General Physics (PHY 2140) Lecture 21 ¾ Modern Physics Elementary Particles Strange Particles – Strangeness The Eightfold Way Quarks Colored Quarks Electroweak Theory – The Standard Model The Big Bang and Cosmology Chapter Chapter 2930 http://www.physics.wayne.edu/~alan/2140Website/Main.htm
Previously… Nuclear Energy, Elementary Particles Nuclear Reactors, Fission, Fusion Fundamental Forces Classification of Particles
Elementary Particles
First we studied atoms Next, atoms had electrons and a nucleus The nucleus is composed of neutrons and protons What’s next?
30.5 The Fundamental Forces in Nature Strong Force
Short range ~ 10-15 m (1 fermi) Responsible for binding of quarks into neutrons and protons Gluon
Electromagnetic Force
10-2 as strong as strong force 1/r2 force law Binding of atoms and molecules Photon
Weak force
~ 10-6 times as strong as the strong force Responsible for beta decay, very short range ~10-18 m W+, W- and Z0 bosons
Gravitational Force
10-43 times as strong as the strong force Also 1/r2 force law Graviton
30.8 Particle Classification (Classify the animals in the particle zoo) Hadrons (strong force interaction, composed of quarks) We already met the mesons (middle weights) Decay into electrons, neutrinos and photons Baryons, i.e. the proton and neutron (the heavy particles) Still other more exotic baryons: Λ, Σ, Ξ, Ω all are heavier than the proton Decay into end products that include a proton
Particle Classification – cont.
Leptons Small or light weight particles Are point like particles – no internal structure (yet) 6 leptons Electron e, muon μ, tau τ and their associated neutrinos: νe, νμ, ντ Also, their antiparticles Neutrinos have tiny mass, ~3 eV/c2
Some members of the Zoo
Particle Physics Conservation Laws So far in Physics we have conservation of energy, momentum (linear and angular), charge, spin. Now we add more to help balance particle reactions
Baryon number:
B = +1 for baryons, -1 for anti-baryons Eg. Proton, neutron have B = +1 p, n , antiparticles have B = -1 B = 0 for all other particles (non-baryons)
More Conservation Laws Lepton number L = +1 for leptons, -1 for anti-leptons L = 0 for non-leptons
Example for electrons: Electron e, electron neutrino νe have Le = +1 Anti electron and antineutrino have Le = -1 Other leptons have Le = 0 BUT have their own lepton numbers, Lμ, Lτ Refer to table 30.2
Example neutron decay
Consider the decay of the neutron
n → p + e + νe +
-
Before: B = +1, Le = 0 After: B = +1, Le = +1 -1 = 0
Quiz 30.2
Which of the following cannot occur? (a) p+p → p+p+p (b)
n → p + e + νe
(c)
μ → e + ν e + νμ
(d)
π → μ +νμ
-
-
-
-
-
Quiz 30.2 - answer
The disallowed reaction is (a) because Charge is not conserved: Q = +2 → Q = +1 Baryon number is also not conserved: B = +2 → B = +2-1 = +1
p+p → p+p+p
Strangeness
Several particles found to have unusual (strange) properties: Always produced in pairs π- + p+ → K0 + Λ0 but not π- + p+ → K0 + n Decay is slow (indicative of weak interaction rather than strong) Half-lives of order of 10-10 to 10-8 sec
Members of the strange club: K, Λ, Σ
More Strangeness
Explanation lies in the addition of a new conservation law – Strangeness, S One of the pair of strange particles gets S=+1 the other S=-1. All other particles get S=0. So in the previous reaction, strangeness is conserved: Before S=0; After S=+1-1 = 0 Second reaction violates strangeness
Example 30.6: Strangeness Conservation Consider:
π - + n → K+ + Σ -
Before: S=0+0=0 (no strange particles) After: K+ has S=+1, Σ- has S = -1 thus the
net strangeness S = +1-1 = 0 So reaction does not violate law of conservation of strangeness, the reaction is allowed
The Eightfold Way Consulting table 30.2, Take the first 8 baryons and plot Strangeness vs. Charge. We get an interesting picture. A hexagonal pattern emerges. If we do the same for the spin 0 mesons we also get a hexagonal pattern.
