Notes on Light and Photons

It is very difficult to communicate the authentic nature of a photon without incorporating it into a quantum (wave-like) picture of the atom. (Or more generally, without incorporating it into a quantum view of atoms, molecules and solids --things which contain electrons that interact with photons.)

On Monday we will begin our treatment of quantum physics. We will focus in particular on the simplest atom, the hydrogen atom, and on related --even simpler-- models of confined electrons, which are similar to atoms. Simple does not mean easy. It only means we will strip away any unnecessary complexity so that we can focus in on the essential nature of quantum physics.

Here is a summary of what we should understand so far regarding light:

1) Light is a wave which involves an oscillating electric field. The oscillation has a frequency f and a wavelength, lamda.

2) Frequency and wavelength are related through the wave-like relation f=c/lamda, where c is the wave speed (3 x 10^8 m/s).

3a) Visible light refers to the portion of the frequency range of oscillating electric field waves that can be seen by the eye. This corresponds to frequencies between about 4 x 10^14 Hz and 8 x 10^14 Hz. The lowest frequency part of the visible range is perceived as red light; the highest part is violet. The frequency order of colors is: red, orange, yellow, green, blue, violet.

3b) Frequencies below those of visible light are called infrared. The infrared range extends from about 10^11 Hz to 4 x 10^14 Hz. Below that is the microwave range. [Note that the infrared range covers more than 3 decades; the visible range covers only factor of 2, which less than 1 decade. (Decade means 10x.)

3c) Frequencies higher than visible are called ultra-violet(UV). Higher frequencies than UV are called xray. They are all waves involving oscillating electric fields. A UV photon has more energy a visible light or infrared photon.

3d) electromagnetic spectrum (partial) includes:
...; infrared-red; red-orange-yellow-green-blue-violet; ultraviolet;...

4) A photon is a quantum unit of light energy. The size of the basic unit of light energy depends on the frequency of the light. For light of frequency f, one quantum of light energy is, hf, where h=6.6 x 10^-34 J/Hz. (Note that Joules/Hz is the same as Joule-seconds.)

5) The basic quantum unit of energy cannot be broken. You cannot have amounts of energy in a light wave that involve a fraction of hf. For light at a frequency f, the energy of the oscillating electric field must always be an integer multiple of hf.

6) The quantization of light energy becomes increasingly important and relevant to physical phenomena at high frequencies. That is because the basic quantum unit of energy, hf, is big when f is big. (A UV photon has more energy than any visible or infrared photon.)

Chat Session has begun. Please post your question here.

Let's try posting and responding to posts via comments here. If you have trouble with that, you could also try gchatting me at zacksc@gmail.com , and I will paste your question into a comment here and respond here. Everyone should feel free to respond to anyone else's question. Even if you are not sure you can say what you think a good approach might be.

Homework help sections this week

This week there will only be one HW help session, which will be on Thursday at 6:00 PM at Nat Sci (Annex) room 101,
unless a number of people (more than 8) request an additional one which could be on Wednesday at 3 or 4 PM. Post a comment here if you do want and would come to a Weds section and you can indicate a time preference for that.

(There is HW due on Friday. It is in a post 3 or 4 below this one.)

Notes on Circuit Theory

For a "simple" circuit consisting of a battery and a resistor (and wires), like we discussed in class on Monday, there are some subtle and tricky things to bear in mind. Familiarity with these will help you conceptualize and carry out circuit problems like those on the HW for this week (see earlier post).

The first has to do with current, I, which has units of coulombs per second. A key premise of circuit theory is that current is the same at each point in the circuit! It does not diminish!

(Also, as an aside, when the voltage is first applied, the current starts moving everywhere in the circuit at once. The charge carriers (electrons) in the metal of the wire and in the resistor all start moving together at the same time and in the same "direction" as soon as the voltage is applied. (When we cover relativity we will see that there is a slight correction to this related to the finite speed of light.))

