MechanicsMechanical ResonanceBackground:A system often studied in classical mechanics is the "damped, driven oscillator". This is a system that is subject to three forces: a restoring force, a resistive force, and a sinusoidal oscillating force. Consider the simplest possible example of these three forces: a Hooks Law restoring force (F=-kx), a linear damping force (F=-bv), and a sinusoidal driving function (Asin(wt)). A physical example of this system would be a spring that provides the restoring force, light friction to provide the damping, and a motor to move one end of the spring back and forth. Put the spring on a horizontal air track to keep friction small, and imagine one end of the spring attached to a cart to anchor it. Imagine the other end of the spring attached to a motor that can drive back and forth according to Asin(wt), where w is the angular frequency and can be adjusted. Use Newton's second law to derive an equation for the position of the cart as a function of time. Assume b is much less than k and that A is much less than l, where l is the natural relaxed length of the spring. What assumptions do you need to make about the spring to solve this equation? Your solution should predict a formula for the amplitude of the cart's motion, as a function of w (with some of the other constants, too). Task: Set up a real apparatus that corresponds to your model of a damped, driven oscillator. Measure the amplitude of the cart's motion as a function of driving frequency. Measure as many of the quantities involved in the apparatus as you can (m, k, A, l, etc.), and use your best-fit solution to your data to estimate the others. How good is your model? Interpret your estimates. What assumptions are the most important in determining the relevance of your model? Warning: be very, very careful about how you think your model applied to your apparatus design. Is your apparatus one-dimensional? Note that A is often misinterpreted as displacement. What is it really? How does it map to your equipment?
Young's Modulus of metalsBackgroundYoung's modulus has to do with the model that there is a linear relationship between stress and strain. For a piece of material that has a constant cross-sectional area, the relationship can be written as: Stress = (force applied)/( cross sectional area) = E * strain = E* Dl/l where E is Young's modulus (a constant), l is the length of the material and Dl is the change in length when the stress is applied. An optical lever is a device used to measure small changes in distance or angles. It consists of a mirror attached to a cylinder and a laser. The laser beam is directed towards the mirror. After reflecting off the mirror, it makes a spot on the wall a distance D from the mirror. If the cylinder turns an angle q, then the laser spot moves a distance X along the wall. The angle that the cylinder turned is then 1/2 the angle that the spot moved, so q = X/(2*D). Experiment Measure the cross-sectional area of the wire. Clamp it at the top of the apparatus. Wrap the wire a couple of times around the cylinder and below the cylinder and hang about 1 kg weight on the end of the wire. Measure the length of the wire between the top clamp and the cylinder. Set up the optical lever and mark the laser spot on the wall. Add a second weight to the holder at the bottom of the wire. Then carefully remove the weight (leaving the original 1 kg still on the hanger) and measure how much the spot moved. From these values, determine how much the wire shortened when you removed the weight. Repeat this for several different weights and lengths of the wire. Determine a value for Young's modulus for the wire.
Conservation of Angular Momentum in Rotational CollisionsBackground If a rigid object is rotated at an angular velocity (w vector) about some axis, the angular momentum (L vector) of that object about the axis of rotation is given by: L=Iw where I is the moment of inertia of this rigid object about the axis of rotation. If the net torque acting on the system is 0, then the total angular momentum of the system remains constant. This is the statement of the conservation of angular momentum. Task Read the instructions for using the air bearing apparatus. Design a set of experiments that will demonstrate that if the net torque acting on the system is zero, the total angular momentum is conserved. Make sure that you show that if the net torque is not zero, the angular momentum is not conserved. Is "no external torque" a legitimate assumption for this apparatus? How would you check that and define a domain under which that assumption is not wrong? Make sure your surfaces are thoroughly cleaned. Grit will cause frictional torque between the surfaces and dissipate your angular momentum. Speed of sound in airBackground There are two different speeds that sound travels in air. The energy in a pulse of sound waves travels at the group velocity of the waves. The individual phases (such as a tone with a very pure pitch) travel at the phase velocity. These two values do not have to be the same. To measure the phase velocity, one measures the wavelength, l , (assuming it has just a single value) and the frequency, f (in Hertz) of the sound wave. The phase velocity, vp is defined as: vp = f l If you plot measured frequency vs 1/(measured wavelength), the slope of the line should be the phase velocity. On the other hand, if you were to generate a short (time) pulse of sound {a short pulse has no well-defined pitch}, and measure the time it takes for the pulse to travel a distance d, you can determine the group velocity by plotting distance vs. time. The slope of this graph would be the group velocity, vg. Task: You should measure the group velocity of a pulse of sound waves traveling in air. We have sound detectors to go with the ULI and Logger Pro. Attach two of the sound detectors to the ULI and set up an experiment that shows the output as a function of time. Place the detectors a known distance apart. Generate a short pulse of sound using two blocks of wood. Measure the time it takes for the sound to get from the first detector to the second. Repeat this for a number of different distances. Plot distance vs time. Do you get a straight line? What sort of model does this support? What is the value of the group velocity for sound waves in air that you determine from these data? How well do you know this answer?
