Just for fun

LASERS PROVIDE ANTIMATTER BONANZA
A research team used lasers to produce more positrons
(anti-electrons) inside a solid than any previous experiment,
according to the researchers involved. In the 13 March Physical
Review Letters, the team describes firing short pulses from an
intense laser onto thin gold targets and creating a high-density
positron source that could be used to investigate exotic phenomena
near black holes or supernovae.

Hui Chen et al., Phys. Rev. Lett. 102, 105001

COMPLETE Focus story at http://focus.aps.org/story/v23/st8

Studying for the Final + Practice Problems

Several Things I would recommend for studying for the final:

First, go through all posts of the last month on this site, especially things like "Notes on..." or "...what we should know". Try to understand those posts and ask questions, as comments on this web site, regarding anything you do not understand. The more specific the questions are, the better, but just ask about anything that you are confused about. This is very important.

If you ask via a post here, please be clear about what topic and post you are referring too. I will also try to check for questions at the end of all recent posts.

Second, try to understand the last 2 quizzes and most problems from all HW since the midterm, as well as any HW on the relationship of temperature to microscopic motion and on energy and especially potential energy from the first half of the class. Ask questions about that also via comments to this post.

Topics that will be emphasized for the final are:

1) quantum physics: implications of the uncertainty principle; quantum jumps that involve light emission or absorption; and maybe something related to spectroscopy or color.

2) the nature of conducting materials; the difference between a metal and a semiconductor or insulator from an atom/electron counting point-of-view. Bonus if you understand the relevance of the uncertainty principle here.

3) Simple circuits: the relationships between I, V, and R; and also energy disipation and power in circuits P=V I (Watts). Understand that I = amperes = coulombs/second; and P= Watts = Joules/second. Know what that means.

4) the motion of a mass in a potential energy, like the problem (5) on the midterm. If you are truly comfortable with that, it will be valuable.

5) possibly something related to temperature and how, in absolute units, it is fundamentally related to atom motion (in a gas).

Finally, keep checking this site for updated information and, especially, discussion stimulated by student questions.

I'll add practice problems here as I come up with them. These are only a supplement to the above guide and topic outline. (As discussed in class, it is ok to bring a 3x5" card of equations, relationships and units to the final. Please don't get carried away.)

For a circuit with a battery, wire and resistor, describe the what happens in the circuit including the current flow and especially the energy conversion processes.

For a circuit with a battery, wire and a light bulb, describe the what happens in the circuit including the current flow and especially the energy conversion processes.

For a circuit with a 10 Volt battery, wire and 5 Ohm resistor, how much current flows though the resistor? How much heat energy, in Joules, appears in the resistor each second. How much in 5 seconds?

For a circuit with a 10 Volt battery, a resistor and wire (all in series), suppose there is 3 coulombs per second flowing through the wire. How much current flows though the resistor? How much heat energy, in Joules, appears in the resistor each second. How much in 4 seconds?

extreme extra credit: Describe the energy conversion processes associated with an LED (light emitting diode). Is there a quantum jump involved??

For blue light, what is the wavelength, frequency and energy of a typical photon?

For red light, what is the wavelength, frequency and energy of a typical photon?

Discuss the relationship of temperature to microscopic atom motion in a noble gas.

For a composite gas, like air, in thermal equilibrium, do heavier atoms tend to move more slowly than lighter atoms? Explain why. What are your basic assumptions?

Explain the uncertainty principle and its relevance to understanding the origin of the size of atoms.

What is the wavelength, frequency and energy of a green photon?

Present an illustrated discussion of atomic spectra, including what they are, why they were unexpected, and what people infer from atomic spectra regarding the nature of the energy levels of an atom.

Suppose an electron in an atom has allowed quantum energy levels at exactly 2 eV, 4 eV, 5 eV and 5.5 eV. If 2 eV is the energy of the ground state and all the atoms in a cold gas start out in the ground state, what are the a) energies, b) frequencies and c) wavelengths of possible quantum absorption events in which a single photon is absorbed and the electron jumps from the ground state to another state? (actually, you can start with d) if you like and then do parts a), b) and c)...)
d) How many sharp lines would there be in the absortion spectrum for this atom?
e) Make a graph of an absortion spectrum for this atom.
f) Are these absorptions in the infrared, visible or UV? If visible, what color are they?

For green and orange light, what are the wavelengths, frequencies and energies of typical photons, respectively?

What is the composition of He? What is the composition of an He+ ion? What is the difference between He+ and He? What is the difference between He+ and H?

Balmer Series: emission spectrum

Here is a graphic of an emission spectrum set-up and an emission spectrum. For an emission spectrum, the gas of atoms you wish to study is the source. Photons are emitted from the hot gas of atoms when electrons in the atoms drop down from a higher potential energy state to a lower potential energy state. Energy is conserved, and the electron energy is converted to photon energy in this transition. The photon is created in this process. It does not exist before this transition takes place; it does exist after the transition. The electron falls from a high energy (excited) state to a lower energy state; the energy it loses goes to creating the photon. These photons come out at very specific frequencies.