As electrons go through the resistor, they go from a region of ____ potential energy to a region of ___ potential energy (fill in). In the resistor, potential energy is converted to heat energy (or sometimes to something else like light (from the point of view of circuit theory, a light bulb is a resistor). Kinetic energy does not play a role in this. Circuits are all about conversion of potential energy to heat or other forms of energy!

The equation for this is P = V I, where V is associated with the size of the potential energy change (drop) and I is associated with the number of charge carriers (electrons) that get converted. Units are Volt-coulombs/second , which is the same as Joules/second, also known as Watts.

Solutions for HW on Waves and Sound

Note on units: For all these problems it is good to bear in mind that Hz just means 1/seconds .

Ch 19.
1. a) 10 Hz b) 0.2 Hz c) 60 Hz (frequency is one over period. units are Hz = 1/sec)

2. a) .1 sec b) 5 sec c) 0.017=1/60 sec

3. If the distance between crests is 15 meters and the time between crests passing by is 5 seconds, then the waveform must be traveling 15 meters in 5 seconds, hence at a speed of 3 m/s .

4. twice each second. I think its frequency is 2 Hz and its period is 1/2=0.5 sec. The amplitude is i think 10 cm since its goes 10 above and 10 below an equilibrium point for a total excursion of 20 cm. (That is usually how amplitude is defined.)

5. wavelength is speed over frequency. In this case 3x10^8m/s divided by 100.1x10^6 Hz or about 3 meters.

7. a) period=1/f =1/(262 Hz). This is a little less that 4/1000 = .004 sec.
b) wavelength in air is 340 m/s divided by 262 Hz. This is in the neighborhood of 1.2 meters i think.

Chapter 20:
1) Wavelength of a 340Hz tone in air is about 340 m/s divided by 340 Hz = 1 meter.
Wavelength of a 34,000 Hz tone (ultrasound) is much shorter, i.e., 340 m/s divided by 34,000 Hz, which is about 1/100 =0.01 meters = 1 cm. Does that seem correct?

Chapter 21:
3) octaves correspond to factors of 2, i believe. 2000 Hz, 4000 Hz, 500 Hz, 250 Hz

5) This is a bit hard since you have to realize that for the fundamental mode the wavelength is twice the length, so in this case the wavelength is 1.5 meters. Wave speed is wavelength times frequency, which for this problem is 1.5 x 220 Hz = 330 meters/second .

Homework on Conducting Materials and Circuits

For homework due next Friday (Feb 27) please do the following:
(This covers two very different areas and types of problems, so I would suggest starting soon and expecting it to involve more time and effort than usual. Also, it may count up to 2x more than other HW's.)

1-3) The problems from the virtual quiz (see previous post).

4) Based on considerations similar to those you used in the above problems (from the quiz), discuss your thoughts on what the nature of gold (Au) might be. Include discussion of the total number of electrons per atom, how many might stay localized and how many, if any, go into non-localized states...

5) (Extra credit) Do the same for Ge (germanium). [Hint: For Ge, try assuming that there is a core which is like Ar (argon) but with exactly 10 extra electrons filling a "d-state mini-shell"

6) [Extra credit) If Ge is similar to Si, then speculate as to what a semiconductor which is exactly half Ga atoms and half As atoms (gallium and arsenic) would be like. Assume that they are in a perfectly ordered structure with each Ga having 4 nearest neighbors of As and visa versa. (Ask me to draw this in class if you like). How many electrons does each atom have, where do they go, etc? Is this similar to salt* or to Si or ...?
*NaCl

Also please do book problems: Chapter 23, Problems 2, 3, 4, 6, 7 and 8 , with 6 being extra credit.

