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Lecture 42Final Exam Review

Final Exam - Monday Dec. 201045-1315

Equations and values boxed in red in this review appear on Equation Sheet 3

Lecture 16: Review for Midterm I

Lecture 33: Review for Midterm IIRegular office hours and help sessions this week

The Physics 101 Final ExamOn Monday, Dec. 20, 10:45-1:15 we have the Final Exam, covering Chapters 2-8 and 10-35 of Hewitt. It will be similar in format to the midterms, with about 100 pts of multiple choice questions and 100 pts of free-response questions. Closed book; calculators needed.

All three equation sheets provided on the Final.

All equation sheets are posted on the course web page and copies have been distributed.

Bring a scientific calculator with good batteries. (Cell phones, iPads, computers, etc. not allowed.)

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Studying for the FinalStudying for the FinalStudy carefully the lecture notes for the three review lectures (this one plus Lectures 16 and 33). If you need more detail on a topic, read appropriate text sections.Practice using the Equation Sheets as you work through old homework, quizzes, and exams.Re-work old homework problems. Go through all the quizzes and try to understand where you went wrong on questions you missed.Go through both midterm exams as if you were re-taking them.

Midterm #1 MaterialChap. 2: NEWTON'S FIRST LAW OF MOTION: All sections

except “The Moving Earth”Chap. 3: LINEAR MOTION: All sections Chap. 4: NEWTON'S SECOND LAW OF MOTION: AllChap. 5: NEWTON'S THIRD LAW OF MOTION: All sections Chap. 6: MOMENTUM: All but “More Complicated Collisions”Chap. 7: ENERGY: All except “Sources of Energy”Chap. 8: ROTATIONAL MOTION: All but “Simulated Gravity”Chap.10: PROJECTILE AND SATELLITE MOTION: only

“Projectile Motion”, “Fast-Moving Projectiles—Satellites”Chap.11: ATOMIC STRUCTURE: All but “Antimatter” and

“Dark Matter”Chap.12: SOLIDS: “Density” onlyChap.13: LIQUIDS: All but “Surface Tension” & “Capillarity”Chap.14: GASES: All except Plasma

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Midterm #2 MaterialChap. 15: Temperature & Heat: All but “Expansion of Water”Chap. 16: Heat Transfer: All but “Newton’s Law of Cooling”Chap. 17: Change of Phase: AllChap. 18: Thermodynamics: All but “Meteorology”Chap. 19: Vibrations & Waves: All but “Bow/Shock Waves”Chap. 20: Sound: All but “Beats”Chap. 21: Musical Sound: All but “Fourier Analysis” & “DVD”Chap. 22: Electrostatics: All but “Supercond” &“Elec. Storage”Chap. 23: Electric Current: All but “Speed of Electron”&”CFL”Chap. 24: Magnetism: All but “Meters”,”Motors”,”Cosmic Ray”Chap. 25: Electromag. Induction: All but “Turbogen” & “MHD”Chap. 26: Prop. of Light: All but optical illusionsChap. 27: Color: All but “Sky Blue”, ”Sunset Red”, ”Clouds

White”Chap. 28: Reflection/Refraction: All but “Principle Least

Time”, “Total Internal Reflection”, “Lens Defects”

Material Since Midterm IIChap. 29: LIGHT WAVES: All sections except “Holography”Chap. 30: LIGHT EMISSION: All sections except CFL & LEDChap. 31: LIGHT QUANTA: All Chap. 32: ATOM & QUANTUM: All sections except “Quantum

Mechanics” and “Correspondence Principle”Chap. 33: ATOMIC NUCLEUS & RADIOACTIVITY: All except “Radiometric Dating”Chap. 34: NUCLEAR FISSION & FUSION: All except “The Breeder Reactor”Chap. 35: SPECIAL RELATIVITY: All but “Addition of Velocities” and “The Correspondence Principle.”

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Huygens’ Principle & Diffraction• A line of small particles striking a barrier with an opening in

it would cast a sharp shadow.• Plane waves striking the same barrier would cast a “fuzzy”

shadow -- wavefronts would spread into shadow regions• Each point on the wavefront in the opening is a new source

of spherical (circular) wavefronts• As the width of the opening narrows, the spreading of

waves into the shadow region becomes more pronounced.