The role of the prism is to separate the photon beam into its different colors; before the prism all the photons are moving together in a single light beam. After the beam goes through the prism, whatever colors are present are separated, as shown.

The moving aperture allows only one frequency (color) to pass though at a time. As it moves it scans through the spectrum. The graph shows the Intensity measured at the detector as a function of frequency.

An absorption spectrum is the complement of this. The atoms are located in the beam and instead of emitting photons they absorb photons in a process opposite to that of emission. That is, the electron starts out in a low-energy state of the atom and goes to a higher energy state. A photon is anihilated (absorbed) in this process, thus energy is conserved via the equation E1 + hf = E2, where E1 is the energy of the state the electron starts in and E2 the energy of the state it goes to. hf is the energy the photon gives to the electron, after which the photon ceases to exist. (This is a "zero sum game". )

This leads to dark "absorption" lines, in an otherwise broad and featureless reference spectrum. These dark lines are due to the quantum absorption process described in the preceding paragraph. Using the energy it gets from the photon, the electron makes a quantum leap upward to a higher energy state.

Balmer Series Quiz Solution and comments

Let's start by talking about energy units and then doing parts 1) and 4).
We use f=c/wavelength for 1), and then E=hf for 4). Almost everyone got 1), but for many people there was some confusion regarding units of energy for 4). Electron Volts (eV) is a unit of energy that is not the same as Joules. 1 eV = 1.6 x 10^-19 Joules, so an eV is a much smaller unit of energy and one that works well for atoms in the sense that it gets rid of the large negative exponents that occur if one uses Joules.

eV has its origin in the potential energy of an electron, so it makes some sense that it is close to the right size for electrons in atoms; Joules, on the other hand, has its origin in the kinetic energy of a 2 kg mass moving at 1 m/s, and is way off (too big) for atom energies.

Now to the problem:

f=c/lamda = (3 x 10^8 m/s) /656 x 10^-9 m = (3/656) x 10^17 sec-1 = 4.57 x 10^14 Hz .

Getting the exponent right in the 3rd step is critical. Exponents are very important!
For the others you should get: 6.17, 6.91 and 7.31 x 10^14 Hz, respectively. (All are multiplied by 10^14. All are in cycles per second, which is the same as Hz and sec-1.)

4) For 4, you multiply each one by h=4.14 x 10^-15 eV-sec to get the energy in eV.

E= h f = 4.14 x 10^-15 eV-sec 4.57 x 10^14 Hz = 18.9 x 10^-1 eV = 1.89 eV.

[Note that this is a nice, friendly number. No exponents.]

The other ones are: 2.56 eV, 2.86 eV and 3.02 eV.
These photon energies correspond to something like: 1.89 eV (red or maybe orange), 2.56 eV (greenish blue?), 2.86 eV (blue) and 3.02 (violet).

The answer is very different in Joules. For example, for the first frequency you would get about 3 x 10^-19 Joules.

We could just forget about eV if people would rather work with Joules. There is sort of a tradeoff between the extra work and confusion of learning a new unit for energy, and the benefit of using a unit (eV) that is more atom friendly. Please let me know your preference via comments here.

Atoms: what we should know, part II

As we discussed today in class, for an electron in an atom there is a sequence of states, or energy levels, in which the electron can reside. (See part I.) These wave-like states have characteristics which are reminiscent of the modes of a string of length L stretched between two posts.

5) The lowest energy state in this sequence is called the ground state. Rather amazingly, the ground state has kinetic energy.

6) This is one of the most surprising results of quantum physics and is intimately related to the uncertainty principle.

7) The uncertainty principle says that the more an electron is confined, the higher its momentum will be. Momentum, speed and kinetic energy (K.E.) all go together, so confining an electron causes it to have kinetic energy, and the more confined it is the more kinetic energy it must have.

8) Just as the fundamental mode of a guitar string has a higher frequency when the string is shortened (f=v/2L), so will an electron have a higher kinetic energy when it is more confined (K.E.~h^2/mL^2). Here L is the length of the string, which is a measure of the confinement of the string wave; and L is the diameter of the electron cloud around the atom, which is a measure of the confinement of the electron. (Smaller L in each case means more confinement.)

9) Note that in each case there is an inverse relationship: smaller L means higher frequency (for the fundamental mode of the string, smaller L means higher kinetic energy for the electron in the atom.

Atoms: what we should know, part I

1) Atoms are composed of a heavy, fixed nucleus which has a positive charge and electrons which are attracted to the positively charged nucleus. Our attention is focused on the electrons, which are light and therefore behave in very interesting and unexpected ways.