Virtual Quiz: the nature of conducting materials*

Yesterday we had a virtual quiz, which is a quiz you do on your own. It shows what material we are currently covering and emphasizing and, like a real quiz, contains material you may be tested on in the future. I hope you all do well on this "virtual quiz". In fact, we are giving everyone 100% ...
(PS. I added two extra problems over what we showed in class.)
(*edited, Sunday, Feb 22)

Problem 1. a) Describe the nature of copper (Cu) and aluminum (Al) paying particular attention to how many electrons remain localized (with an atom core) and how many electrons go into non-localized states and become part of the electron sea. Which electrons enable the conduction of electricity?
b) Do the electrons go into the electron sea when a voltage is applied, or are they always there waiting to conduct electricity?
c) Why is it difficult to explain in simple terms why some electrons leave their atoms and go into the non-local states of the electron sea? What is the benefit for that? What is the reason or motivation for some electrons to do that?

2. a) Describe the nature of pure silicon (Si). How many electrons does it have? What are their roles?
b) What happens when you mix in some phosphorous (P) atoms in silicon? Suppose the phosphorous atoms substitute for some of the Si atoms. How and why does that change the nature of the material and how does it effect its conductivity? (How many electrons does a P atom have?)

[Note that silicon (Si) is an element and an elemental material and not related at all to silicone (sealent), which is a complex, soft polymer material. Si, on the other hand, is the 14 element of the periodic table and forms a crystalline solid which is dark grey, shiny, has a hard surface and is somewhat brittle.]

3. (extra credit) What is something unusual about the microscopic nature of conduction in a superconductor?? What is an interested macroscopic (phenomenological*) feature in the of a superconductor?

* Phenomenological is a big word that refers to ordinary impressions of what something is like. As in, for example, "genotype and phenotype" where genotype refers to the microscopic nature of the base-pair sequence in the genome, and phenotype means what something looks like, etc, as in " a dog has four legs, etc".

Homework Help Section Thursday, Feb 19th 6:00pm

Nat. Sci II Annex Room 101 6pm.

Help Section today (Weds), 3 PM, Thimman 339

Midterm Solution note and guide

1. the equation for kinetic energy is (1/2) m v^2.
[side note: This little equation relates the two parts of this class. It is the equation for kinetic energy for macroscopic masses, and for microscopic atoms (where it is intimately involved in the microscopic definition of temperature.]

2. a) At T=0 K there is no motion; atom motion ceases...
b) Energy is not create or destroyed; it (only) transforms from one form to another.

3 a) He: 2,2,2; Li: 3,3,3 ; Ne: 10,10,10 (The number of neutrons is flexible. In fact, for Li 4 neutrons is more common than 3.)
b) Ne is heaviest because it has the most protons and neutrons.
c) Li is largest.
d) Mass is simple; size is subtle due to the wave-like nature of electrons and the critical role that electrons play in establishing atom size. This was not understood until the wave equation for electrons was discovered and solved around 1930.

4. H2 molecules go faster by a factor of 4. This is because they are 16 times less heavy (H2: amu=2 (2 protons); O2: amu=32 (16 protons; 16 neutrons)). To be at the same temperature means that their m v^2 must be the same, so to balance of the 16 times less mass one needs 4 times more speed (to get the same K.E.), since v is squared and m is not.

5. a) I'll upload a picture later. The lowest point is P.E. = 0 at x =0. At x=1 m, P.E. = (1/2) 8 (1^2) = 4 Joules

b) There is no friction, but as it moves its K.E. transforms into P.E. and it slows down. It starts with a K.E. of (1/2) m v^2= 16 J, and it will go until all its K.E. is transformed to P.E., which is x=2 m (where P.E. = (1/2) (8 J/m^2) (2^2 m^2)= 16 J).

c) It will slow down, stop and reverse direction at x=2. Then it will speed up to the left and go as far as x=-2, where its P.E. is also 16 J, and it will turn around there and go back-and-forth forever between -2 m and 2 m as long as there is no friction.

d) With a starting speed of 4 m/s, its motion is confined to the range -2 m to +2 m. This confinement comes about due to conservation of energy.