Classical ScatteringThis experiment is currently very loosely defined. You will have to do some reading on scattering theory to develop a clearly stated model to test. The basic idea, though, is to use the apparatus to fire BBs at a target, and use the pattern that the scattered BBs make on spark tape to deduce the shape of the target. If you want to try this one, let's talk together to make the task more specific. [Get more information from Rex about this one.] DispersionThis experiment has two parts. First, use a weight of known mass to put a string under tension. Drive the string with a known frequency to set up a standing wave. Get the wavelength from the nodes. Plot angular frequency vs. wavenumber and see if the slope is not different from sqrt(T/mu) as predicted by theory. (T is tension and mu is mass per unit length.) Second, try it again with a steel wire. Does the theory still work? Water Drop ChaosThis is a neat experiment that still needs a little more rigor. The central idea is very simple. You get two tanks of water and some tubes. It's important to be able to control the flow rate precisely for a long time, so you put one tank up on a high shelf and the other on the counter. Place a run-off hole at a particular point in the lower tank (this will keep the level of the bottom tank steady and thus the flow rate). Lower down, make another hole and attach tubing. This tube should be cut at an angle such that water will build up and drip from the tip. Make sure the drop will fall through a photogate. You can then measure the time between drops as a function of flow rate. For low flow rates, you should get a constant. As you increase flow rate, you will see other kinds of behavior. Plot the time to next drop vs. the time from the previous drop. Once you find some interesting behavior, you will even want to make a 3-d plot of successive drop times. Beware: after each drop there are usually secondary droplets. Don't count these in your time measurements. If you cut the tube properly, you can line up the photogate so that the secondary drops will miss the beam. If you are the first to want to try this experiment, you will have to get the tanks and tubing. Also, the experiment as it is described here is missing some quantitative rigor. That is, it's all well and good to make pretty pictures, but what do they tell you? You should do some reading to determine what kinds of parameters people use to characterize chaotic behavior, and use those parameters to describe this phenomenon. |
ThermodynamicsWork into HeatThis experiment provides a way to quantitatively measure the work done by friction. You turn a crank that rotates an axle. The axle is wrapped by a cord from which a heavy weight is hanging. As you turn the crank, you work against the frictional force, and the axle heats up. The axle is filled with water, and a thermometer measures the temperature of the water. You can calculate how much energy is required to raise the temperature of water by one degree, and you can calculate how much work is done by rotating the crank one turn. Is the number of turns of the crank consistent with the increase in the water temperature?
Absolute ZeroNote: there is a compatability issue you will have to work around. The apparatus to do this experiment is manufactured by PASCO. The pressure and temperature gauges are made by Vernier. They don't hook up. You can, however, adapt the tubes to attach the Vernier pressure sensor to the PASCO hoses. The temperature gauges may not be so easy -- you may have to use a manual method of measuring the temperature.Background: Read Thom Espinola's Thermophysics book, Chapter 1. Read the instruction manual for the absolute zero apparatus. Task: Use the apparatus to do your best to measure the value of absolute zero in SI units. Pay close attention to units and explain your procedure in your presentation. Boyle's LawBackground: For an ideal gas, Boyle's law says that the product of the pressure and the volume of a gas is proportional to the product of the temperature of the gas and the number of molecules in the gas: PV = NkT. Task: Use the pressure sensor and the pump apparatus to test this model. Note that there are four possible parameters you can vary -- make sure you only vary one at a time, and that you do vary all four by the time you are finished. If the model is not wrong, how many air molecules are in the apparatus chamber? Does that number make sense? If the model is wrong, what do you think is wrong about it? I.e. why does it fail? You should think carefully about the sources of error in this experiment. What "ifs" are behind this law -- do they apply to your apparatus?