2) The electrons in an atom must exist in states which have specific energies. These are called discrete energy states. (Discrete, in this context, means isolated, detached or separate (from other states)-- not part of a continuum.)

3) Transitions in which an electron goes from one discreet energy state to another are the reason behind the sharp-line spectra seen in absorption and emission spectroscopy.

4) The existence of these discrete energy electron states is explained by a "wave theory" of electrons (~1930), which leads to a lowest energy state known as the "ground state" (fundamental), and a sequence of states at higher energies ("harmonics"). This is analogous to the theory of a wave on a string, which leads to a mode of lowest frequency (fundamental) and a sequence of discrete harmonics at higher frequencies.

5) ...to be continued... (see part II)

Quiz due monday --Balmer Series

This is a take-home quiz that is due Monday (at the beginning of class):

Balmer Series Quiz, Due Monday March 9, 2009

In the emission and absorption spectra of a hydrogen atom gas, sharp lines are seen at the following wavelenghts: 656 nm, 486 nm, 434 nm and 410 nm.

1. Determine the light frequency (in Hz) corresponding to each of these wavelengths.

2. a) Sketch a spectroscopy set-up for an absorption spectrum, and then graph:
b) a reference spectrum, and c) an absorption spectrum (intensity vs frequency). Start your frequency axis at zero for both graphs. For the absorption spectrum there is a gas of cold atoms in the beam; for the reference spectrum there are no atoms in the beam and no sharp features.

3. Sketch a spectroscopy set-up for an emission spectrum, and graph an emission spectrum (intensity vs frequency) for the same four line sequence. For an emission spectrum the light source is a hot gas of H-atoms.

4. Using h= 4.14 x 10^-15 eV-sec, calculate the energy of a photon at each of these four frequencies in eV. eV (electron-Volts) is a energy unit which is good for atoms.)

Spectroscopy

Optical spectroscopy

Electrons exist in energy levels within an atom. These levels have well defined energies and electrons moving between them must absorb or emit an energy equal to the difference between them. (Energy is conserved.) In optical spectroscopy, the energy absorbed to move an electron to a more energetic level and/or the energy emitted as the electron moves to a less energetic energy level is in the form of a photon (a particle of light). Because this energy is well-defined, an atom's identity can be found by the energy of this transition. The wavelength of light can be related to its energy. It is usually easier to measure the wavelength of light than to directly measure its energy.

Optical spectroscopy can be further divided into absorption, emission, and fluorescence.

In atomic absorption spectroscopy, light is passed through a collection of atoms. If the wavelength of the light has energy corresponding to the energy difference between two energy levels in the atoms, a portion of the light will be absorbed. The relationship between the concentration of atoms, the distance the light travels through the collection of atoms, and the portion of the light absorbed is given by the Beer-Lambert law.

Waves on strings: websites

Here are some links to web sites where you can explore the nature of waves on strings. Understanding waves (on strings) is relevant and helpful for understanding the quantum physics issues we will be covering for the next few days.

http://www.ngsir.netfirms.com/englishhtm/StatWave.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html

http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html

Homework help section Thursday. 6 PM

There is a HW help section as usual in Nat Sci 2 annex room 101 at 6 PM.
HW for this week is posted tow posts below this.

Homework on Conducting Materials and Circuits: Solutions and Discussion

This includes solutions to the HW problems from last week. and some additional discussion contextualizing and nuancing the solutions.

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.

a) Cu has 29 electrons. 28 of those stay with their atom core, which then becomes a Cu+ ion (since it has 29 protons and only 28 electrons). One electron per Cu atom goes into an electron sea. The electrons of the electron sea are not associated with any particular atom core (Cu+ ion) and, indeed, their wave-functions extend through the entire solid. These non-local electrons in the electron sea are the electrons that enable the conduction of electricity.

b) They are there waiting to conduct electricity all the time. When a voltage is applied, they move freely, but they are always there waiting to flow. The Cu+ cores form a rigid crystal lattice. The non-local electrons are like a liquid waiting to flow when a voltage is applied, which is like tilting a pipe with water in it.

c) It difficult to explain in simple terms why some electrons leave their atoms, and go into the non-local states of the electron sea, because it involves the wave nature of electrons and the uncertainty principle. Basically, the benefit, and motivation for some electrons to do that, is that by going into non-local states the electrons can lower their kinetic energy. This is because non-local states have very uncertain position and thus can have very low momentum and kinetic energy (which is proportional to momentum squared).

Al is similar in all respects except that the details of the electron counting are different. For Al, 3 electrons per Al atom leave “home” to go into the non-local states of the conduction electron sea. This leaves behind a simple 10 atom Ne-like core which is the ion Al+3, since there are 13 protons and only 10 electrons.

Cu has a less simple core. In the Cu core there are 18 electrons in a argon-like “noble gas” configuration, and 10 more electrons in a filled 3d mini-shell. Don’t worry if you don’t know what that means, and if you do, great! These d mini-shells come up once you go beyond the lightest elements, and it is just a complexity we have to live with if we want to relate our basic knowledge to real materials.

