ISP209s10 Exam2 Review -1-
Today – Exam#2 Review• Exam #2 is Tuesday 3/30• The exam is 40 multiple choice questions.• Bring your calculator• You can use 5 (!) pages (front and back) of notes. I
don’t care if you hand write or type them.• List of topics to study is up on the web under today’s
reading assignment• As with exam 1, there will be an exam 2 extra credit
opening in CAPA at 4pm on Tuesday 3/30 due byThursday morning.
ISP209s10 Exam2 Review -2-
Energy, Work, etc.
• Two kinds of energy: Kinetic – energy of motion, Potential– energy of position
• Energy is measured in Joules, J• Power = Energy/time . The unit is Watts = J/s• Energy is always conserved. Energy conservation can be
used to find how high something will go.• Work = force x distance, converts energy from one form to
another.
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Chemical Energy
• 1 Calorie = 4184 J• How many Calories are used by a person to
lift 200 kg 1m? Assume people are 10%efficient in converting chemical energy towork.
Work = mgh = 200 x 9.81 x 1 = 1962 JChemical energy=Work/eff=1962J/.1=19620.#Calories = 19620 J/(4184 J/Cal) = 4.69 Cal
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Which of the following is correct concerningtemperature?
A. The average kinetic energy of molecules in a gasincreases at the temperature is increased.
B. Thermal motion Is highly organizedC. As a gas is cooled, the molecules more more rapidly.D. Temperature is a measure of the average potential
energy of atoms.E. Temperature is not related to energy.
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Entropy• Entropy is a measure of the number of ways a system can be
arranged. S = kBln(# of arrangements)• S = Heat/T – thermal energy goes toward increasing the entropy• Second Law of Thermodynamics – The entropy of a closed system
always increases.• As the pendulum swings useful energy is lost to increasing the
random motion of the air and pivot (heat)• 2nd law => There is no way to recollect the thermal energy and
make the pendulum swing higher as in the frictionless case.
(slighly less correct definition sometimes used that “entropy is the measure of microscopic disorder” in a system)
ISP209s10 Exam2 Review -6-
Energy and Entropy - Pendulum Example
Ener
gy
The thermalenergy (heat)is “lost”
If there is no friction, the pendulum swingsforever, always following the same trajectory.
The figure shows how the energy is split into KineticAnd Potential energy at each point in the trajectory.
ISP209s10 Exam2 Review -7-
Energy and Entropy - Pendulum Example
Ener
gy
The thermalenergy (heat)is “lost”
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Coin Toss Example• Suppose we have 10 coins: HHHHHHHHHH
S = k ln(1) = 0
3.181015.254526.6112037.3821047.6325257.3821066.6112075.254583.18109
Entropy (J/K) *10-23Number of waysHeads
ISP209s10 Exam2 Review -9-
Why does time always move in one direction?• The Universe was created with very low entropy. Much too
low for its size. It is like the Universe started with all heads.• Hence, everything in the Universe moves toward reaching the
correct amount of entropy. It is very improbable to go theother way. In this case very means so improbably that it neverhappens.
• Time has a direction because going back in time would implythe entropy could be decreased. That is very improbable.
• The Universe tends toward increasing entropy.
ISP209s10 Exam2 Review -10-
Clicker Question
What principle of Nature distinguishes between the forward and backward directions of time?
A) Newton’s 3rd law (“law of force pairs”)B) Time dilationC) Entropy always increases (2nd law of Thermodynamics)D) E = mc2
E) The concept of the “absolute zero” temperature
Indeed, with the exception of some rare subatomic processes, the Laws of Physics (aside from the 2nd-law of Thermodynamics)Don’t distinguish between forward and backward flow of time.
ISP209s10 Exam2 Review -11-
Clicker question
Which statement applies to the 2nd law of Thermodynamics?
A) The total entropy or microscopic disorganization of allParticipants in a physical process always increases.
B) It is the reason why we never see a broken egg on the floorspontaneously reassemble itself on the table from which it fell.
C) Thermal energy flows from higher to lower temperatures
D) You can never convert 100% of thermal energy into work.
E) All of the above.
ISP209s10 Exam2 Review -12-
Our current understanding of Forces
• There are 4 known forces in nature (Gravity, weak,EM- electromagnetic , strong)
• Gravity does not fit well in our understanding withthe others– It is very weak compared to the others. Why?
• Our current understanding of nature is by Quantumfield theory: EM - quantum electrodynamics,EM+weak - electroweak theory, Strong - quantumchromodynamics).