Stefan's LawBackground: For a blackbody (a hypothetical object that absorbs all the radiation that hits it, with no reflection, and reradiates the same amount of energy as it absorbs, so that its temperature remains constant), theory predicts that the total energy output in photons per unit area of its surface should be proportional to the temperature to the fourth power (in Kelvin, naturally). This relationship is called Stefan's Law. You should do some more background reading to better understand the idea of a blackbody and where this law comes from. Task: Use the oven and the thermopile to test this hypothesis. If the model is not wrong, use the textbook value for the proportionality constant and see if the effective surface area that implies yields a sensible value. The infrared thermometer may also be helpful here, but the oven will likely get too hot for it. Make sure to use the water cooling shield. Heat of fusion of iceBackground Many normal materials go through simple phase changes as the temperature, pressure and volume change. These phase changes can be from solid to liquid, solid to solid, solid to gas, liquid to gas, liquid to liquid, etc. The different phases of the material have different physical properties. Water, for example, has a number of different phases in the solid and gaseous phases, but only one liquid phase. At atmospheric pressure ( about 104 Nt/m2), there is a phase change between the solid phase and the liquid phase at a temperature of about 273 K. The thermal energy (Q) /mass that it takes to go through this phase change is called the 'heat of fusion' of water (Lf): Q=mLf. The heat capacity (c) of a substance is the energy that it takes to change the temperature of the object where there is no phase change: dQ/dT=mc. For many materials, c is a constant over a reasonable temperature range. Task: Look up the values for the heat capacity at constant pressure for the liquid and solid phases of water. There is an ice machine in the kitchen next to the library on the first floor of Frank. Ask Don for a key. Set up the calorimeter. Set up the Logger Pro Interface to measure the temperature of the water in the calorimeter. Make sure that the calorimeter works properly by placing a known mass of cold water in the inner container and letting it reach equilibrium. Then mix a known mass of hot water with the cold water that is in the calorimeter and determine the final temperature. Find out how much heat energy was lost during the mixing process. This will give you an estimate of how well the calorimeter maintains isolation with the environment. You will need to account for this when dealing with the ice (next paragraph). Get some ice and place it in a cooler. Measure the temperature of the ice. Place a known mass of hot water in the calorimeter and let it reach equilibrium. Dry off a piece of ice and measure the temperature change in the calorimeter as it melts. Determine the mass of the melted ice (same as the solid ice) by finding the increase in the mass of the contents of the calorimeter due to the melted ice. Find the heat of fusion of ice. Repeat this a few times so that you can determine the uncertainty in the value of the heat of fusion you measure.
Newton's Law of CoolingNewton's Law of Cooling suggests that the rate of heat transfer across an object in thermal contact with two reservoirs will be proportional to the product of the cross sectional area of the object with the temperature gradient across it. There is a bar of aluminum with pipes attached. By flowing hot water through one pipe and cold water through the other, you can set up an equilibrium situation. If you measure how much the temperature of the cold water changed for a given flow rate, you can determine how much heat transfered across the bar per unit time. Other physical properties of the bar can be measured. This will allow you to test Newton's model, and if it is not wrong, you can deduce a measurement of the thermal conductivity of aluminum. You will need to design this experiment. Think carefully about what your control variable is, and how changing this variable will enable you to test Newton's Law. Go over your design with Don before you begin. |
Properties of Light
Index of Refraction of a WaterYou should use Pfund's method to get n. Shine a laser down on a block of glass with a piece of white graph paper below. (The original experiment design calls for the glass to be painted white. Not sure if this is necessary. Don't paint glass without checking with me.) Light should scatter off the bottom in all directions, then pass back out through the top. Some of the light will internally reflect back down from the glass-air interface at the top, and then reflect off the bottom again. The diameter of the resulting circle will give you the index of refraction of the glass. By using blue, green and red lasers, you can see if n depends on frequency. If you put a layer of water on the top of the glass, you can generate a second ring of reflection. The diameter of this ring can give you the index of refraction of the water. See here for more information. A Microwave InterferometerBackground: Microwave radiation is light that has wavelengths of order of a few centimeters. We have an apparatus (a microwave transmitter and reciever) that will allow you to pass microwaves through slits in a conducting plate of metal. This will split the microwaves into two paths. Each path reflects off a conducting plate and returns. You can use this apparatus to test if microwaves interfere according to wave theory. Based on the difference in path length, you should get either constructive or destructive interference when the waves recombine. If the theory is not wrong, deduce the wavelength of the microwaves. Note: this is essentially the same experiment as the Wavelength of a Laser experiment. You won't want to do both. Spectrum of the SunThe basic idea of this experiment is simple. Point the E86 spectrometer at the sun and derive the spectrum of solar light. Before you make any measurements, you should do some research and try to predict what you think your spectrum should look like. Try to be as quantitative as possible, so you can compare your prediction with your measurement and actually test your hypothesis. There are several complicating factors you will have to consider. For one thing, you don't want to fry the equipment by pointing it at a source of light that's too bright for it. For another, the detector efficiency of the CCD in the spectrometer depends on wavelength, so you will need to correct for that. Furthermore, if you can see any absorption lines at all, how do you know they're coming from the sun and not the atmosphere? You could take the apparatus/computer up to the roof, but there should be a fiber-optic cable that could be used to point at the sun out the window. I don't know where this cable currently is. Presumably in the optics lab somewhere.