2. a) Describe the nature of pure silicon (Si). How many electrons does it have? What are their roles?

2) Si has 14 electrons. It forms a crystal lattice in which each atom has 4 nearby neighbors. Si atoms are very social and like to share an electron with each of their 4 neighbors. These shared electrons form strong bonds between Si atoms which are called covalent bonds. (This is the strongest form of chemical bond.) Anyway, as far as counting goes, each Si puts a total of 4 electrons into covalent bonds (one for each of its closest neighbors) and the remaining 10 electrons form a neon-like core. There are no conducting electrons in Si.
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 affect its conductivity?

P has 15 electrons. It wants to fit in. It substitutes for a Si atom. P wants to fit in so it too provides 4 electrons to covalent bonds with neighbors and has a 10 atom neon core. But there is one electron left over. That one goes into a non-local state joining other electrons form other P atoms in an electron sea that can conduct electricity. This is where the conductivity of the semi-conductor Si comes from. It is from the extra electron in the phosphorous “doping” atom.

3. (extra credit) What are unusual macroscopic and microscopic characteristics associated electrical conduction of a superconductor?

On a macroscopic level, superconductors are unusual in that they conduct electricity with ZERO resistance. Other metals have resistance. Superconductors have no resistance at all. They are “frictionless” even if there is some disorder in their structure. This was very surprising. It took more than 50 years for scientists to solve the mystery of superconductors. Part of the solution leads to the surprising result that electrons in superconductors pair with each other! On a microscopic level the electrons in a superconductor are paired. For reasons that are difficult to explain and related to a quantum property known as “phase” pairs of electrons move with zero resistance.

4. Gold is difficult since it has so many electrons to wonder about. Wow, it has 79 electrons and the nearest noble gas is Xe, which has 54 electrons. The bottom line is this : 1 electron per Au atom goes into the electron sea. Those are the ones that are responsible for the conductivity. Of the ones left behind, 10 are in a filled d-level “mini-shell”, 14 are in a filled f-level “mini-shell”. I am amazed that the counting then seems to work: 54 + 14 + 10 +1 = 79. The last 1 is the one that counts for conductivity. Sorry. Didn’t realize this would be quite so hard. My mistake. I thought it would be interesting because gold is a familiar material and a good conductor. Copper, silver and gold are all in the same column of the periodic table and all similar metals.

5. Ge is like Si except the noble gas core is the next one down and there is a filled d-level mini-shell in addition to the 4 electrons in covalent bonds (as in Si). So it is a semiconductor with a phenotype very similar to Si.

6. This is very hard problem, but important since GaAs is a very common and useful semiconductor (lasers, LED’s…). Ga and As are on either side of Ge, so if each As gives each Ga one electron then they can formed a semiconductor with 4 covalent bonds to nearby neighbors just like Si and Ge. In the since that each Ga receives one electron from each As, it is sort of like a NaCl, where each Na loooses an electron to each Cl forming a lattice of Na+ and Cl-. Through this ionic electron exchange, however, it becomes a semiconductor, like Ge and Si. This raises the interesting question "Why isn't NaCl a semiconductor?" which we won't answer here.

Chapter 23, problems:

2) I=V/R can be rearranged as R=V/I.

R=120 Volts/20 amps = 6 Ohms.

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3) P= I V. 1200 Watts = I x 120 Volts. I = 1200 Watts/120 Volts =10 amps.

R=V/I = 120 Volts/10 amps = 12 Ohms

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4) Capacity is 60 ampere-hours. Headlights draw 6 amps.

6 amps x 10 hours = 60 ampere-hours, so they can do this (draw 6 amps) for 10 hours.

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6) P=I V . In this case 4 Watts = I x 120 Volts, so I =4/120 = (1/30) amps

b) R=V/I = 120 V/(1/30 amps)=30x120 Ohms = 3600 Ohms.

c) 4 Watts = 4 Joules/sec. There are about 365 x 24 x 60 x 60 seconds in a year. So the total power utilized in one year is 4 x (365 x 24 x 60 x 60) (Joules).

d) to get watt hours in one year we multiply 4 watts times the number of hour in a year, which is 365 x 24. Then divide by 1000 to convert from watt-hours to kilowatt-hours.

Total cost would then be: $0.15 x [4 x (365 x 24)].

7) Power is I V which is 9 amps x 110 V = 990 Watts. Watts is just an word that means Joules per second. To find the number of Joules generated in one minute we multiple Joules/second by 60 seconds to get 990 Joules/sec x 60 seconds = 60 x 990 Joules.

8) 9 amps is just another word for 9 coulombs per second. Total number of coulombs in one minute (60 seconds) is: 9 coul/sec x 60 = 540 coulombs.