• Our understanding of force involves the exchange offorce carrying bosons between particles
ISP209s10 Exam2 Review -13-
The particles of nature
T. Kondo
Charge
+2/3
-1/3
anti-particleshave oppositecharge
0
-1
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How nature is put together from the pieces…
Atoms AtomicNucleus
A proton (uud)
Made of nuclei andelectrons. Size: 10-9m
Made of neutrons andproton. Size 10-14 m
Made of quarks:Size 10-15 mA neutron hasddu
ISP209s10 Exam2 Review -15-
A summary of the forces of nature
anything withmass
quarks, electrons(leptons) ,neutrinos
anything withcharge
quarks
Acts on
infiniteGraviton(?)
6x10-39Gravity
10-18
Only 0.001width of proton
VectorBosons
W+, W-, Z0
10-6Weak
infinitephoton1/137Electromagnetic
10-15 size of aproton
Gluon, g1Strong
Range (m)CarrierStrengthForce
ISP209s10 Exam2 Review -16-
Our Picture of Force
A charge creates a field…
!4
htE "##
Virtual particles can exist for a shorttime.
Feynman diagram
Picture ofthe field
ISP209s10 Exam2 Review -17-
Coulombs Law• Charge comes in units of 1.6E-19C.
• The force between two charges is:
• Example (inverse square law): 4 times thedistance
2
2
9
2
12
21 1099.8;C
Nmk
r
qkqF !== 1 2
r12
( ) dd Fr
qkq
r
qkq
r
qkqF
16
1
16
1
4
1
42
12
21
2
12
21
22
12
21
4====
ISP209s10 Exam2 Review -18-
The Earth behaves as a large magnet
The Earth is like a large magnet with a southmagnetic pole at the North geographic pole.
NS
NS
T/F• T North pole of a compass points north innorthern hemisphere• F North pole of a compass points south insouthern hemisphere• T North pole of a compass points towardsthe north in the southern hemisphere
ISP209s10 Exam2 Review -19-
Map for the Electric Field
Note: we could make similar maps for all the fields in nature(gravity, weak, EM, strong).
ISP209s10 Exam2 Review -20-
The relation between electric and magnetic fields
• Charge creates an electric field (and potential, V)• Moving charge creates a magnetic field• The photon is responsible for transmitting both the
electric and the magnetic forces• Maxwell’s equations describe the following;
– Charge makes electric fields– Changing magnetic field makes electric fields– Changing electric fields make magnetic fields– Magnets always come with a north and a south pole– EM waves travel at the speed of light (in a vacuum)
ISP209s10 Exam2 Review -21-
Sample Problem
What is the magnitude of the electricfield at 2.0 m?
( )( ) C
N
m
V
mm
VVE 0.200.20
04
800
x
V- ==
!
!!=
"
"=
ISP209s10 Exam2 Review -22-
Sample Problem
Electric field is the rate of change of potential with position.
HighestMagnitudeOf e-field
Zero e-field
Zero e-field
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Simple Problem
F = E q
If a charge of 1.5 C is placed on an electric field of 15.5V/m, what is the magnitude of the force on the charge?
Answer:F = 15.5 N/C x 1.5 C = 23.3 N
ISP209s10 Exam2 Review -24-
Flow of Charge - Current
• Batteries are like pumps that lift charge to ahigher potential. The charge flows down thehill to the other side of the battery.
A batteryis like apump.
Moving Chargedoes work on theway downV
ISP209s10 Exam2 Review -25-
Quantum Mechanics Review• Light can be described as an electromagnetic wave or a little
bundle of energy (a photon). Light has particle and wavecharacter.
• Waves can overlap – this is called interference. Destructive ifthey cancel, Constructive if they reinforce.
• Particles, for example electrons, have wave and particleproperties.
• The thing that is waving in the case of a particle is probability.The square of the height of the wave (wave function) is ameasure of the probability density.
• All objects (atoms, molecules, etc.) exist in defined states ofenergy. The energy is quantized (quantum mechanics)
ISP209s10 Exam2 Review -26-
The Uncertainty PrincipleWhat is the meaning of the Uncertainty Principle?
A. The entropy of a closed system always increases.B. It is not possible to know the exact position
and momentum of a particle at the same time.C. It is not possible to ever know the exact position
of a particle.D. Small objects have a wave function.E. Energy is conserved in a closed system.
!4
hpx "##
ISP209s10 Exam2 Review -27-
Antiparticles and Antimatter
• All particles have a corresponding anti-particle with oppositequantum numbers. We write the anti-particle with a bar overthe top, e.g. proton – p anti-proton p
• Antimatter (matter made of anti-particles) is very difficult tomake. It can artificially be produced only at large particleaccelerators (“atom smashers”).
