More nuclear Physics, then begin chemistry notes

Lecture notes 7-3-07

Atomic number, atomic mass number and symbology example: ₉₂²³⁵U, : ₉₂²³⁸U

Recall isotopes being atoms with same number of protons and different number of neutrons.  Isotope means “same place,” in this case same place in periodic table.

Half life.   The time it takes for half of a sample of radioactive elements to decay. Independent of how much you start with.  Half of what was there is gone (decayed to another element) in one half-life, so you have half of what you started with, then half of that, then half of that...on down to when only a few of the original radioactive atoms are left, and then the half-life concept is no longer valid.

For anything that has “rate of decay or growth proportional to amount present” you have this sort of exponential time relationship: a decrease for decay and an increase for growth.  (gave example eating cake in hell, where you have your cake and eat it too, always some left but you only get a tinier and tinier crumb in each bite as time passes, but of course hell is for eternity which means time doesn't pass, so never mind) 

See previous lecture notes for another example....half of a half of a half ... of a hamburger.

Fission and Fusion.  The most stable atoms are in the middle of the periodic table.  See figure 10.20 for the reason why fission and fusion produce energy.  Who discovered fission has been a controversial issue for many years.  Lise Meitner, Otto Hahn and Fritz Strassmann worked together in Berlin until M. escaped from Nazis because she was Jewish.  But she had the correct idea along with her nephew Otto Frisch.  She should have won the nobel prize too, along with Hahn.

Biological effects of radiation.  Alpha, beta, gamma, neutrons and x-rays are ionizing radiation. Ionizing means they can knock electrons out of an atom, or even hit the nucleus and change its electrical charge (adding or subtracting a proton).  The result in either case is that the atom becomes an ion, meaning it isn’t electrically neutral.  Ion means “an atom, or chemical combination of atoms, that has a net electric charge.” Absorbed nuclear radiation can cause unwanted chemical reactions, can kill cells, can cause genetic defects that will show up in a future generation.

The average US citizen today receives a small amount (about 0.2 rem) of natural and man-made radiation. It’s a small amount but it’s a long term exposure, and is also an average. About 82% of this comes from natural sources and the rest from human activities.  The rem measures dosage and its biological effectiveness, whereas the rad is 0.01 joule of energy deposited per kg of tissue.

Chemistry, the chemical elements.

Classification of matter:  elements, compounds, mixtures. 

Pure substances can be elements or compounds.  Element: a substance that is just a bunch of the same type of atoms.  Compound:  two or more elements chemically bonded in a definite mass ratio. Water H2O, Salt NaCl.

Then there’s the mixture, a type of matter that has varying proportions of two or more pure substances that are physically mixed together but are not chemically bonded.

Heterogenous mixture:  Two or more substances can be seen in a heterogeneous mixture—it is not uniform in appearance or texture.  Italian dressing and the mixed green salad you put it on are two examples.  Others are pizza and zinc mixed with sulfur (as opposed to the compound zinc sulfide).

Homogenous mixture:  There are two or more substances making up the mixture but it appears to be just one substance.  All for one, one for all.  Another name for homogeneous mixture is solution.  Solids, liquids and gases can be solutions. Air, coffee, brass (zinc and copper), saltwater are examples. 

Solutions are composed of a solute and a solvent.  The solvent is the substance present in the largest amount.  When you make coffee or tea, water is the solvent and the coffee molecules or tea molecules are the solute.  Remember, they just mix together very well, they don’t combine chemically.

Discovery of the elements>  Robert  Boyle in 1661 proposed that substances that could not be separated into components by any method were elemental or fundamental and should be called elements.  Figure 11.8 shows how the number of identifiable elements has increased over the years.  Now the elements can be broken down by nuclear bombardment, but are still called elements.

Molecules  are stable, chemically bonded configurations of atoms. 

Occurrence of the elements:  in our bodies, 65% oxygen and 18% carbon.  In  the earth, about 47% oxygen and 27% silicon.  In the universe (and in the sun) hydrogen 75% aand helium 24%, then the other stuff is only 1% of the total and comes from supernova explosions.

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Two or more forms of the same element that have different bonding structures in the same physical phase are called allotropes.  Carbon example, figure 11.14.

The periodic table.  The idea it’s based on is that the properties of the elements repeat in a systematic or periodic fashion. The Russian scientist Mendeleev invented it.

Like any table, it has rows and columns.  The seven rows are called periods. Similar properties in each row occur at definite places as you go across the table.  The columns are called groups.  They are groups of elements with similar chemical properties.

What kind of properties are we talking about?  Four, as far as we’re concerned.

1. metal vs non-metal.  Metals are defined as any elements that tend to lose electrons in chemical reactions. Nonmetals are elements that tend to gain or share electrons during chemical reactions.
2. electron configuration/valence…  Introducing “Shells.”  The principle quantum numbers, n, designating the main energy levels of the electrons in an atom, are referred to as shells.  The outer shell is called the valence shell and is our only concern in here.  It’s important because the number of “valence electrons” in this shell determine the chemical properties of an element.  Elements in a given group (column) in the periodic table have the same number of valence electrons and thus have similar chemical properties.  The shells fill up going from left to right in the table.  The number of shells is equal to the group number.  “octaves” ridiculed, but turned out to be true.
3. atomic size…  increases as you go down a column (group); decreases as you go across left to right—more tightly bound outer electrons, no shells being added.
4. ionization energy…increases as you go across left to right.  Again it’s because the shells are filling and the outer electrons becoming more tightly bound.