Error checking is welcome. Have I made any mistakes on these? Please feel free to comment.

Homework on Light; newest version with solutions added.

This is the final up-to-date version of this assignment with solutions added. This assignment was due on Friday (March 6).

Ch 26. Problems: 3 (1st part only), 5, 6, 7
[hint for 5: radio waves travel at the speed of light=3 x 10^8 m/s. time is distance/speed.
For 7, someone in the class got a wavelength to atom size ratio of about 10,000. Does that seem about right? Feel free to post your result and comment.]

3. time =distance/speed of light = 500 sec

5. time =distance/speed of light = 1.4 x 10^8 sec (a much longer time than 500 sec)

6. f=c/lamda = 5 x 10^14 sec-1 . It is important to get the exponent right!

7. lamda =c/f = 0.5 x 10^6 meters = 500 nm. In these problems (6 and 7) it is important to get the exponents right and to be mindful of any nm to meter conversions. Atom size is typically 0.1 to about 0.3 nm. So that is about 1000 times (or a little more) smaller than the wavelength of visible light.
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Ch 30: Exercises: 3, 5, 15, 48
Problem "1" (there is only one problem, it has no number)

3. blue light emitted corresponds to a greater change in energy of the electron in the atom.

5. If you double with wavelength, the frequency decrease by a factor of 2 (f=c/lamda), so the energy of a photon would be half as much. (Not twice.)

15. infrared is lowest frequncy range, UV is highest frequency and therefore has highest photon energies. Visible is in between IR (lowest photon energies) and UV (highest phton energies).

48. see attached jpg image. After you do this you can sort of see the solution visually from the picture!

Problem: One key thing for this problem is to realize that wavelength is inversely related to frequency, so if the frequency for a transition is higher, the wavelength must be shorter!

Balmer Series Problem: [Because this problem was posted late, it will count as extra credit and, because it is long, triple credit. I suggest you do it because it is relevant to things we will emphasize regarding both the quantum nature of the atom and spectroscopy.]

In the emission and absorption spectra of a hydrogen atom gas, sharp lines are seen at the following wavelenghts: 656 nm, 486 nm, 434 nm and 410 nm.

a) Determine the light frequency (in Hz) corresponding to each of these wave-lengths.

b) Sketch a spectroscopy set-up for an absorption spectrum, and then graph an absorption spectrum of intensity vs frequency. (This means intensity as a function of frequency, with intensity on the vertical axis and frequency on the horizontal axis. It is highly preferable to start the frequency axis at zero frequency; that way it is easier to see patterns of frequencies.) For your sketch of the spectroscopy set-up, you can limit it to a source, a source aperture, a prism, a moving aperture and a detector. (The book shows mirrors and that is more correct, but for your sketches you can skip the mirrors for simplicity.)
Remember that for an absorption spectrum there is a cold gas of atoms in the beam. Actually, there should be two graphs: one of the intensity vs frequency when there is no H-atom gas in the beam, which is called a reference spectrum; the other the actual absorption spectrum that you get when the H-atom gas in in the beam. (For the reference spectrum assume a broad, featureless spectrum spanning the entire visible range as well as some IR and UV.)

c) Sketch a spectroscopy set-up for an emission spectrum, and then graph an emission spectrum of intensity vs frequency for the same four line sequence. For an emission spectrum the source is a hot gas of H-atoms.

d) Using h= 4.14 x 10^-15 eV-sec, calculate the energy of a photon at each of these four photon frequencies in eV.

Reading on light, spectroscopy and atoms

Please read the posts below on this web site on: Notes on light and photons, and Notes on atoms: part1, atomic spectra.

In addition, there is related material in our conceptual physics book is in chapters 30, 31 and 32. Chapter 30 has a discussion of emission and absorption spectra. Chapter 32 (page 623) has a brief discussion of a pattern observed by a Swiss schoolteacher, J. Balmer, which we will cover in class (Atomic Spectra: Clues to Atomic Structure). You can find out more about that by searching on the phrase "Balmer Series", which is very famous and probably the most important experimental result which lead to the discovery of quantum theory.

This is a difficult and confusing subject and you are very much encouraged to post any questions you have either here, or at the end of the posts: Notes on Light..., or Notes on Atoms...

Be sure to come to Wednesday's class.

Wednesday's Class ---Don't miss it!

We will have a special visitor on Wednesday giving a presentation designed to elucidate the nature of atoms and atomic spectra to an audience of non-scientists. Please don't miss this class. I think it will be very interesting and very relevant to what we are learning for the rest of the quarter.

Notes on Atoms: part 1, atomic spectra

Today (Monday) we began our treatment of the quantum atom. I am hopeful that this will be the most interesting and important part of this conceptual physics course. Understanding the quantum nature of matter is a big thing.