Wavelength of laser lightLook up how a Michaelson interferometer works. Set up the Michaelson interferometer that we own and align the mirrors such that you see clear fringes when the laser illuminates them. Convert the reading of the micrometer on the back scale to movement of the back mirror in meters. Pay close attention to the geometry of this process. Slowly move the back mirror and measure the number of fringes pass as the meter moves known distances. From these data, determine a value and uncertainty in the value of the wavelength of the laser that illuminates the mirrors in the Michaelson interferometer. The Index of Refraction of AirBackground: An interferometer usually works by varying the path length along one arm of the split beam as compared to the other. However, you can achieve a similar effect by changing the index of refraction of the medium through which the laser travels along one beam and not the other. If the laser passes through a vacuum chamber, its wavelength will lengthen as the light speeds up, and fewer wavelengths will fit along that arm of the path, thereby changing the relative phase of the beams when they recombine later. The change in the number of fringes tells you the number of wavelengths that shifted, which tells you (given the size of the chamber) how much the light sped up when you pumped the air out, which tells you the index of refraction of air. Task: Find the interferometer in which one arm of the laser path must go through a transparent chamber. Set up the interferometer and connect the vacuum pump to this chamber. Pump the air out of the chamber and count the number of fringes that pass by your detector. Use this number and the physical parameters of the interferometer to calculate the index of refraction of air.
The Index of Refraction of a PrismBackground: A beam of light that enters into one face of a prism at some angle of incidence i will be deflected through some angle d (from its original path), given the opening angle a between the two faces of the prism. This deflection also depends on the index of refraction n of the prism, which will depend on the wavelength of the light. Derive an expression for d as a function of i, n, and a. Set dd/di=0 to find an expression for the minimum angle of deflection. This angle will depend on a and n, so if you measure a, you can determine n. See Hecht's Optics for more detail. Task:
Get a prism from the optical drawer. Use the gaussian lamp to make sure that the optical bench is level and that the prism is properly perpendicular to the light beam. Then swing the beam around to another face and level it again: the difference between these beam positions is the opening angle of the prism faces (not all three opening angles will be the same, so don't lose track of which one you used.). Use the Mercury and Cadmium lamps to generate spectral lines of specific wavelengths. Run them through the slit without the prism present to determine the location of no deflection. Then insert the prism and rotate the tray and the viewfinder to identify the angle of minimum deflection. Repeat for at least eight different colors. Plot n vs. 1/(wavelength)2. Glass is often identified in terms of the coefficients of this linear relationship. The slope is B and the intercept is A. Look up your values for A and B in a manufacturer's chart. What kind of glass is your prism? Things to be careful about: this device will measure angles very accurately if you are careful. Be aware of uncertainties. The width of your line will matter -- figure out which side of the line is due to the fixed edge of the slit and always measure your angle from that side of the line, for consistency. The Speed of LightBackground: Light supposedly moves at 186000 miles a second. Galileo tried to measure the speed of light by having a friend stand on a hill 10 miles away with a lantern. When Galileo uncovered his lantern, the friend could see the light and uncover his own. Galileo figured that if he divided the distance between the hills by half the time between his uncovering his lantern and seeing his friend's lantern, he would have the speed of light. Why do you think he concluded light moved infinitely fast? Foucault had a better idea. Read links like this one or this one to get more ideas of how Foucault's method works. Task: Design an apparatus in the optics lab to measure the speed of light. You will have to use the duct in the ceiling to get a long enough baseline. Use Foucault's method and make sure you understand your uncertainties. Once you get a value, you can also try to measure it using standing wave theory and a row of marshmallows in a microwave oven. Again, pay close attention to uncertainty. Poisson's SpotIf Huygen's Principle is not wrong, light waves should converge behind a small object and make a bright spot. Use a laser and a magnetized ball bearing as a target and find the Poisson Spot. Make sure you work through the math to predict where it should be, and test your prediciton. See this article for more information. (You don't have to go for the second order spot.)