DiffractionAmount of diffraction depends on wavelength of the wave compared to the size of the obstruction that casts the shadow. Diffraction effects are greater for longer wavelengths (lower frequencies).

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Superposition and Interference

InterferenceExperiment

Detail of InterferencePattern

Polarization of EM Waves• Direction of Electric field determines

polarization

Polarization Direction

Polarization Direction

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• If unpolarized EM wave strikes filter, transmitted wave is polarized:

(Half of original brightness

Two Polarizers CombinedAmount of light passing through depends on

relative alignment of transmission axes

(Half of original brightness

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Production of Light• Incandescent (hot) source (Stars; light

bulb)– Give off continuous spectrum (all frequencies)

of EM waves (electrons vibrate randomly)– Inefficient source of visual light unless

temperature very high – most radiation is IR (heat)

• Electrons moving between energy states in atoms, molecules, solids– Fluorescent light– Light-emitting diode (LED)– Laser

Optical Spectrum of Hydrogen

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Lamp Efficiency• Incandescent (hot) source (Stars; light bulb)

– Only about 10% power used gives visual light –most radiation is IR (heat) – 10 lumens/Watt

• Atomic transition sources– Fluorescent light – 45-50 lumens/Watt– Light-emitting diode (LED)–70 lumens/Watt

Lasers

Lasers can produce light that is monochromatic AND coherent

• Coherent light of identical frequencies in phase

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Quantization and Planck’s Constant• Quantum physics states that in the microworld of

the atom, the amount of energy in any system is quantized—not all values of energy are possible.– Example: The energy in a beam of laser light,

which is a whole-number multiple of a single lowest value of energy—one quantum

• The quanta of light, and of electromagnetic radiation in general, are photons.

• Energy of a photon of frequency f:E = hf where h is Planck’s constanth = 6.6 x 10-34 J/Hz or 6.6 x 10-34 J·sNote: Value of h on text p. 549 is wrong!

Example

• What is the energy of a photon of frequency 3 x 1014 Hz?

(h = 6.6 x 10-34 J/Hz)

E = hf = (6.6 x 10-34 J/Hz)(3 x 1014 Hz)= 2.0 x 10-19 J

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Particles as waves: electron diffraction• Every particle of matter is associated with a

corresponding wave. According to de Broglie, a particle’s wavelength is related to its momentum.

where h is Planck’s constant. (h = 6.6 x 10-34 J·s)

Particles as Waves: Electron Diffraction

momentumWavelength = h

λ = h/p

Example• What is the de Broglie wavelength of a

particle of mass 1 x 10-20 kg moving at a speed of 6.6 x 105 m/s? (h = 6.6 x 10-34 J·s)

• λ = h/p = h/(mv)• = (6.6 x 10-34 J·s)/[(1 x 10-20 kg)(6.6 x 105 m/s)]• = 1 x 10-19 m

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Uncertainty PrincipleUncertainty principle (continued)• German physicist Werner Heisenberg called

this the uncertainty principle.• When the uncertainties Δp and Δx in

measurements of momentum p and position xfor a particle are multiplied together, the product must be equal to or greater than Planck’s constant, h, divided by 2π, which is represented as (“ h-bar “).

ΔpΔx ≥

h

h

ATOMIC STRUCTUREATOMIC STRUCTURE

e- e-p+nono p+

NucleusNucleus

Electron CloudElectron Cloud

Model of aModel of aHeliumHelium--44((44He) atomHe) atomZ = 2Z = 2A = 4A = 4

Z is atomic number = # protons = # electrons

A is atomic mass number = # protons + # neutrons

Nucleons: Proton (charge +e); Neutron (no charge)

Electron charge e = 1.6 x 10-19 C

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Bohr’s Model of the Atom• Bohr reasoned that electrons occupy

“stationary” states (of fixed energy, not fixed position) at different distances from the nucleus.

• Electrons can make “quantum jumps” from one energy state to another.

• Light is emitted when such a quantum jump occurs (from a higher to a lower energy state).

• Frequency of emitted radiation is determined by

ΔE = hf

where ΔE is the difference in the atom’s energy when the electron is in the different orbits.