This has two aspects. One is bizarre experimental results which were discovered in the 1900's. In particular spectroscopic measurement showed the presence or absence of sharp lines at particular frequencies (colors) in emission and absorption spectra respectively. This were quite a surprise and mystery, and they were completely unexplained until the wave concept for electrons was imagined and the wave equation for electrons* was discovered. *Also known as the "Schrodinger equation".

The other aspect focuses on the theoretical nature of atoms when the wave-like character of the electron is appropriately incorporated. In this class we will not do the wave calculations of the Schrodinger equation --that is done in physics 101 and 139-- but what we can and will do is look at the consequences of the wave theory: the phenomenology of atoms which emerges after the grungy math is done, which is really the most interesting part!

On Monday we discussed the nature of a spectrometer --how it involves a source, an aperture, a prism, a second aperture, and a detector. The 1st aperture "colimates" the beam, making it so that all the light the gets through it is going in the same direction. The prism splits the source beam into colors (frequencies). The second aperture slowly moves across the beam allowing only one color, or frequency range, to get through at a time. Then the detector measures the intensity of what gets through. By measuring what gets through (intensity) as a function of the position on the 2nd aperture one obtains what is called a "spectrum": a measured graph of Intensity as a function of frequency.

There are two types of spectra that are important to us. One is an emission spectrum, in which the light source is a heated atomic gas. In this case one will see zero intensity at many frequencies (or a very low non-zero background) punctuated by dramatic narrow spikes (peaks) at which there is a lot of intensity at a particular frequency. These are called "bright line spectra". "Line" refers to the narrowness of the peaks; they are so narrow they look like vertical lines in the graph. "Bright" means high intensity.

The other type of spectrum is an absorption spectrum. For these the source is essentially an ordinary light bulb, i.e., a hot piece of metal. This will emit a continuous spectrum with no sharp lines or anything dramatic. The drama begins when you put a cold gas of atoms in the beam. One then finds that the gas of atoms has absorbed almost all of the light at very specific frequencies, thereby creating lines in the spectrum where the intensity that reaches the detector is close to zero. These are called "dark line spectra".

We looked at both emission and absorption spectra for the example of a hydrogen atom where there were sharp lines at: 4.6 x 10^14 Hz, 6.2 x 10^14 Hz, 6.9 x 10^14 Hz and 7.3 x 10^14 Hz.
These correspond to red, green, blue and violet light respectively. On Wednesday we will begin the task on unravelling the mystery of where these sharp lines come from and why.

On Wednesday we will have a special visitor, Nina X. McCurdy, who has been working on explaining the origin of quantum spectra to a general audience. This will be a very important class. Please do not miss it!

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

Homework on atoms and temperature; due Friday, Feb 6

This HW is due at the start of class on Friday (Feb 6), the day of our 2nd quiz. Doing these problems should also be good preparation for the quiz (and for the midterm on Feb 11).

Also, this week there will be an extra homework help section at 2 PM Wednesday in ISB 339.

1. What are atoms made of?

2. What components of an atom are most important in establishing its mass?

3.a) How does the mass of an oxygen atom compare to that of a hydrogen atom? How does it compare to that of a proton?

b) How does the mass of an carbon atom compare to that of a hydrogen atom?

c) How does the mass of an neon atom compare to that of a hydrogen atom?

d) How does the mass of an helium atom compare to that of a hydrogen atom?

4. a) What is deuterium? b) How does the mass of an carbon atom compare to that of a deuterium atom? c) Hydrogen is much more abundant than deuterium, but there is something about H that is a little odd or unconventional, regarding its nucleus, compared to that of other light elements. What is it?

5. What is the mass of an H2O molecule? What is the mass of a D2O molecule?

6. Thinking about the size of atoms:
a) Which is bigger: H or He?
b) Which is bigger: Li or O ?
c) Which is bigger: O or Ne ?

7. Why is it more difficult to explain the size of atoms than it is to explain the mass of atoms?

8. What part of the atom determines its size?

9. Suppose the average speed of an oxygen molecule in air at "room temperature" is 600 m/s. Would the average speed of a nitrogen molecule be the same, less or greater?
How about the average speed of a hydrogen molecule or a helium atom? Explain your reasoning briefly.

10. Suppose the average speed of a helium molecule in a gas is 500 m/s at -73 C. You add heat and observe that the average speed goes up from 500 m/s to 1000 m/s. What is the new temperature of the gas? [Give your answer in both C and K temperature scales.] Explain your reasoning briefly.

11. Suppose the average speed of an oxygen molecule in air at "room temperature" is 600 m/s. What is the average speed of a helium atom in that air?

Matter and Atoms

Most matter is made up of atoms. That includes gases, like He or air, where atoms are free and go zipping around with an average speed proportional to the square root of the temperature of the gas (see post on heat and T); solids where atoms are stuck together on a semi-rigid lattice; and the in between state called liquids where atoms are close together, like atoms in a solid, but have a sense of disorder, freedom and flow reminiscent of the gas state.