Atomic physics & begin nuclear physicks

Lecture notes 28 June

Atomic physics:

Early concepts of the atom

Dual nature of light

Bohr theory of the hydrogen atom

MicroWAVE ovens, x-rays and lasers

Heisenberg’s uncertainty principle

Matter waves

Electron cloud model of atom

Now, how to present it?

Chapter 9:  A coupla things you all need to know.

1)     Beginnings of quantum theory:  Light, which was once thought to be purely a wave, also behaves like a particle. In particular in its interaction with matter, light is absorbed and emitted as if it were a particle. Max Planck discovered the first quantum effect in 1900 when he noticed that if he added up the energies at different frequencies being emitted from a heated ideal radiator he could get the correct spectrum (the spectrum observed in experiments) only by using a discrete sum rather than a continuous sum (summation symbol Sigma used instead of contiunuous sum of calculus integration process, see?). Einstein in 1905 extended the discovery by describing the photoelectric effect in terms of light behaving as a particle.  The particle of light soon came to be called the photon (coined by G. N. Lewis in 1916).  This was the beginning of quantum mechanics, which also says that particles like protons, neutrons and electrons also sometime behave like waves (de Broglie and Schrodinger).  When you try to find the precise position and speed of one of these particles, you find that it behaves like a wave—it doesn’t have a precise position and speed.  This is the basis of the uncertainty principle, which is also called the indeterminacy principle, which says, for instance, that the position and speed of a particle can’t be determined simultaneously with unlimited accuracy.

2)      The Bohr model of the hydrogen atom.  The Rutherford model of the atom (1911) claims that electrons orbit the nucleus somewhat like planets orbit the sun, and came about from experiments involving shooting alpha particles at gold foil.  Why gold?  Didn’t oxidize, but remained “pure” so it would give the least complicated experimental results.  Even with the Rutherford nuclear model, the neat, discrete spectrum emitted by atoms was not explained. Light with precise frequencies is observed to be emitted from atoms, not a smeared out spectrum, like light from a rainbow or sunlight refracted through a prism.  Another problem was if electrons orbit like planets, they have centripetal acceleration.  That should cause them to lose energy and fall into the nucleus.  But atoms are stable!  In 1913, Niels Bohr proposed that electrons in atoms occupy stable orbits called energy levels, and that electrons only radiate when they fall from a higher orbit to a lower one. When an atom absorbs light, an electron jumps from a lower energy level to a higher one. (Draw picture.)  Also, for the rotational and vibrational states of molecules, longer wavelength radiation is absorbed and emitted.  Microwaves are a good example.  Also for heavy atoms, x-rays can be emitted by an electron being knocked out of lowest energy level and one from a high energy level falling into that lowest level.  This spontaneous jumping of electrons to a lower energy level is not suprisingly called "spontaneous emission."  Then there are lasers, L A S E R, light amplification by stimulated emission of radiation.  A photon hits an atom in an excited state, knocking the excited electron down to a lower state, and in the process stimulating the emission of a photon which goes on off with the photon that came in.  Stimulated emission, but not the laser itself, was predicted in 1917 by Einstein in his superdooper derivation, via thermodynamic equilibrium of light and atoms in a box, of the Planck spectrum.

Chapter 10:  This is Nuclear physics, not rocket science.  Rocket science has big equations, and is complicated.  Nuclear physics has little equations and is really pretty simple.

Hydrogen is the simplest atom. One electron orbiting one proton.  If there were just the gravitational and the electromagnetic forces, hydrogen would be the only element in existence.  But there is a force stronger than the electromagnetic force that causes protons and neutrons to clump together, and form atoms heavier than hydrogen. This is the third fundamental force we’ve talked about, the first two being gravity and electromagnetism. This force that holds nuclei together is called the strong force, because it’s stronger than electromagnetism. 

But the strong force is only operative over a short range, and the electromagnetic force operates over an infinite range. (So does gravity, but it’s too weak to have an influence at the atomic level.)  The bigger a nucleus gets, the less effective the strong force is in holding it together, because the electrical repulsion of the many protons overwhelms the short-range strong force.  For atoms with more than 83 protons, the electrical repulsion between protons starts to overcome the strong force, and the nucleus decays radioactively.  So atoms with atomic numbers greater than 83 are unstable.   They decay into more stable atoms with fewer protons.

What is the atomic number?  The number of protons in an atom.  It determines the place of an element in the periodic table.  The atomic mass is the number of protons plus the number of neutrons in an atom.

Radioactivity and half-life.

The last and least-strong force that is known today is called the weak force, so called because it’s weaker than the electromagnetic force.  It causes a nucleus to emit electrons, turning a neutron into proton in the process. Also recall that a free neutron—one that’s outside a nucleus—decays with an average lifetime of about 11 minutes, so it also decays by emitting a fast-moving electron, which is called a beta ray. This type of radioactivity is important because it involves all three fundamental particles that make up an atom—proton, neutron and electron.  There are other types of nuclear radiation also.   In Greek alphabetical order the three common types are:  alpha rays (helium nuclei, 2 protons and 2 neutrons) beta rays (electrons), and gamma rays (very high energy electromagnetic waves). There is one more type, not as common but very important, and that is neutrons.  X-rays also are dangerous (ionizing), but not microwaves—they’re low energy.  X-rays produced by – draw picture.  HV supply, vacuum tube, electrons attracted to postive plate, x-rays produced when atoms in plate are hit by electrons.  Like TV, but it aint as high voltage. (wrote on the board some other stuff, just table 10.5 mainly: positrons added to list of nuclear radiation.)

