Physics 2D Lecture Slides Jan 21 Vivek Sharma UCSD Physics - PowerPoint PPT Presentation

Physics 2D Lecture Slides Jan 21 Vivek Sharma UCSD Physics

Particle Accelerators as Testing ground for S. Relativity

When Electron Goes Fast it Gets “Fat” = γ 2 E mc v → γ → ∞ As 1, c ∞ Apparent Mass approaches

Relativistic Kinetic Energy & Newtonian Physics γ − 2 2 Relativistic KE = mc mc 1 −   2 2 u 1 u 2 << ≅ − + When u c , 1- 1 ...smaller terms   2 2 c 2 c   2 1 u 1 ≅ − − = 2 2 2 so K mc [1 ] mc mu (classical form recovered) 2 2 c 2 Total Energy of a Pa r ticle = γ = + 2 2 E mc KE mc For a particle at rest, u = 0 ⇒ 2 Total Energy E= m c

= γ ⇒ = γ 2 2 2 2 4 E mc E m c Relationship between P and E = γ ⇒ = γ 2 2 2 2 2 2 p mu p c m u c ⇒ − = γ − γ = γ − 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 E p c m c m u c m c ( c u ) 2 2 2 4 m c m c − = − = 2 2 2 2 2 4 = ( c u ) ( c u ) m c − 2 2 2 u c u − 1 2 c = + 2 2 2 2 2 E p c ( mc ) ........important relation F or particles with zero rest mass like pho ton (EM waves) E E= pc or p = (light has momentu m!) c − = 2 2 2 2 4 Relativistic Invariance : E p c m c : In all Ref Frames Rest Mass is a "finger print" of the particle

Mass Can “Morph” into Energy & Vice Verca • Unlike in Newtonian mechanics • In relativistic physics : Mass and Energy are the same thing • New word/concept : Mass-Energy • It is the mass-energy that is always conserved in every reaction : Before & After a reaction has happened • Like squeezing a balloon : – If you squeeze mass, it becomes (kinetic) energy & vice verca ! • CONVERSION FACTOR = C 2

Mass is Energy, Energy is Mass : Mass-Energy Conservation Examine Kinetic energy Before and After Inelastic Collision: Conserved? K=0 S K = mu 2 Before V=0 1 2 v v 1 2 After Mass-Energy Conservation: sum of mass-energy of a system of particles before interaction must equal sum of mass-energy after interaction = E E be f ore after 2 2 mc mc 2 m + = ⇒ = > 2 Mc M 2 m 2 2 2 u u u − − − 1 1 1 Kinetic energy is not lost, 2 2 2 c c c its transformed into Kinetic energy has been transformed into mass increase   more mass in final state   2 2 K 2 m c   ∆ = = = − 2 M M - 2 m mc   2 2 c c 2 u −   1 2  c 

Conservation of Mass-Energy: Nuclear Fission M M 1 + M 3 M 2 + Nuclear Fission 2 2 2 M c M c M c = + + ⇒ > + + 2 Mc 1 2 3 M M M M 1 2 3 2 2 2 u u u − − − 1 1 1 2 1 3 2 2 2 c c c < 1 < 1 < 1 Loss of mass shows up as kinetic energy of final state particles Disintegration energy per fission Q=(M – (M 1 +M 2 +M 3 ))c 2 = ∆ Mc 2 → × = 236 143 90 1 -27 U Cs + R b +3 n ( 1 AMU= 1.6605402 10 kg 931.49 Me V ) 92 55 9 2 0 ∆ × = -28 m=0.177537u=2 .9471 10 kg 165.4 MeV= energy release/fission =peanuts What makes it explosive is 1 mole of Uranium = 6.023 x 10 23 Nuclei !!

Energy Released by 1 Kg of Fissionable Uranium × 2 3 1 Mole of Uranium = 236 gm, Avagadro''s # = 6.023 10 Nuclei × 23 6.023 10 × = × 24 So in 1 kg N = 1000 g 2.55 10 nu clei 236 / g mole ∴ = × × 3 24 1 Nuclear fission = 165.4 MeV 10 g 2. 55 1 0 165.4 MeV × - 20 Note 1 MeV = 4.45 1 0 kWh If the power plant has conversion efficiency = 40% × 6 Energy Tr ansformed = 748 1 0 kWh ⇒ 1 100 W lamp ca n be lit for 85 00 yea rs !

Nuclear Fission Schematic Excited U Oscillation Absorption of Neutron Deforms Nucleus Unstable Nucleus

Sustaining Chain Reaction: 1 st three Fissions Average # of Neutrons/Fission = 2.5 Neutron emitted in fission of one U Needs to be captured by another To control reaction => define factor K Supercritical K >> 1 in a Nuclear Bomb Critical K = 1 in a Nuclear Reactor

Schematic of a Pressurized-Water Reactor Water in contact with reactor core serves as a moderator and heat transfer Medium. Heat produced in fission drives turbine

Lowering Fuel Core in a Nuclear Reactor First Nuke Reactor :Pennsylvania 1957 Pressure Vessel contains : 14 Tons of Natural Uranium + 165 lb of enriched Uranium Power plant rated at 90MW, Retired (82) Pressure vessel packed with Concrete now sits in Nuclear Waste Facility in Hanford, Washington

Nuclear Fusion : What Powers the Sun Opposite of Fission Mass of a Nucleus < mass of its component protons+Neutrons Nuclei are stable, bound by an attractive "Strong Force " Think of Nucle i as molecules and proton/neut ron as atoms making it Binding Energy: Work/Energy required to pull a bound system (M) apart leaving its components (m) free of the attractive force and at rest: n ∑ 2 2 Mc +BE= m c i i=1 4 2 2 He + 23.9 Me V = H + H 2 1 1 Helium Deuterium Deuterium Th ink of ene rgy r elease d i n Fusion as Dissociati on en ergy in Chem × ⇒ 26 38 Sun's Power Output = 4 10 Watts 10 Fusion/Sec on d No wonder S un is consi dered a God in m any cultures !

Nuclear Fusion: Wishing For The Star • Fusion is eminently desirable because – More Energy/Nucleon • (3.52 MeV in fusion Vs 1 MeV in fission) • 2 H + 3 H � 4 He + n + 17.6 MeV – Relatively abundant fuel supply – No danger like nuclear reactor going supercritical • Unfortunately technology not commercially available – What’s inside nuclei => protons and Neutrons – Need Large KE to overcome Coulomb repulsion between nuclei • About 1 MeV needed to bring nuclei close enough together for Strong Nuclear Attraction � fusion • Need to – heat particle to high temp such that kT ≈ 10keV � tunneling – High density plasma at high temp T ≈ 10 8 K like in stars – Confine Plasma (± ions) long enough for fusion » In stars, enormous gravitational field confines plasma

Inertial Fusion Reactor : Schematic Pellet of frozen-solid Deuterium & tritium bombarded from all sides with intense pulsed laser beam with energy ≈ 10 6 Joules lasting 10 -8 S Momentum imparted by laser beam compresses pellet by 1/10000 of normal density and heats it to temp T ≈ 10 8 K for 10 -10 S Burst of fusion energy transported away by liquid Li

World’s Most Powerful Laser : NOVA @ LLNL Size of football field, 3 stories tall Generates 1.0 x 10 14 watts (100 terawatts) 10 laser beams converge onto H pellet (0.5mm diam) Fusion reaction is visible as a starlight lasting 10 -10 S Releasing 10 13 neutrons