All known atoms can be presented in something called the Periodic Table of Elements. This organizes the elements in a profound and amazing way. Some degree of familiarity with the nature of the periodic table and its organizing principles is an essential part of your education.

One of the puzzling things we noticed about atoms has to do with their size. The size of an atom is determined by its electrons, but it does not increase in any simple or systematic way with the number of electrons in the atom. For example, Hydrogen, which has one electron, has a radius of about 0.1 nanometers (nano means 10^-9). Neon, which has 10 electrons, also has a radius of about 0.1 nanometers --about the same as Hydrogen. The graph of atom size (radius) as a function of its number of electrons is very interesting and perplexing. This is a nice graph to be familiar with and to appreciate the subtlety of its origins, which lie in the wave theory of the electron (Edwin Schrodinger, 1928).

This complex and interesting behavior of the size of atoms contrasts with the relative simplicity of the mass of atoms, which is basically equal to the number of protons and neutrons in the nucleus of the atom time the mass of a single proton (or neutron), which is 1.67 x 10^-27 kg. All this mass is concentrated in very tiny nucleus, which is much much smaller than the size of the atom. So an atom consists of a positively charge nucleus which is very tiny but contains essentially all the mass of the atom, surrounded by a light, wave-like electron.

Heat and temperature

"Heat" is the title of Part 3 of our class book which starts with chapter 15. For that chapter (15), I would suggest trying to answer problems 1 ,2 ,3 and 5. For chapter 16, I think review question 1 provides a good point of focus. Heat is energy. Putting heat into something makes it warmer; it increases its energy content and its temperature. Temperature is actually not such a simple concept and it is surprisingly difficult to come up with a general definition for temperature. For gases it is proportional to the kinetic energy of the molecules or atoms that make up the gas. Temperature is something that when it is the same, between two materials, no energy will flow from one to the other. We call that thermal equilibrium. Actually creating such a quantity leads to some subtle and somewhat tricky math involving exponentials, logarithms and Taylor series expansions.

For this class what you should know two things:
1) the "phenomenological definition": T is the quantity which, when equal between two materials leads to zero heat flow (equilibrium), and when not equal between two materials the amount of heat flow (energy which goes from one material to another per second) is proportional to the temperature difference.
2) for a gas, the temperature is proportional to the average kinetic energy of the molecules of the gas.

Online Work. PLEASE READ!!!

Okay, I know a lot of you have been having trouble with the online work. We've worked out a couple of things.

1) All online quizzes & tutorials assigned thus far will have a new deadline of February 10. If you've done everything ontime already, then you've been prepared for the homework and quizzes, and if you've had trouble, then now you can catch up.

2) Two of the previously assigned tutorials do not have the option to be saved! If you've had trouble with "Newton's Third Law" and/or "Vectors", then it's not your fault.

To summarize:

Tutorials: "Parachuting and Newton's Second Law", "Momentum and Collisions", "Energy", Projectile Motion", and "Orbital Motion".

Quizzes: As far as I know, the quizzes from each chapter ARE recordable. Quizzes assigned so far are from chapters 2, 3, 4, 5, 6, 7, 10.

3) Please make sure you are signed up for our class! On the left-hand side of links, at the top, you might see a link "Join A Class". If you haven't done so, click that, and enter our class code cm799640.

I'm sure there are bound to me more problems, please let me know as soon as possible so I can try and help, thanks.

-Eliot

Quiz Solutions and Discussion (Quiz 1)

These two pages provide a guide to our quiz from last Friday. This much longer than what you were expected to do on the quiz, and provides some insight into the thinking behind the questions and their solutions.

For the first problem the most important thing was go a nice graph for (b), with labels and scales, and, for (a), to realize that being at the highest point of the motion corresponds to having zero speed, and that it takes 1 second to slow down from 10 m/s to zero under the influence of gravity.

The second problem was a conservation of energy problem and you needed to use P.E.= mgh and the expression for K.E. in terms of m and v.

The third problem(extra credit) involves competing considerations --time of flight and launch speed. [It is analogous to the problem regarding the optimal angle for a cannon..., which is governed by the same considerations (time in the air and horizontal speed).] Identifying those two considerations, and the qualitative nature of their dependence on s, is the key thing for problem 3.

Help section tonight, 6 PM -highly recommended!

There will be a very excellent help section this evening at 6 PM. It will help you with your homework and with your preparation for the quiz. I strongly recommend going to that. It is in Nat Sci. (Annex) 101. -Zack

Quiz notes

The quiz will be fairly short; there will be 2 or 3 questions. One will be on conservation of energy. Another will probably be on vertical motion under the influence of gravity. There will be some graphing. When you create graphs it is important to: 1) label your axes, 2) scale your axes, and 3) indicate units next to the label. For example, y (meters) could be the label (with units) for the vertical axis of a graph of y vs time. t (sec) could be the label for the horizontal axis. Scale your axes means put some numbers and tic marks (not too many, just 2 or 3 per axis is usually just right). Typically, the size of your graphs should be about 3x3 inches.