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Half-life.  What’s the half-life of a hamburger?  "I only want half a hamburger."  "Well, I only want half of a half of a hamburger."  "I only want half of a half of a half of a hamburger."  Which can go on indefinitely.   If you actually ate half of a hamburger in one second, handed the remaining half to your brother, who ate half of that in one second, which he handed back to you (now one fourth is left), which you ate in one second... and so on, the half life of the hamburger would be one second.  The rate at which the hamburger is eaten, you see, not constant.  It slows down. In order for the concept of half-life to be valid, the rate must be proportional to the amount remaining. (Well, you could use a 1/10th life or a 1/3rd life, or similar, but half-life is the standard measure.)

Later: Nucular reactions and uses of radionuclides. Fission and Fusion.

Biological effects of radiation.  Alpha, beta, gamma, neutrons and x-rays are ionizing radiation. Ionizing means they can knock electrons out of an atom, or even hit the nucleus and change its electrical charge.  The result in either case is that the atom becomes an ion, meaning it isn’t electrically neutral.  Ion means “an atom,or chemical combination of atoms, that has a net electric charge.” 

Electric circuits; magnetism & electromagnetism

Lecture notes for 26 June 2007

Electric circuits and electrical safety

DC or direct current, from batteries.  AC is alternating current, produced by generators.  The equations in this chapter, Ohm’s law and the power equation, apply to DC and AC cases.  Electronic devices are inherently DC, have to have a “power supply” to convert AC to DC.  Power is wasted in the process, and heat is generated.

Electrical devices are often represented as resistances, because they do have some amount of resistance, large or small, and therefore use power according to P = I2R.  The power in watts how the device is rated, but because of this equation,  it could be rated by its resistance instead. Thus this squiggly symbol is important because it is a way of model real devices in a simple circuit.

Series and parallel resistances:     Two basic ways to connect two or more resistances or electrical devices:  series or parallel.  What y’all need to know.  SERIES:  Resistors in series each have the same current in them, and connecting more resistances in series increases the total resistance.  PARALLEL: Resistors in parallel each have the same voltage across them, and connecting more resistances in parallel decreases the total resistance.

What they look like:  Series:  draw it with 3 R’s.          Parallel:  Draw it with 3, too. Show open circuit in each.   Same voltage across parallel.  Thus parallel is used in electric utility wiring, for homes and all users of the electric grid.  Series would make no sense, as in the old Christmas tree lights.   New lights have a parallel (shunt) resistor/insulator combination.

Circuit breakers are needed because as more appliances or higher wattage ones are connected, the total resistance is decreasing—this is one of the two characteristics of a parallel circuit. That means current is increasing in the circuit, because the voltage isn’t changing.  Different parts of the house have different circuit breakers to protect them.

A bimetallic strip is used to trip the circuit breaker and open the circuit so that no current will flow.  Fig 8.12.

SAFETY: Discuss fig 8.9.  Stereo unlikely to be 220v.  What is the neutral wire?  It’s at zero voltage, literally the potential of the earth or ground.  Hotwire varies from 0 to 120.  Other hotwire varies from zero  to –120 v.  Ground wires and polarized plugs are the ways that electrical devices are made  safer.  If the hot wire comes loose and touches the metallic case then current flows to ground through the “dedicated” ground wire, not through you.  What then is advantage of polarized plugs?

Electrical safety highlight---your wet body has much less resistance than your dry body, possibly allowing a lethal amount of current in the wet body case whereas for the same voltage the dry body would get a slight shock.

Magnetism!

 

What is a magnet?  Any material that’s capable of being magnetized, meaning it can exhibit external N and S magnetic poles.  Poles come in pairs also!   External magnetization is really the result of the lining up of the magnetic fields of many spinning electrons in a material. That wasn’t fully know until the 1920s, about one hundred years after the connection between electricity and magnetism was discovered in 1829, when Hans Oersted was giving a lecture in and noticed that an electric current in a wire caused a nearby compass needle to deflect. 

All magnetism is the result of electric charge in motion.  In the ferromagnetic elements, iron, nickel, & cobalt for example, the magnetic fields of many atoms (the outer electrons in the atoms actually) line up with the magnetic poles in the same direction and produce tiny magnets within the material.  For an external field to be created, these “magnetic domains” must be forcibly lined up in the same direction by an external magnetic field.

Demagnetizing by heat:  Rapid and random motion of atoms of a magnetized material above the Curie temperature causes magnetic domains to become unaligned. 770 degrees F for iron. Also hitting a permanent magnet hard enough can cause domains to be shaken out of alignment.

Current in a wire always is accompanied by an external magnetic field.  When a wire is coiled in a helix formation, the magnetic field external to the wire is just like a bar magnet’s field.  If the coil is wrapped around an iron bar then the bar becomes magnetized and greatly increases the strength of the coil’s magnetic field.  See fig 8.18.  This is an electromagnet.

Earth’s magnetic field.  Resembles a bar magnet inside the earth with its south pole pointing approximately to geographic north. Thought to be caused by earth’s rotation causing currents of electrically charged particles deep below surface.  Magnetic declination is the angle between geographic north (“true north”) and magnetic north.  This must be corrected for when using a compass in navigation.