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Electricity and MagnetismB field of a solenoidUse the Hall Effect Probe to map out the B-field of a solenoid. Determine the dependence of the magnitude in the solenoid on I and test Ampere's law with a simplified model.This experiment is deceptively simple, so make sure you really understand what your equipment is doing and what the uncertainties are. How much uncertainty can you attribute to fringe fields? See the manual for the Hall Effect Probe for more detail on how it works.
Magnetic ForceBackground: The Biot-Savart law allows you to calculate the magnetic field along the axis of symmetry of a loop of current. The force experienced by a magnetic dipole in an external magnetic field is proportional to the gradient of the magnetic field at the position of the dipole. (You should make sure you understand why this is.) Task: Familiarize yourself with the magnetic force apparatus. Show that the magnet at the center of the apparatus experiences no force when both coils are carrying the same current, no matter the orientation of the magnet. Then disconnect one coil and use the spring to measure the force on the magnet as a function of distance along the coil's axis of symmetry. Compare with theory and estimate the magnetic dipole moment of the magnet. Try for three different values of I and see if you get the same answer for mu. If you have time, try measuring B(z) along the magnet's axis with a hall effect probe and see if you get the same dipole moment.
Magnetic MomentBackground: A magnetic dipole in a magnetic field will feel a torque that tries to align it with the direction of the magnetic field. However, once it reaches the angle of alignment, it will have kinetic energy that will cause it to overshoot. The torque will then push it back. Equating mu cross B with I alpha yields a simple harmonic motion equation that predicts a particular value for the oscillation frequency as a function of the magnetic moment of the dipole and the strength of the B field. Task: Read the manual for the magnetic torque apparatus. You may use their calibration as a check, but you must calculate B(I) yourself to be sure. Measure the frequency of the magnet's oscillation for a variety of magnetic field strength values. (This is experiment II in the manual.) Why is it important to use a small amplitude of oscillation? Derive from your data (if your model is not wrong) a value for the magnetic dipole moment of the magnet. Does your answer make sense? If you have time, you could also try using a Hall Effect probe and measuring B(z) along the axis of magnet to get the magnetic moment that way to see if you get the same answer.
The Magnetic Susceptibility of AluminumBackground For a large class of magnetic materials (called linear isotropic materials) the magnetic dipole moment per volume, M, produced in the material when it is placed in a magnetic field B is given by: M = cB/(mo*(1+c)), where c is called the magnetic susceptibility, mo is the permeability of free space and B is the applied magnetic field (in Tesla) . If the susceptibility is much smaller than 1 and positive, the material is paramagnetic. If the susceptibility is small and negative, the material is diamagnetic. The force exerted on an magnetic dipole that is placed in a magnetic field that is a function of position (not a constant magnetic field) is: F=(m dot Del) B, where m is the dipole moment, and del is the gradient operator. If the magnetic field points only in the x direction, then F = mdB/dx=MVdB/dx= (Vc/(mo*(1+c)))*B*dB/dx, where V is the volume of the linear isotropic material. TASK
Current into Heat EquivalenceBackground: According to theory, a current-carrying resistor will give off energy at a rate of P=I2R. We know that most substances (liquid water in particular) will change temperature as heat is transferred in or out of them at a rate of dQ/dT=mc. Therefore, if a known current is passed through a resistor of known resistance, while it is submerged in a known mass of water, the temperature of the water should increase at a particular rate over time. Task: Measure the resistance of the filament in the calorimeter. Use a particular potential difference to send a current through the filament for a specific amount of time while it is submerged in a known mass of water. Measure the increase in temperature of the water and test whether energy is conserved. Repeat for several different values of the input variables: potential difference, time, and mass of water. You should have a plot in the end with DT vs. V2t/m, which should yield a straight line with a predictable slope. Remember to measure the efficiency of the calorimeter, as described in the instructions for the "Heat of Fusion of Ice" experiment. Think carefully about uncertainties. Your goal in the end is to say that two numbers are not different from one another, and without meaningful uncertainties, that is impossible.