6) If k=2 J/m^2 instead of 8 J/m^2, it would be able to go twice as far, all the way to x=4 m, before loosing all its K.E. since the potential is 4x weaker (smaller). A potential with k=2 instead of 8 (J/m^2) is thus weaker and less confining.

Homework: Waves and Sound

Here is a homework assignment on waves and sound which is due next Friday (Feb 20). It includes 9 book problems and 2 other problems which are as follows:

Chapter 19: Problems 1, 2, 3, 4, 5 and 7
Ch 20: Problem 1
Ch 21: Problems 3 and 5

For a string fixed between two posts how does the wave spend depend on tension, mass density (kg/meter) and length?

For a string fixed between two posts how would the frequency of the fundamental mode change if you shorten the length by a factor of two and keep everything else (tension, mass density, wave speed) the same?

Reading

At this point we are moving from the section on sound (waves that move through air at 330 m/s) toward the section on light (waves that move through a vacuum at 300 million meters/sec). In between there is a very interesting and important section on electricity and magnetism. (Light is a wave involving electricity and magnetic fields.)

Suggested reading starts with chapter 22, especially emphasizing the parts on Coulomb's law, electric potential energy, and electric energy storage. After that we will cover chapter 23, including electric current, circuits...

Homework Help Section, Thursday Feb. 12th.

Hi everyone, sorry about the late notice, but without any homework assigned this week, there will be no homework help section tonight.

Don't worry, the time is being put to good use, your midterms should be back tomorrow...

-Eliot

Midterm Study Guide

Physics tends to naturally organize itself in terms of concepts and classes (types) of problems. The midterm is designed to emphasize the most important concepts and problems from the material we have covered so far, (emphasizing what we have covered in class) and to test your understanding of that. Here is an outline of what to expect:

1) Conservation of energy is important. Review energy conservation principles and understand how to do problems related to that. Understand the idea of an abstracted potential energy (P.E.) curve. For example, for a mass in a gravitational field P.E. = m g y, where y is height, and for a mass attached to a spring P.E. = (1/2) k x^2 .

Be able to graph a potential energy curve, like the above, and to understand motion under the influence of a potential energy. (There is an example of a problem involving motion under the influence of a P.E. in the earlier midterm post.) This is important.

2) Review the concept of center of mass. Be able to calculate tension on ropes supporting a scaffold. Understand the value of symmetry in such problems. Be able to solve rope-tension problems in symmetric and non-symmetric situations. Understand how to recognize and exploit symmetry, which is a key concept.

3) The idea that overall macroscopic quantities can be related to microscopic (atomic scale) phenomena is a important part of physics. Review temperature and understand its relationship to molecular motion. Understand/appreciate the advantages of the Kelvin temperature scale. How is it aligned to make it more fundamentally meaningful than other temperature scales?

Understand how to do problems, like those of the HW and quiz, where you compare speeds of thermal molecules which have differing masses or you figure out how speed changes with temperature or visa versa. Understand how to do this quickly via scaling ideas, e.g., if you double T, how much does v change? If a molecule is 4 times heavier how much slower would it have to go to have the same kinetic energy?...

4) Matter is made of atoms, which are very small. The atomic picture of matter is important. In preparation for the midterm familiarize yourself with the composition and size (atomic radius) of the following relatively light atoms: H, D, He, Li, C, O, Ne .

You should know which has the largest size (atomic radius) and which has the smallest size (atomic radius). Most of the others have roughly the same size, so don't worry about the details of that, but make sure you do know roughly the size of the largest one*, to one significant figure is sufficient (i think it is either 0.2 or 0.3 nm), and also be sure you understand what a nanometer is. (What does it have to do with the number 1 billion?) [ *I think it is Li, but you should probably look that up.]

Midterm Help Session Today (Tuesday), 3:00 PM

There will be a help session for the midterm today at 3:00-5:00 PM in Thiman room 339.