 Electromagnetism

Two main points:  1) Moving electric charges create magnetic fields. Already discussed. 2) A magnetic field exerts a force on a moving electric charge.  This is how motors, generators and most speakers work.  Motors convert electrical energy into mechanical energy by the magnetic force on a wire carrying a current (electric charge in motion). Generators convert mechanical work (energy) into electrical energy.  Same set up as motor but the wire is rotated by mechanical force, so that a current is created in the wire and in the external circuit.

Transformers make it possible to step up or step down an AC voltage but not DC.  The  changing magnetic field created by the AC current in the primary coil creates an AC current in the secondary coil, as predicted by Faraday’s Law. This is one big reason that early in the history of power transmission, AC was chosen instead of DC.  Edison versus Tesla (immigrated from Russia).  Edison won.  See figure 8.30.  High voltage used to transmit electricity because then current is lower and heat losses, P = I²R, are less.

Electric charge & electric current

Lecture notes for 6-21-07

Electric charge and current, Chapter 8.

(review some of the previous ideas, and the idea of  F  E  W = the take-home message)

Another fundamental quantity or base unit is introduced in this chapter: ELECTRIC CURRENT.  Others we’ve already seen are LENGTH, TIME, MASS and the one that slipped by in chapter 5, TEMPERATURE.  Two more are coming up later.

Electric current is the motion of electric charge.  Current is much easier to measure than charge, so current is now used as the fundamental unit.  Why do we have electric charge in the universe? Because we have protons and electrons.  Protons carry positive charge, electrons carry negative charge.  Neutrons are neutral.  Atoms are made of protons, neutrons, and electrons.  The mass and charge of each of these particles is given in Table 8.1. 

The base unit of electric charge is the Coulomb.  Electrons (–) and protons (+) have exactly equal but opposite charges of 1.6 x 10^–19 Coloumb.  Why is that?  Not known!  There is no theory that tells why electrons have exactly the same charge (with opposite sign) as the proton.  How then do we know they are precisely equal?  If they weren’t, atoms wouldn’t exist.  A slight difference in the charge of the proton and electron would make atoms unstable. 

Electric current is the rate of flow of electric charge, defined as

Current = charge / time, or in symbols

 I = q/t .  The unit of current is the ampere: amperes = coloumbs/second.

Some materials, such as metals (gold, silver, copper, aluminum) are good electric conductors.  The outer electrons of these atoms are loosely bound.  These materials also are good heat conductors. 

Poor electric conductors have tightly bound outer electrons—wood, glass, and plastic are examples.  There are a few materials that fall in between good and poor conductance: semiconductors.  The main one used in semiconductor devices is silicon.  But there is also carbon, which is used in resistors.

Electric Force   Like charges repel, unlike charges attract.  In terms of a force being a push or a pull, like charges push each other away, and unlike charges pull on each other.  The book brings up Newton’s 3^rd law.  Why or how does it apply to both pulling and pushing? 

(Aside: We don’t have a two-particle interaction in physics where one is attracted and the other repelled. In life, between elementary particles known as persons (purse-AHNS), we do have this interaction, as you may know from experience…):

What is the electric force?  Coloumb’s law: 

F = k q₁q₂ /r²

Same form as gravity, an “inverse square law,” but when one q is negative and the other is positive, the force is attractive (has a negative sign), and when both q’s are the same sign, the force is repulsive.  Gravity is always attractive, meaning it always exerts a pull and never a push.

Negatively charged objects have an excess of electrons, positively charged objects have a deficiency of electrons.  How does something become charged?  Friction is a common and usually unwanted way of creating an excess or deficiency of static charge.  But in humid weather like we usually have in summer, moisture in the air keeps excess charge from building up.

Bringing a charged object near an uncharged one can cause a separation of charges in the uncharged object, as in the comb and paper case (see textbook).  The plastic comb is charged by rubbing (friction).  Molecules in the paper become polarized when the comb is brought near, meaning they possess definite regions of separated charge.  Polarization induces the separation of charges, so charging by polarization is called charging by induction.  The case of a plastic balloon attracted to wall or ceiling occurs because first the balloon has picked up excess negative charge from being rubbed (static charging by friction), then the molecules of wall or ceiling or whatever become polarized.  Opposite charges are closest to each other, so attraction occurs.

Water is a polar molecule.  Figure 8.3 shows the effect.  Also, water is a solvent, although quite slow in most cases.  Plastic water bottles unopened slowly dissolve.

Voltage and electrical power

Work is required to separate unlike charges, and when the charges are separated, they have electric potential energy.  But this is not convenient to use except in theoretical physics and plasmas.  In electric circuits it’s more convenient to use the electric potential difference called voltage, which is the work done per unit charge, or equivalently the potential energy per charge.

V= W/q.  The Volt is the standard unit of voltage, and is defined as a joule per coloumb.

Opposition to the flow of charge is called resistance.  Materials naturally have some resistance, and the measurable effects of resistance are 1) a voltage must be maintained for a current to exist, and 2) heat is generated when a current passes through a resistance.  The exception occurs for some materials when they are cooled to near absolute zero and have no resistance, so that once current is started it will flow even without an applied voltage, and the current generates no heat.  The name for this process is superconductivity.  But the low, low, low temperature must be maintained, such as 4 degrees above absolute zero.  Not economical, but can be used in certain cases, such for the high currents needed in elementary particle accelerators.

