (TOE). • Both above theories are considered to be Quantum Gravity Theories, integrating Quantum Theory with the General Theory of Relativity.
Particle Accelerators • The LHC = Large Hadron Collider in Geneva is best. It accelerates particles and collides them at high speed so that the kinetic energy can create unusual particles and states (by E = mc2). • Soon it is hoped that supersymmetric partners (sparticles) of particles with large mass may be formed, confirming Supersymmetry, which is the foundation of the string theories. • We have found the large mass Higgs Boson (The God Particle), which in unifying theories lends mass to different particles.
NOTES: Proofs of the Hot Big Bang (of Georges LeMaitre): 1. The red shift of distant galaxies. 2. The cosmic microwave background. Penzias and Wilson 1976. A black body curve at T = 2.7 K results from electrons combining with protons to make hydrogen. Ultraviolet stretched to microwave with the expanding universe. This has small lumps in different directions of about 1 part in 10,000 indicating early inflation. 3. Nucleosynthesis–Burbidge, Fowler, and Hoyle in 1960 calculated Big Bang made 75% He, 25% He–observed in unrecycled material. Georges LeMaitre theorized The Big Bang in 1927 two years before Hubble observed it.
Proofs of the Hot Big Bang: 1. The red shift of distant galaxies Implies Hubble’s Law
Proofs of the Hot Big Bang: 2. The cosmic microwave background. observed and identified by Penzias and Wilson in 1965. Predicted by Cosmologist George Gamov in 1948
A black body curve at T = 2.7 K results from electrons combining with protons to make hydrogen. Ultraviolet stretched to microwave with the expanding universe.
WMAP Satellite—observes the microwave Background. This has small lumps in temperature in different directions of about 1 part in 10,000 indicating early inflation.
Proofs of the Hot Big Bang: 3. Nucleosynthesis–in 1960 Burbidge, Burbidge, Fowler, and Hoyle calculated Big Bang made 75% H, 25% He–observed in unrecycled material.
For about a second, the Big Bang was hotter than 10 million K, and fused 25% of H into He.
The ‘primordial soup’ Was thus 75% H and 25% He by mass.
Post-1998 Cosmology –A funny energy in space At the present epoch the velocity of receding galaxies is given by Hubble’s Law:v = Ho d , where Ho is the Hubble constant. 1. This holds only for galaxies at moderately low distances.