Solutions

Quiz 2 Solutions

Homework 3 Solutions

Quiz 2 Solution notes

Detailed, down-loadable solutions to the quiz are posted above. This is a less technical, conceptual solution guide and discussion which should be complementary to that:

1) "kinetic energy". Acually you should say " average kinetic energy of the individual atoms and/or molecules of the gas". +1 for mentioning "average" or "molecules"...
If you mentioned pressure, sorry, that has nothing to do with this class. Conceptual physics is about understanding seeing the connection between a familiar macroscopic property (temperature) and a the microscopic (atomic scale) behavior to which it is fundamentally related, in this case atomic K.E. and speed.

2) Mass just depends on adding up the number of protons and neutrons. 1 amu for H, 4 amu for He, 16 for O, 12 for C, 14 for N. Except for H they all have a 1:1 ratio of protons and neutrons. (D (deuterium) is an "isotope" of hydrogen which has a neutron, in addition to its proton. It can reasonably be viewed as the most important isotope, partly because it has twice the mass of H...)

Size: For an H atom and an O atom they are nearly the same. Pretty surprising since O has 8 electrons and H has only 1! This mystery is buried in the wave nature of electrons (which we will cover in the last few weeks of this class).

3) This is all about working in Kelvin and scaling. Twice the speed means 4 times the temperature. But only in Kelvin, which is the T scale where v=0 at T=0, and thus the only scale with fundamental physics credibility.

4) See solutions for nice pictures of the modes.


http://people.ucsc.edu/~epaisley/phys1%20-%20quiz2%20sols.pdf

Tuesday Review Section

There will almost certainly be a review section on Tuesday at either 3 or 4 PM (for about 2 hrs). We are just waiting to here about the room and will update this post when we do.

update: it is 3:00-5:00 PM in Thiman 339 (see recent post on that as well)

Post on Midterm content / study advice

Here is a sense of what will be on the midterm with an updated from Monday, 9:00 PM (see below). Please check for further updates tommorrow as well as questions and comments.

A lot the content will be similar to the quizzes. Know the atoms from H to Ne: what they are made of, what determines mass and size...

Understand temperature and its relationship to microscopic atomic motion. Understand the difference between macroscopic and microscopic quantities. Known which T scale has fundamental meaning and what that meaning is.

In addition, there will be a question(s) regarding masses moving in a potential energy. Kind of like we discussed for pendulum and harmonic oscillator (mass on a spring), and with gravitational potential energy. Familiarize yourself with the 1/2 k x^2 potential (harmonic oscillator) and the motion associated with that and how to think of that in terms of energy and especially a mass in a potential energy function or "well". This will be reviewed and discussed in class Monday.
------

Midterm study guide (Monday, 9:00 PM):

Known the rough mass, in amu, of each atom from H(1) (and D) to Ne (20). Also, how many electrons each atom has.

Know that atom size is controlled by electrons. And that H is somewhat bigger than He. Li is even bigger and then as you go across the row the atoms get progressively smaller all the way to Ne, which is the smallest.

Know how to work problems which involve relating atom speed to gas temperature. Like those on the HW.

Understand how to work problems involving potential energy. For example:

Suppose a mass, m, is subject to a force such that its potential energy as a function of x is (1/2) k x^2 (like if it were attached to a spring...). a) Where is the lowest point of this potential? b) graph this potential as a function of x. c) suppose the mass starts out at the lowest point of the potential with an initial speed of v (to the right). What will happen? How far will it go before its speed decreases to zero? What will happen after that? Assume there is no friction.

Does this make sense? Is this problem understandable?
------

If anyone has any ideas for other problems, please feel free to post them here.
Also, any questions, etc.

Help Session Thursday night, 6 PM: NS2, 101

This is just a reminder of the help section at 6:00 PM in Nat. Sci.2 room 101 every Thursday.