Resistance, on the other hand, is actually useful.  It allows control of currents and voltages, which is what allows appliances and electronic devices to exist.  Two other current-controlling devices are the capacitor and the inductor, not covered in text but widely used in circuits.

Ohm’s law gives the relationship between voltage, current and resistance:  V = IR  hee.

Water analogy is helpful.    Circuits need an energy source, and batteries are analogous to a water pump in that respect.  Batteries convert chemical energy into the kinetic energy of electrons in a circuit.  Light bulb produces light and heat because work is done on electrons by the battery (or by electrical generator in the case of AC electricity).  A switch is like valve, and the light bulb offers resistance like the water wheel being made to turn by water in the picture in the book.  The turning of the wheel changes gravitational potential energy of water into kinetic energy, which can be used to turn a millstone or do other work.  Electric current analogy would be the turning of the armature of an electric motor.

Conventional DC electric current flow goes from positive to negative, opposite from electron flow.

Gotta talk about POWER now, since electric devices are rated according to how much power they use.  Power in general is work per unit time.  Using the fact that charge times voltage equals work, we find power can be expressed as

P = W/t = (qV)/t = (q/t) V = IV  = current times voltage, whoopee.  Also P =  I(IR) = I²R,  called  Joule heating.

Example 8.1, the 60-watt bulb.  How much current passes thru it?  P = 60 W, V=120v.  Find current, and resistance of the bulb:    I = P/V = 60W/120V = 1/2 A, or one-half amp.  That’s quite a bit of current, and most of the power for the incandescent bulb goes into heat.   Resistance of bulb  R = P/I².  = 60/.5squared = 240 ohms.

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Electric circuits and electrical safety

DC or direct current, from batteries.  Electronic devices are inherently DC, and must have a power supply to convert AC to DC.  AC is alternating current, produced by generators.  The equations above, however, apply to DC and AC cases, where the AC is expressed in rms (root-mean-square) form.

In circuit analysis, devices that require electrical power are often represented as resistances, because they do have some amount of resistance, large or small. (Examples: hairdryer, loudspeaker, your whole house as part of the entire electric grid.) There are two ways to connect two or more resistances or electrical devices:  series or parallel.

Series and parallel resistances: What y’all need to know.  Connecting more resistances in series increases the total resistance, and changes the voltage across each resistance; the same current passes thru each resistor element. Old style Christmas tree lights were purely a series connection, in which one burnt-out bulb (an open circuit, not a short circuit) caused all bulbs to not glow.

 

 Connecting resistances in parallel decreases the total resistance of the circuit, changes the current in each resistor, but the voltage across each resistor remains the same.

 

Elementary optics discussion

O  P  T  I  C  S    A  N  D    W  A  V  E     E  F  F  E  C  T  S

Light rays are what we deal with in Sections 7.1 – 7.4.  This is geometric optics.  Light is represented by a straight line with an arrow on it to show direction of travel of the light beam or “wavefront.”  Sections 7.5 and 7.6 deal with physical optics, the wave nature of light.

When can you see a reflected image of yourself?  Not in most situations—pages of the book, desktop, walls, floor.  Sometimes you can see a glare, a blurry reflected image of a light source, but these surfaces are not good reflecting surfaces because they are rough-textured as in (b) of fig 7.2.  If a surface is smooth and polished, like a mirror or glass window or even a clean car fender your reflection can be seen.

7.1 Reflection:  The law of reflection is “the angle of reflection is equal to the angle of incidence.”   Snell’s law, dates from about… when?  (Baghdad 984, says Wikipedia.) It applies to all surfaces, but the reflection from most surfaces is diffuse, meaning the individual light rays go off in all directions away from the surface.  When you have a polished surface, it’s “regular reflection” and reflected rays travel parallel to each other.

7.2 Refraction and dispersion: 

Refraction: (get some equipment do demo or lab!)  “the deviation of light from its original path because of a change in speed.” In other words, a beam of light bends when going from one medium to another.  What is a medium?  The substance that a wave travels through.  Electromagnetic radiation can travel in a vacuum, without a medium.  The speed of light in the absence of a medium (in free space) is 299792458 meters per second, a universal constant.

The "index of refraction" of a medium tells how much bending of a light beam will occur when light goes from one medium into another, such as from air into water (making a pencil in a glass of water appear bent).  Index of refraction is defined as (speed of light in vacuum / speed of light in medium), and given by the letter n .

Density variations: oasis and illusion of water on hot roadway = refraction by different air density (due to temperature difference).  Also, just above the surface of a hot object, you can see a shimmering from the changing index of refraction if you look along the surface. 

Reflection by refraction:  also known as total internal reflection.  When going from higher density material to lower density material --- higher n to lower n --- light is refracted “away from the normal.”  Draw a picture.  When incidence angle gets big, the refracted ray can be totally reflected back into the substance, fig. 7.10.

Dispersion:  prisms and rainbows: White light has spectrum of red (longest wavelength) through violet (shortest), with mnemonic ROY G. BIV.  The index of refraction varies with the wavelength of light, so that there is more bending for shorter wavelengths.   The “phenomenon of colors” or the “spectrum” of light is seen.  The different wavelengths are spread out or dispersed, thus giving the effect the name “dispersion.” The higher the index of refraction the more the light is spread out, or dispersed.  Thus a prism made of crown glass or of leaded crystal, both of which have higher n than regular glass, can disperse the colors better.