Faraday's LawConsider two concentric solenoids. According to Faraday's Law, a changing current in one solenoid will induce a current in the other. Try to calculate (predict) what an AC current in one coil would induce in the other. Find two concentric solenoids in the lab. Send an AC current through one solenoid and measure the current in the other. Then send the current through the second coil and measure the induced current in the first. Are the results what you expect? Be careful with this one. There are several ways you could generate an AC current (including a wall socket, so remember Safety First!). You could ramp up a power supply at a steady rate, you could try a sine wave on a function generator, or you could go directly from the wall socket. If you use a sine wave (generator or socket) you can use a multimeter to measure the RMS amplitude, or (for the generator) you could try an oscilloscope. Obviously, don't use the oscilloscope with the wall socket! You will have to also think very carefully about the coils you use. The easiest apparatus to grab would be a couple of nested solenoids I've seen in the lab, which also happen to be square in cross-section. If you use that, you will have to think carefully about how (or if) the square cross section will affect your results. Impedence of a Light BulbBackground: Impedance (Z) is defined as the relationship between the driving function (D) applied to a system and the response function of the system (Y): D = Z Y For an electrical system such as a light bulb, the driving function is the electrical potential placed across the bulb, and the response function is the current drawn by the light bulb. The electrical impedance of a system is measured in Ohms. The electrical power dissipated by the impedance is given by the product of the driving fucntion and the response function Task: You are to measure the impedance of a typical 100 Watt light bulb. Drive the system using a variable 100 VAC power supply. Set one of the meters to measure the AC current and the other to measure the AC potential difference. Measure the current drawn by the light bulb as the RMS potential across it is varied from a few Volts to 120 Volts. From these data, determine the impedance of the light bulb. Does this make sense to you? Why? Is the light bulb a resistor? Curie Temperature of Iron and NickelThe background and design for this experiment are described in this article. No one has done this experiment here before, so you will have to figure out how to implement and/or modify the design as presented in the article. Make sure you understand how a thermocouple works! |
The Quantum WorldFlourescenceThis is another emission line experiment. It has two parts. I put a question mark next to the difficulty because I'm not sure our equipment will actually do this. Make sure you investigate before committing to this experiment. The first part is to illuminate some rocks with UV light and measure the spectrum of the emission with a spectrometer. Can you identify the elements in the rocks? Second, if you put a source of alpha particles very near to objects, the surface will flouresce in X-rays. I believe our PHA will be able to detect these X-rays, but it might only be sensitive to gamma-rays. If this will work, you will need to make sure the alphas aren't hitting the PHA themselves. Be careful with background on this one. If this works at all, you should be able to (a) identify the quantum numbers for the transitions and verify that the sqrt of the energies is linear with the atomic number, minus a screening number for the other electrons in the atom. What screening numbers can you determine? See the University of Michigan Experiment for more information. In particular, there's a lab manual that explains the math. Frank-Hertz ExperimentBackground: You have probably all seen the emission lines of an excited gas presented as evidence for the quantized nature of atomic energy levels. But what if those quantized energy states were a result of the properties of light, and not of the atom? Frank and Hertz set out to test this hypothesis by exciting the energy levels of a monotomic gas by bombarding it with electrons. Conservation of momentum indicates that an electron bouncing off an atom will not lose much energy (think of a tennis ball bouncing off a truck). However, if that atom changes its energy state, that energy has to come from the kinetic energy of the electron. If the electron has enough kinetic energy to excite the atom, it will lose that much of its kinetic energy. The Frank-Hertz experiment, therefore, accelerates electrons to a certain amount of kinetic energy (this is the independent variable), sends them through a cloud of gas, and then puts a small electric potential drop in front of the electron beam. The electrons that do not lose energy will not be stopped by the drop, so for small accelerating potentials, there should be a large current. As the acceleration is increased, the KE of the electrons will increase, until they reach the level necessary to excite the atoms. Electrons in such collisions will lose most of their KE, and will therefore not be able to make it over the final potential drop. The current will fall. As the acceleration continues to increase, electrons will gain enough KE to excite two atoms, and you will see another drop in current as they lose that energy. As you keep increasing the accelerating potential, you will see regular drops in energy that, if the energy states of the atom are indeed quantized, should be spaced apart by the same amount of energy. Borrow Don's copy of Melissinos to read more about this experiment. Task: In theory, we have all the pieces you need to carry out this experiment. In practice, I don't know where they are. No one has done this experiment in the time I've been here. You'll have to track down (and perhaps order) the pieces we need. Rex can help us find them. Once you have all the pieces, you will need to test the hypothesis that the atomic energy levels are quantized by measuring the output current as you increase the accelerating potential of an electron beam passing through a monotomic gas. You can check the spacing of the current drops against the textbook values for the smallest ground-state jump for that particular atom.