The Eightfold Way
The Original Quark Model (in B/W)
Gell-Mann (1961) proposed hadrons have structure, i.e. composed of a more fundamental type of particle. Quarks have fractional charge e/3 or 2e/3 Three types u, d, s: up, down, strange Mesons were made of 2 quarks: q, q¯ Baryons were made of 3 quarks
But that wasn’ enough!
Soon after, experimental discrepancies required the addition of three more quarks Top, bottom and charm: t, b, c And three more conservation laws: C, B, T for charm, bottomness and topness
Properties of Quarks and Antiquarks
Fundamental Particles: Properties Quarks Particle
Rest Energy
Charge (e)
u
360 MeV
+2/3
d
360 MeV
-1/3
c
1500 MeV
+2/3
s
540 MeV
-1/3
t
173 MeV
+2/3
b
5 GeV
-1/3
Size of quark: < 10-18 m
Fundamental Particles Properties continued Leptons Particle
Rest Energy
Charge
e-
511 keV
-e
μ-
107 MeV
-e
τ-
1784 MeV
-e
νe
< 30 eV
0
νμ
< 0.5 MeV
0
ντ
< 250 MeV
0
Quarks in Mesons and Baryons
We should still be in B/W!
Color
Because of the Pauli exclusion principle (all quarks are spin ½ particles) can’t have three of the same particles occupying the same state. Example: Ω- is (sss) so need three different yet strange quarks So colored quarks were proposed
Color continued
Three color charges were added Red, green blue: r, g, b
And…three anti-colors antired, antigreen and antiblue: r¯, g¯, b¯
Mesons have a color anticolor pair Spin is either zero or 1 so can have ↑↑ or ↑↓
Baryons must have three different colors Spin is ½ so have ↑↑↓ or ↓↓↑
Quarks combinations with color Total spin is 0 or 1
Total spin is ½ or 3/2
Quantum Chromodynamics In analogy with photons and the electromagnetic
force, an interaction between colored quarks is the result of color force – 8 colored gluons. The general theory is complex but explains experimental results better. Numerical results can be very hard to calculate Opposite colors attract, red-antired, in analogy with electromagnetism. Different colors also attract though less strongly Residual color force is responsible for nuclear force that bind protrons and neutrons.
Interactions in the Yukawa pion and quark-gluon models
Yukawa’s pion model
Quark QCD model In both cases a proton-neutron pair scatter off each other and exchange places.
The Standard Model
History of the Universe and of the four forces
Energy: 1028 Time:
0
1024 10-40
10-35
1021
1017
1013
1011 10-11
eV sec
Time
Big Bang Model A broadly accepted theory for the origin and evolution of our universe. It postulates that 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit. In the beginning, there was a Big Bang, a colossal explosion from which everything in the Universe sprung out.
Experimental Evidence of the Big Bang
Expansion of the universe
Abundance of the light elements H, He, Li
Edwin Hubble's 1929 observation that galaxies were generally receding from us provided the first clue that the Big Bang theory might be right. The Big Bang theory predicts that these light elements should have been fused from protons and neutrons in the first few minutes after the Big Bang.
The cosmic microwave background (CMB) radiation
The early universe should have been very hot. The cosmic microwave background radiation is the remnant heat leftover from the Big Bang.
Cosmic Microwave Background 99.97% of the radiant energy of the Universe was released within the first year after the Big Bang itself and now permeate space in the form of a thermal 3 K radiation field.
COBE CMB Measurement
• CMB spectrum is that of a nearly perfect blackbody with a temperature of 2.725 +/- 0.002 K. • Observation matches predictions of the hot Big Bang theory extraordinarily well. • Deviation from perfect black body spectrum less than 0.03 % • Nearly all of the radiant energy of the Universe was released within the first year after the Big Bang.
How did we get from there…
… to here?