The best material is diamond, with index of refraction 2.42.  (From comparison, water is 1.33, and normal glass is about 1.5.)  Besides the good separation of the colors, the total internal reflection of diamond is more than for other materials.

Rainbow, see highlight, page 160.  You can see rainbows in the sky when there are enough water droplets and when the sun is in the right position, which is about 42 degrees above the horizon.  Total internal reflection AND refraction are occurring in a rainbow.  Two internal reflections produce a secondary rainbow.  Where else do you see rainbows?  Fooling around with the water hose—spraying fine mist of water.  Oil on water, soap bubbles.

7.3 Spherical Mirrors.  Concave, convex.  Introduction to focal length.  Rays hitting a concave mirror converge at what’s called the focal point.  (Draw it.)  Spherical and parabolic reflectors are used to collect light or radio waves at a point.  Convex mirror = diverges light away from a point.

Ray diagrams.  Won’t do these too muchly.

7.4 Lenses.  Do all this as if it’s an introduction and they will continue on in physics…  no, forget it.

Human eye:  The main thing I want you to know is the lens of the eye, the "crystalline lens,” can change shape and is able to focus light on the retina. Know the difference between nearsightedness and farsightedness in terms of where the image appears—in front of the retina or behind it.  Near: in front of retina.  Far: behind retina.  And know which type lens corrects for each. Diverging for nearsightedness, converging for farsightedness.  Also, what happens to near point with age?  Recedes=gets further away.  Inability of the eye’s lens to focus. 

7.5 Polarization:  Light is a transverse wave, its oscillation is perpendicular to its direction of travel.  Looking at this wave I draw on the board, you can see its oscillation is up and down in the plane of the board.  That means it is polarized vertically.  Most light in the room is unpolarized—no preferred direction of oscillation.  P. 171, fig 7.28. Polarization is the preferential orientation of the field’s oscillation  (book says field vectors). 

A Polaroid or polymer sheet will block all polarization directions except one.  The light coming out of a Polaroid will be linearly polarized, as shown in fig. 7.29

"Crossed" Polaroids will block all the incoming light.  Polaroid sunglasses reduce glare off of water and off of car windshields because in both cases reflected light is horizontally polarized and the sunglass lenses only pass light with a vertical polarization. 

7.6  Diffraction and Interference

Diffraction—formation of a new wave front because of waves striking a small object or going through a small opening.

Interference—the addition of the amplitudes of two or more waves.  Constructive and destructive.

Kinetic theory, thermodynamics; wave terminology

(Dr. Evil doesn't "do" phases, but in physics we do, in two different contexts--phases of matter, and the phase relations between waves.)

Phases of matter.  Show diagram at top of page 109.  Gas, liquid, solid. And what the process of converting from one to another is called.   What determines whether a given substance is in the solid, liquid or gas phase?  The temp and pressure! 

Solid has a definite volume and shape. Liquid has definite volume but no definite shape.  A gas has no definite volume or definite shape. 

Most solids have a microscopic crystalline structure (lattice), and some have a MACROscopic, visible crystalline structure—quartz crystal, diamonds, other gems.  Two substances mentioned in book that have “amorphous” structure are glass and asphalt.  Don’t have a particular melting temp, where bonds are broken and solid becomes liquid.   Remember melting and latent heat of fusion. 

Kinetic theory of gases.  How do you smell perfume, by some kind of smell rays being emitted by the liquid?  No, by individual molecules of the perfume being deposited in your nasal passages/olfactory glands.  How do the molecules get there?  By being converted from liquid to gas and bouncing in all directions off air molecules.   Some of these bounce into your nose.

Kinetic Theory describes a gas as consisting of molecules (or atoms) moving independently in all directions at high speeds.  Confined gas molecules bounces off walls of container, and molecules bounce off each other. See pages 116 and 117.

Four variables needed: pressure, volume, temp and number of molecules in the container.   How does the pressure of the gas vary as V, T, and N are varying?  Well,  using the symbol α as shorthand for “is proportional to,”  we have:   P α N,    P α T,    and    P α 1/V.

Combining these gives  P α NT/V,    the ideal gas law, which can be written as an equation if Bolzmann’s constant k is used:  P = kNT/V.  Kicking V over to the left side gives the familiar

                                                                                PV = kNT 

“Ideal gas” means a model of a gas in which no forces act between the molecules or atoms constituting the gas, they merely collide with each other like billiard balls and collide with the walls of the container and go on their merry way.  (But, of course, like billiard balls, where the bounce of a collision is ultimately due to electromagnetic forces, there must be some very short range electromagnetic or other force acting in a collision, or the molecules/atoms would not even sense each other’s presence.)

Thermodynamics:  1^st law and heat engines; 2^nd law (Entropy); 3^rd law.   

Thermodynamics is about the dynamics of heat.  It deals with heat production, heat flow, and the conversion of heat to work.  In dynamics or mechanics, we have Newton’s 3 laws.  In thermoshermo, we have also three laws.  Nobody alone discovered them all, though.  Several people contributed to each one, actually, over the course of 50 to 60 years in the 19^th century.

The first law of thermodynamics is THE CONSERVATION OF ENERGY.  In all processes, including thermodynamic ones, energy is neither created nor destroyed.  When heat is added to a closed system it is converted into either the internal energy of the system or into doing work.  Can be written as simple equation: 

H = ΔE_i + W.  