Please feel free to post questions or initiate discussion here.

home work 1 solutions

click on the pages to make larger

Reading - January 17-24

Consistent with the content of this weeks homework, your current reading should emphasize chapters 7 and 10. Those chapters have some very helpful tutorials and interactive figures that I would recommend. The concept of energy plays a central role in physics and related disciplines and is worth a lot of attention.

Looking ahead to the next section of the book --properties of matter-- our emphasis there will be on material related to chapter 11. Chapters 12-14 can just be lightly skimmed.

Please feel free to post any comments or questions here.
-Zack

Homework 2

For homework 2, please do the following book problems:
Ch 6: Problems 5 and 7
Ch 7: Problems 4 and 9 and
*Calculate how much energy it requires to ride a very efficient bicycle up a hill for which the elevation change is 300 meters. Assume the bike has a mass of 10 kg and the person has a mass of 50 kg. Extra credit if you calculate this in joules (the default) and then convert that into kilocalories, which are what is conventionally refer to as calories when describing the energy content of food.
Chapter 8: Problems 4 and 5 (see interactive figure 8.18, Torque and Equilibrium)
Ch 10: Excercises 2, 3, 11, 34 and Problems 1 and 3*
*double credit for "the bike problem" and problem 3

as well as the following on-line work at the Pearson "10e" site:
tutorial on energy (Ch 7)
tutorial on projectile motion (Ch 10)
tutorial on orbital motion (Ch 10)
the tutorials on Black Holes and on Tides are extra credit. (They seem very interesting.)

Also at the Pearson site please do the END OF CHAPTER quizzes (these are under "chapter features").
Chapter 7 ( the answer to 7 is 0.25)
Chapter 10: (the answer to 7 is "yes both would increase)

This is due next Friday. Please post any questions here for quick, cogent answers and discussion. Questions, and responses to questions, are appreciated.

Homework 1

Homework 1 includes both book problems and online work at the Pearson web site. The online work must be completed by 11:30 AM on Friday, Jan 16th. For your solutions to the book problems please show your work and make it very neat and well-organized. Clarity and good presentation is required. These are due in-class that same day (Jan 16). The book problems are as follows:
Chapter 3: Excercises 20, 21, 34 and 45 and Problems 3, 4 and 5.
Chapter 4: Problems 2, 6 and 7.
Chapter 5: Problem 3.
Chapter 6: Excercise 45 and problem 6.
Please feel free to post any questions regarding the book problems here and to answer, discuss or nuance other peoples posts.

The online work includes:
the end of chapter quizzes from chapters 2 through 6,
the tutorials associated with chapters 2-6, i.e., Newton's 2nd Law, Newton's 3rd Law, Vectors, and Newton's 3rd Law and Momentum.

Questions, comments and discussion regarding the online work is also welcome here.

Powerpoint from Jan 10th class

Here are images of a powerpoint related to what we will cover in today's class.

Textbook/Website Information

Here's some info on registering for the website regarding the textbook.

To register, go to
http://wps.aw.com/wps/media/access/Pearson_Default/5632/5768114/login.html
or just google "media 10e" (and select the 1st result), and follow the steps to register.

You'll need an Access Code to complete this.
If you've purchased the Media Update 10e copy of the textbook, the code is included there.
If you have any other edition of the text, that's fine. You can purchase the Media Update without the book online:

https://register.pearsoncmg.com/reg/buy/buy1.jsp?productID=34427

This is only $30, and includes an e-copy of the book online.
However, be aware. Homework problems Zack assigns from the text will correspond to 10th Edition. If you use an older version, you'll need to look at the e-copy to find the correct problem.

You'll also need the class number to register, which is:
Class ID: cm799640

If there are any questions with this, whatsoever, please post them, as you can be sure you're not the only one having the same problem.

-Eliot

Reading

Our first classes will deal with material from Chapters 2-10, the chapters on motion (mechanics). Reading from those chapters, in that order, should be relevant to what we will cover in class over the next week. Also, I have found the interactive online figures to be excellent, for the most part, and recommend playing with those. Additionally there are online tutorials available (e.g., Newton's 2nd Law, Newton's 3rd law, ... and Momentum, Energy...), which i think are helpful (and will be part of the first HW (wich will be officially posted tomorrow)). The first HW will also include the quizzes from most of these chapters. Please feel free to pose questions about the material, raise discussion topics, and contribute generously to discussions via "comments" to this post.

Welcome to Physics 1

Hi. Welcome to Physics 1, Conceptual Physics. The first jpeg document here has some basic information and a brief discussion of the class. The second one is an image of the powerpoint from our 1st class meeting.