Let there be light: 400,000-700,000 years
Mini Review
Coulomb’s law 9 the superposition principle
JG F
F = ke
q1 q2 r2
The electric field
0 Flux. Gauss’s law. Q Φ = cos θ = EA 9 simplifies computation of electric fields net ∑ εo
ΔPE Potential and potential energy ΔV = VB − VA = q 9 electrostatic force is conservative 9 potential (a scalar) can be introduced as potential energy of electrostatic field per unit charge
E=
q
Equipotential surfaces 9
They are defined as a surface in space on which the potential is the same for every point (surfaces of constant voltage)
The electric field at every point of an equipotential surface is perpendicular to the surface Capacitance and capacitors
1 Q2 1 U = QV = = CV 2 2 2C 2
Current and resistance
C = κε 0
Resistance and Ohm’s law
I = nqvd A
Resistivity
9 9 9 9
Capacitors with dielectrics (C↑ if k ↑) Current and drift speed I is proportional to V material property
V = IR
A , C = κ C0 d
I=
ΔQ Δt
RA ρ= l
Current and resistance
R = Ro ⎡⎣1 + α (T − To ) ⎤⎦
9 Temperature dependence of resistance
ΔV ) ( 2 P = I ΔV = I R =
9 Power in electric circuits
R
DC Circuits
ΔV =E − Ir
9 EMF
Req = R1 + R2 + R3 + "
9 Resistors in series and parallel n
9 Kirchoff’s rules
∑I i =1
9 RC circuit
2
n
i
= 0, ∑Vi = 0
(
i =1
q = Q 1 − e−t / RC q = Qe− t / RC
1 1 1 1 = + + " Req R1 R2 R3
)
Charging Discharging
Magnetism
Induced voltages and induction
Magnetic field Magnetic force on a moving particle Magnetic force on a current Torque on a current loop Motion in a uniform field Application of magnetic forces Ampere’s law Current loops and solenoids Magnetic flux Generators and motors Self-induction Energy in magnetic fields
AC circuits
F = qvB sin θ F = BIl sin θ F = NBIA sin θ r = mv / qB
∑ B Δl = μ I &
o
Φ = B⊥ A = BA cos θ ΔI E = −L Δt
L=
NΦ I
1
Resistors, capacitors, inductors in ac circuits PEL = LI 2 2 Power in an AC circuit 1 X L − XC 2 2 XC = , X L = 2π fL tan φ = Z = R + ( X L − XC ) 2π fC R
AC circuits
f0 =
Resonance in RLC circuits Transformers Electromagnetic Waves
Δv = ΔVm sin ( 2π ft + φ )
c=
1 2π
1
μoε o
LC
N2 ΔV2 = ΔV1 N1
= 2.99792 × 108 m s
Modern physics
Introduction Gallilean relativity Michelson-Morley Experiment Relativity
Time dilation, length contraction Relativistic energy, momentum Relativistic addition of velocities
vab =
vad + vdb v v 1 + ad 2 db c
Δt =
Δt p 1− v c 2
p≡
L = Lp 1 − v 2 c 2
2
mv 1− v c 2
2
= γ mv
KE = γmc2 – mc2
Quantum physics
Blackbody radiation Planck’s hypothesis Photoelectric effect X-rays
Wave function Uncertainty relations Atomic Descriptions Atomic Spectra Bohr’s Atomic Theory Quantum Mechanics Quantum Numbers
λmaxT = 0.2898 ×10−2 m ⋅ K En = nhf ,
n = 1, 2,3,...
KE = hf − Φ hc λmin = e ( ΔV ) h ΔxΔp ≥ 2π
h ΔE Δt ≥ 2π
2π r = nλ , n = 1, 2,3,... Ei − E f = hf me vr = n=, n = 1, 2,3,... ⎛ 1 1 ⎞ = RH ⎜ 2 − 2 ⎟ ⎜ n f ni ⎟ λ ⎝ ⎠ 1
Quantum physics
Electron Clouds (Orbitals) The Pauli Exclusion Principle Characteristic X-Rays Atomic Energy Levels Lasers and Holography
Nuclear physics
Nuclear properties Binding energy Radioactivity The Decay Process Natural Radioactivity Nuclear Reactions Medical Applications Radiation Detectors
A Z
X
4ke Ze 2 d= mv 2
r = r0 A1/ 3
Nuclear Energy, Elementary Particles
Nuclear Reactors, Fission, Fusion Fundamental Forces Classification of Particles – Making sense of the particle zoo Conservation Laws
Remember: Electricity: Electric field and electric potential are different things
Moreover, field is a vector while the potential is a scalar Remember the difference between parallel and series connections Remember that formulas for capacitors and resistors are “reversed”
Magnetism:
Use right hand rule properly
Special relativity: If the problem involves speeds close to the speed of light, use relativistic formulas for momentum, energy, addition of velocities
In particular, KE=mv2/2 is a NONRELATIVISTIC expression for KE
Atomic and nuclear physics:
In the way of handling, nuclear reactions are very similar to chemical reactions
Good Luck on the Final Exam!