Engines do useful work.  They make something move, whether it’s a generator rotating in a power plant to produce electricity, your car moving down the road, or electrons moving in a wire.  Many, but not all, engines operate by using a source of heat, such as a boiler in an electric power plant or the heat of combustion that moves the pistons in your car.  Electricity supplied by batteries or by electric motors are exceptions—they don’t use heat to do work, they use electrons directly, by forcing the electrons to move and consequently to do work.  In doing work they produce unwanted heat, though, so thermodynamics also applies to them.

Idealized examples of a heat engine and a heat pump are shown in the book.  A heat engine uses heat to do work, and heat pump, such as AC unit, refrigerator, or real heat pump, takes work and uses it to move heat from colder environment to hotter environment.

First law doesn’t rule out heat flowing SPONTANEOUSLY from colder to hotter object.  Common sense does, though!  And in fact, there is also a law that tells what can and can’t happen thermodynamically—the 2^nd Law of Thermodynamics.  Heat can’t spontaneously flow from hotter to colder object. 

The 2^nd law can also be expressed as: the disorder of an isolated system never decreases.  Entropy is a mathematical measure of how much disorder a system has, so the other way of stating the 2^nd law is:  the entropy of an isolated system never decreases.

Entropy has been decreasing on earth, but this is due to energy input from the sun.  For the solar system itself, a good approximation to an isolated system, entropy is increasing.

Third law: it’s impossible to attain a temperature of absolute zero.  Reason:  it would take an infinite amount of work.  This is like trying to reach the speed of light: it takes more and more work to increase the kinetic energy of an object as it approaches the speed of light.  As absolute zero is approached, it takes more work to remove heat and lower the temp.

(There's also a "zeroth law" of thermodynamics.)

Now, on to ...

W             A                  V                   E                   S

And their properties.

Waves carry energy:  a shaking or vibrating of matter—a disturbance, the book says—causes energy to be released in the form of waves.  The energy can be carried in air—or in any gas or liquid—in the form of sound waves.  If the vibrating object is electrically charged, it emits electromagnetic waves, which can travel in a vacuum (empty space).

Waves are of two basic types, longitudinal and transverse.  Longitudinal waves oscillate parallel to their direction of travel.  EX:  Sound waves.  See fig 6.3.  Transverse waves oscillate perpendicular to their direction of travel.  EX: waves on a string and electromagnetic waves.  Fig. 6.4.

Wave characteristics:  wavelength, frequency, period, amplitude, velocity.

Wavelength: the length of one complete wave (thus is measured in meters or other length units).

Frequency:  Number of oscillations that occur during a given time, usually taken to be one second.  Unit is hertz, of Hz: 1 Hz is one oscillation, or one cycle, per second. 

Period: reciprocal of frequency. So  f = 1/T.  The time it takes a wave to travel a distance of one wavelength.

EX:  Let f= 4HZ.  Then 4 wavelengths pass by a point in one second.

Amplitude: the maximum displacement of the wave.

Speed of light:  3x 10^8 m/s or 186,000 miles per second.

Speed of sound in air at room temp, 20 degrees C, is 344 m/s or 770mph.

Doppler effect: increasing frequency as object emitting the waves approaches you, decreasing frequency as object moves away from you. 

Resonance: when an object is made to vibrate at one of its characteristic or natural frequencies. Standing waves are created, as shown in 6.18.

This can be good in the case of making music or singing, because the “resonant cavity” of the instrument or the singer’s throat and nasal cavity will amplify the sound.  It can be bad for a structure like a bridge, a wine glass, a building or moving part on a car.

Oh, yeh, we can't forget phases.  This is the relationship in time or distance of where the peaks and valleys of two or more waves are located relative to each other.  We can have IN phase waves (peaks and valleys of one are lined up with peaks and valleys of another), OUT OF phase waves (peaks of one wave are lined up with valleys of another), and all possibilites in between. 

Temperature and Heat

Temperature.  This is another everyday quantity, like time, that we are constantly aware of.  Also like time in that we want control over it.  Hot, warm, cold, freezing: these are some words we use to describe our environment, or how we may feel at any particular time.  Our perception of temperature, however, is influenced by the rate of heat conduction between our skin and some object or substance we’re in contact with, not just the temperature of the object or substance.  So temperature as sensed by us is relative.

If heat is conducted rapidly by an object to our skin, the object feels hot.  If heat is conducted rapidly away from our skin, the object feels cold.  Bread in the oven:  the air in the oven, surface of bread, and metal rack are all at the same temp, but you feel different “temperatures” when you touch any one of these.  The metal oven rack will burn you immediately!  Heat conduction and heat capacity of the substances is what that’s all about.

TEMPERATURE

What is temperature, and how can it be measured accurately?   Temperature is a measure of the average kinetic energy of the molecules of a substance.   A single  molecule doesn’t have a temperature, but it does have a kinetic energy.  If you could measure the KE of each molecule in a cup of coffee, then add those KE’s up and divide by the number of molecules, you’d have the temp of the coffee.  In the oven example, the molecules of the air, the bread, and the metal rack all have the same average kinetic energy.  We need a device that can somehow measure average kinetic energy.  What is often used is thermal expansion.  Liquid-in-glass thermometer uses mercury, or alcohol colored with red dye (safer if broken).  (What do the digital thermometers use?)