Quiz tommorrow: what you should know

For Friday's quiz (Feb 6) consider the following points on which to focus:

1) An understanding of the component nature of atoms. What are atoms made of? Roughly how big are atoms? What determines the mass of atoms? Why is it so difficult to explain the trends in the size of atoms and so straightforward to understand their mass? Quiz questions will focus exclusively on the lighter atoms, i.e., H to Ne (hydrogen to neon). You should know their "mass numbers" and the mass numbers for other important atoms in that range, i.e., H and D, He, Li, C, N , O and Ne. (D is deuterium.) There will be no questions on ions or on isotopes other than deuterium.

2) An understanding of the macroscopic, or phenomenological, definition of temperature. What is the key property, on a grand scale, that we would like temperature to have? When two objects have the same temperature is there any (net) heat flow between them?

3) An understanding of the relationship between what we call temperature and the microscopic character of molecules or atoms in an ideal gas. What property of the molecules or atoms is proportional to the temperature. What does T= absolute zero mean? What temperature scale is most helpful in revealing the relationship between atom motion and temperature? etc. Be able to work problems related to this.

4) For a string stretched between two fixed points, you should have an understanding of the pattern of allowed frequencies for pure modes (standing waves), and the ability to sketch some of the lowest frequency modes. See for example: http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html (Don't worry about all the math there. Just have a clear understanding of the relative frequencies of pure modes and how to illustrate what the look like.)

I think that is everything. If I think of anything else I will post it here before 10 PM tonight; also I will respond to any questions or anything you post tonight in the morning. (I would encourage you to check this in the morning and see what questions, answers and comments have been posted.)

Please feel free to post any questions or comments here. If you think you understand something but you are not sure, feel free to test your understanding via a post here.

Homework #2 Solutions - Thanks Nina!

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Homework help section today, ISB 356

In the original posting about this, there was an error in the room number for Today's homework help section. Today's homework help section will be in ISB 356. (ISB is sort of above "Earth and Marine" on science hill.) It is at 2:00 PM (right after class) and will go for about 1 or 1 1/2 hours. You can ask any sort of question related to this class there. Whether you are somewhat lost or feeling really on top of things, i recommend it very highly.

Question about entropy

Here is a question about entropy:

Suppose your are at a party and someone hears that you have been taking "Conceptual Physics" and they say:
"I have always been interested in entropy. What can you tell me about entropy? Is it related to temperature or what? What would you say?"

Please feel encouraged to post questions, thoughts, comments, entropy-related quotes, poems or anything like that, here.

Homework help sections this week

These week there will be two homework help sections:
one on

Wednesday at 2:00 PM in ISB 356,
(note correction of room number)

and the other at the usual time,

Thursday, 6:00 PM Nat.Sci 2, 101.

Reading for this week, , Feb 2

This week we will finish our coverage of temperature-related physics, possibly with a discussion the role of entropy in the evolution from solid to liquid to gas states of matter. Then we will start on waves and sound. The reading for that (waves and sound) would be chapter 19 up to page 372 and emphasizing the section on standing waves.

On Temperature

Here is something, excerpted and edited, from wikepedia regarding temperature:

In physics, temperature is a physical property of a system that underlies the common notions of hot and cold...
On the macroscopic scale, temperature is the unique physical property that determines the direction of heat flow between two objects placed in thermal contact. If no heat flow occurs, the two objects have the same temperature; otherwise heat flows from the hotter object to the colder object...
On the microscopic scale, temperature can be defined as the average energy in each degree of freedom in the particles in a system- because temperature is a statistical property, a system must contain a few particles for the question as to its temperature to make any sense. For a solid, this energy is found in the vibrations of its atoms about their equilibrium positions. In an ideal monatomic gas, energy is found in the translational motions of the particles; with molecular gases, vibrational and rotational motions also provide thermodynamic degrees of freedom.

The wikepedia site has some nice pictures of thermal motion.
http://en.wikipedia.org/wiki/Temperature