• Matter and anti-matter are created naturally in pairs• So far the total amount of antimatter ever produced by
humankind is a few grams.• Matter and anti-matter annihilate each other when they meet
and ALL the mass is converted to energy
ISP209s10 Exam2 Review -28-
Why is Quantum Theory so strange?
• What you thought were waves can act likeparticles and visa-versa (“wave-particle duality”)
• Quantum uncertainty (Heisenberg)• Nature is intrinsically random• Quantum non-locality• Nature is “digital” and “discrete”• The very act of observing/measuring can change
the outcomeWe don’t see any of the weirdness in our daily lives. But if youlook at microscopically small phenomena (atoms), it seems to indeed be reality!
ISP209s10 Exam2 Review -29-
Look closer, you see light acts like a particle…
EEM = 0, 1hf, 2hf, 3hf, 4hf, …
h*f = energy of 1 photon
EM fields are made of discretebundles of energy (quanta or photons)
h = 6.625E-34 Js Planck’s Constant
Particle-like:
We cannot predict the individual dots position. Quantum theoryCan only predict the pattern that emerges with a large number of dots(probabilities).
ISP209s10 Exam2 Review -30-
Particles acting like waves
Electrons show an interference pattern in the double slit experiment.
And the interferencePatterns show a Discrete “lumpiness”If you look closely.
Each “lump” is anElectron hitting the Screen.
As with light, it is impossible to predict the positionOf each individual dot. Nature is intrinsically random!We can only predict “probabilities”, which is to say the overall pattern that emerges with a large # of dots.
“electron gun”
ISP209s10 Exam2 Review -31-
… and a watched electron doesn’t show interferenceIf you try to find outWhich slit each electronGoes thru, the wave featuresGo away
An electron Detector
Many more weird examples…
Observation can alter the outcome in QM
ISP209s10 Exam2 Review -32-
Quantum Nonlocality
1
2
1
2
After interaction the wave functions areentangled.
If we measure 1 and 2 at the same time thedifference in position forms an interferencepattern.
If we measure 2 before 1, the measurementof 2 defines where 1 must hit. Thisinformation travels faster than the speed oflight.This has been confirmed experimentally.
Interaction
ISP209s10 Exam2 Review -33-
What is “waving” for matter waves?
• Probability – all particles described by a “wavefunction” ψ. The square of ψ gives the probabilitydensity of finding a particle per unit volume.
• The ψ extends over all space, which gives weirdconsequences.
= prob. of finding particle in a small volume V centered at the point r.
ISP209s10 Exam2 Review -34-
Neutrinos
• Neutrinos are subatomic particles that do not havecharge. They only interact via the weak force.
• These are very unusual particles and we still don’tknow much about their properties. They have amass, but it is so small we have not been able tomeasure it.
• They account for about 2% of the universe butinteract weakly. One light-year of lead would haveonly a 50% chance of stopping one.
ISP209s10 Exam2 Review -35-
Equations – sort of
Rules for Feynman Diagrams:
1). The number of leptons and baryons must be conserved.
2). Charge must be conserved.
Not allowed
ISP209s10 Exam2 Review -36-
Some examples
Is the following allowed?Production of a quarkand anti-quark by acollision of an electronand an anti-electron. 010neutrino
01-1electron
1/302/3Downquard
1/30-1/3Up quarkBaryonLeptonChargeName
quark + anti-quark
electron +anti-electron
AfterBefore
ISP209s10 Exam2 Review -37-
Some examples
010neutrino01-1electron
1/302/3Downquark
1/30-1/3Upquark
BaryonLeptonChargeName
1/3 + (-1/3)-1 + 1
0 + 01 + -11/3 + (-1/3)0 + 0
Quark + antiquark
Electron +anti-electron
AfterBefore
allowed
BaryonLeptonCharge
ISP209s10 Exam2 Review -38-
Is this possible?
Yes, it is two quarks interacting via the electromagnetic force.Up quarks have electric charge of +2/3.
ISP209s10 Exam2 Review -39-
Force Carriers
• Stong – Gluons – g• Weak – Intermediate vector bosons – Z,W• Electromagnetic – photon - γ
Two quarksinteracting via thestrong force
ISP209s10 Exam2 Review -40-
Feynman Diagrams and rulesCharge, baryon number, and lepton number are conserved
Consider the decay of a +pion into an antimuon by the Weakforce. Which diagram describes this process?
ud!+
+ - " "
time
correct
ISP209s10 Exam2 Review -41-
Other Examplesud!+
+ - " "
time
Decay ofpion
Charge ofW is notcorrect
Baryon andlepton notconserved
Wrong becauseelectric force doesnot act on neutrinos
Wrong becauseelectric force doesnot act on neutrinos