How does a thermometer work?  Over time, kinetic energy of the substance is transferred to the thermometer.  May be slow or fast (depends on the “time constant” of the particular thermometer), but physical contact insures transfer will happen.  Three minutes for in-the-mouth thermometer?  In the case of the oven, metal transfers heat rapidly, bread less rapidly, and air even least rapidly, but thermometer will read the same in each case, given enough time.

Thermometers, like other measuring devices, need to have two reference points and a choice of unit.  In other words, thermometers need to have a scale that can be assigned numerical values.  Freezing point and boiling point of water at atmospheric pressure are often chosen as reference points for a thermometer scale.

Fahrenheit: Freezing point is assigned value of 32º and boiling point a value of 212º.  Where did that come from?  Supposedly to start with Fahrenheit assigned 100º to the human body by measuring his wife’s body temperature. Then he had to choose the increments of the scale. He came up with the idea of having 180 degrees between freezing and boiling.  Each 1º increment of Fahrenheit scale is thus 1/180 of the temp change between boiling and freezing.

(A professor from Russia who was teaching a thermodynamics class I was in at the University of Texas at Austin told the class about Fahrenheit measuring his wife’s body temperature and choosing that temperature, which he assumed to be the normal temperature of the human body, to be 100º on his scale.  Since 98.6º is the actual normal human body temp, the professor from Russian said of Fahrenheit’s wife: “I guess she had a fever.”  The question of where on or in his wife’s body Fahrenheit used his primitive thermometer wasn’t discussed in the class.)

Celsuis:  0º and 100º, freezing and boiling, so each increment on the scale is 1/100^th of the temp change between boiling and freezing.

Kelvin scale: units are same size as Celsius, but start at absolute zero.  Freezing point at atmospheric pressure of water is 0º C is 273.15 K.  The Kelvin unit doesn’t have a degrees symbol º  associated with it.

Given Celsius temp, how to find Fahrenheit?  T_f = 9/5 T_c + 32.  Subtract 32 from both sides, multiply both sides by 5, divide both sides by 9 and have T_c = 5/9(T_f –32). 

Human body:  98.6º F.  Find Celsius.  T_c = 5/9 (98.6 – 32) = 5/9 (66.6) = 37º C.

HEAT

Total energy or INTERNAL ENERGY in a substance is Ek + Ep.  Rotational and vibrational states of molecules have potential energy.  Does internal energy thus depend on the amount?  Yes.  Does temperature depend on amount of substance?  No.  Average means energy per molecule.

Heat is “net energy transferred from one object to another because of a temperature difference.”  When an object receives heat, it’s internal energy increases.   Some may go into increasing the temp and some may go into vibration or rotation of molecules.

(From fall 2009 class: A student named Savannah said:  “the heat due to friction doesn’t seem to come from a temperature difference.”  I hadn’t thought of that myself, or encountered it otherwise, before.)

Several different units are used for heat measurement.  Heat is a form of energy so the joule is one unit.  A more common one for measuring heat is the calorie.  1 cal = 4.186 joule.  1 cal is amount of heat necessary to raise the temp of one gram of pure water by one Celsius degree (at 1 atm of pressure).  Also, a food calorie, the unit you see most often, is equal to 1000 calories or 1 kcal  = 4186 J.

Food calorie, kcal:  the amount of energy released when a given amount of the particular food is completely burned.  Give me the numbers:   Gram of fat, gram of protein, gram of carbohydrate, gram of alcohol.  How many kcal in each?

(Chapt 5 says 100 Watts is average power output of human body.  How many kcal per minute is this?  How many kcal per day?  About 2,000 as most nutrition labels say.)

Also have the Btu, which is the amount of heat necessary to raise one pound of water one F degree at 1 atm.   Ratings of AC and heating units are Btu’s per hour, often abbreviated to just Btu.

Thermal expansion/contraction.   Freezing of water:  less dense at 0º C than at 4º C. 

Specific Heat and Latent heat.   As already mentioned, when energy is transferred as heat to an object, some of the energy goes into Ek, some into Ep.  Iron and aluminum are given as examples in the book—have to add more than twice as much heat to Al to get the same temp rise as in Fe.  Specific Heat --  “of a substance is the amount of heat necessary to raise the temperature of one kg of the substance by one Celsius degree.”  Since it’s 1º kcal for 1 kg of water. Specific heat of water is 1 kcal/kg Cº. 

Originally “specific heat capacity”.  If substance has high specific heat, can store more energy (heat) for a particular temp change.  Water has high heat cap/ specific heat.

Amt of heat to change the temp by a given amount = mass x specific heat x temp change.

H = mcΔT.   This is true as long as the object/substance is not undergoing a change of phase.

What is a change of phase?  Look at example of ice- water- steam.

Latent heat:  hidden heat, like hidden talent.  The heat released or absorbed when there is a phase change.

Heat needed to melt a substance = mass x latent heat of fusion.

Heat needed to boil a substance = mass x latent heat of vaporization.

Heat transfer.  Three ways heat can be transferred from one object to another:  Conduction, Convection, and radiation.

Conduction: the transfer of heat by molecular collisions.  Example:  when you touch something, heat is conducted to your skin.  In the case of the bread in the oven, air is a poor thermal conductor, bread is a better thermal conductor, but both are no comparison to metal—it is an excellent thermal conductor.  See table 5.3

Convection:  the transfer of heat by the movement of a substance or mass from one position to another.

Radiation: the process of transferring energy by means of electromagnetic waves.  EM waves travel through empty space (vacuum), but they carry energy.  As you can feel from the sun’s radiation (some of that is hot air around you)