Explanation of Quantized Energy Levels: Electron Waves

• The electron orbits in an atom have discrete radii because the circumferences of the orbits are whole-number multiples of the electron wavelength.

• This results in a discrete energy state for each orbit.

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Alpha, Beta, and Gamma RaysRadioactive elements emit three distinct types of radiation:• α —alpha particles: helium nuclei (2 protons

& 2 neutrons); positively charged • β — beta particles: electrons; negatively

charged• γ —gamma photons (very high frequency

electromagnetic radiation); no charge

Radiation Dosage and EffectsRadiation dose measured in rads; rad = 0.01 J/kgBiological effect measured in rem; depends on

type of radiation. rem = RBE*rad

Biological equivalence factors (RBE) of radiationParticle Radiation Dosage RBE Factor Health effectalpha 1 rad × 20 = 20 remsbeta 1 rad × 1 = 1 remGamma 1 rad x 1 = 1 remX-Ray 1 rad x 1 = 1 remneutron 1 rad x 5 = 5 rem• Doses of radiation

– 100 mrem/yr is legal limit for man-made non-medical exposure– Lethal doses of radiation begin at 500 rems (over a short time)

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The Atomic Nucleus and the Strong Nuclear Force

The strong nuclear force holds nucleons together.It is a very short range force (10-15 m distance).

Radioactive Half-LifeThe rate of decay for a radioactive isotope is measured in terms of a characteristic time, the half-life, the time for half of an original quantity of an element to decay.

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Naming of Isotopes

EAZ

H11

Element SymbolAtomic # (# protons)

Mass # (# protons + #neutrons)

Ordinary Hydrogen

He42 Helium-4 (alpha particle)

An element can have several isotopes, all with same Z value, but different A values:

Alpha DecayWhen an alpha particle is emitted by a nucleus, a different element is formed. This is transmutation that occurs in natural events and can also be initiated artificially in the laboratory.

Uranium naturally transmutes to thorium when an alpha particle is emitted.

HeDP AZ

AZ

42

42 +→ −

−

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Beta DecayNatural transmutation by beta emission

• Thorium naturally transmutes to protactinium when a beta particle is emitted.

eDP AZ

AZ

011 −+ +→

Transmutation of the ElementArtificial transmutation

• An alpha particle fired at and impacting on a nitrogen atom transmutes it to oxygen and hydrogen

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Nuclear FissionA typical uranium fission reaction:

Note the mass number as well as atomic numbers balance.

neutron

Mass–Energy EquivalenceE = mc2

• Early in the early 1900s, Albert Einstein discovered that mass is actually a “solidified”form of energy.

• Enormous work is required to pull nucleons from a stable nucleus. This work is energy added to the nucleon that is pulled out, and it makes the nucleon mass larger. .

(E in Joules; m in kg)

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Nuclear FusionTypical fusion reactions:

Postulates of Special Theory of Relativity• All laws of nature are the

same in all uniformly moving frames of reference.

• The speed of light in free space has the same measured value for all observers, regardless of the motion of the source or the motion of the observer; that is, the speed of light is a constant.

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Time Dilation• The relationship between the time t0 (call it the proper time) in

the frame of reference moving with the clock and the time t measured in another frame of reference (call it the relative time) is

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1

1

cv

tt−

=

2

2

1

1

cv

−

=γ

0 tt γ=

Lorentz factor

A factor ≥1 that tells amount of relativistic effect

Length Contraction• As objects move through spacetime, space as well as time

changes.• Space is contracted, making the objects look shorter when

they move by us at relativistic speeds.

L = L0/γL0 is length when stationary; L is length when moving; γ is Lorentz factor

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Mass, Energy and E = mc2

• A piece of matter, even at rest and not interacting with anything else, has an “energy of being.” This is called its rest energy.

• Einstein concluded that it takes energy to make mass and that energy is released if mass disappears.

• The amount of energy E is related to the amount of mass m by the most celebrated equation of the 20th century:

2mcE =

Final Exam -- Monday Dec. 20, 1045-1315

Homework #28 due by 11:00 PM Monday Dec. 13

Regular office hours and help sessions this week