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.)
Saturday, February 28, 2009
Wednesday, February 25, 2009
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.
Tuesday, February 24, 2009
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.)
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.
Monday, February 23, 2009
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 .
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 .
Sunday, February 22, 2009
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.
(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.
Saturday, February 21, 2009
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".
(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".
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