Brownian MotionNote: There still need to be some problems solved to make this possible. It looks like the biology department might have the necessary microscope and camera. If there is interest in this experiment, we will have to schedule a time to use their scope. We have the microspheres! The biologists are interested in exploring this possibility if you are. Background: I have a nice introduction to Brownian Motion, as well as Einstein's famous 1905 paper on the subject, in my office. You are welcome to borrow it. You could also read the wikipedia article (although I would hope you would not limit yourself to that). There's also a very nice book called "Uncertainty" (by David Lindley) that gives a well-written (brief) explanation of the history and significance of Brownian motion. Here is the instruction manual by Steve Wonnell at Johns Hopkins. He is the professor from whom I learned about this experiment, and he should get credit for the design.
Hydrogen SpectrumNote: I think I'd like you to do this a different way. I found a monochronometer in the closet, which uses optics to send a particular (small) band of wavelengths through a slit that you look through. By changing the wavelength, you can scan through the spectrum until you see the emission lines through the slit. The dial tells you the wavelength. In this lab, you will use a computer driven spectrophotometer to measure the wavelength of the visible photons produced when hydrogen gas is excited. You ought to be able to see 5 different wavelength photons. You will use these data to evaluate Bohr's model of the energy levels of hydrogen. You need to make sure that the ambient light is a minimum when you do this experiment TheE-86 spectrophotometer
Data analysis: Convert the wavelength measurements to the energy of the photons detected in eV. From the values, determine the possible energy states of hydrogen (assuming that the lowest energy state has 0eV energy). Fit the hydrogen model of Bohr to these data. Half-life of Potassium 40You may remember measuring the half-life of Barium in the Intro lab last year. But how do people measure halflives for elements with half-lives of billions of years? You can't wait around for ten half-lives and get the slope of a graph! The answer is to go back to the equation for radioactivity. A = dN/dt = -N*lamda, and T1/2 = ln(2)/lamda. If you can determine N and A, you can get T1/2! Get a sample of KCl. From the mass and composition of the sample, determine how much 40K is present. This gets you N. You should make sure (from the table of nuclides) you understand how 40K decays. You can measure the 1.43 MeV line with the PHA. If you take the detector efficiency, background, solid angle, and other factors into account properly, you can determine A from the measured count rate. Once you know N and A, you know lamda. Obviously, the trick with this experiment is a very careful treatment of uncertainties. You'll have to look up the detector efficiency as a function of energy (not every photon that hits the detector registers a count), and carefully examine your geometry (so you can account for photons that don't hit the detector). From your measurements, you can get T1/2 and compare it to the "known" value. Compton ScatteringBackground: There was initially much resistance to the idea that light could be modeled as a particle, as Einstein's theory did. Although the photoelectric effect is seen now as the definitive evidence for the validity of the photon model, historically it was the Compton scattering experiment that served as the tipping point for the success of the photon model. Look up the derivation of the Compton scattering equation. This equation predicts that the energy of a photon should be reduced by scattering through a particular angle. Task: Use a Cs-137 source as a source of gamma-rays. Encase the source in lead. Place the source on the board at the available angles. Place the spectrometer in the holder on the right side of the apparatus. You will likely need to cover the spectrometer in lead (why?). Measure the photon energy as a function of angle, thereby confirming the validity of the Compton scattering equation (and hence, the photon model). If you assume you know the energy of the emitted photon, you should also be able to measure the rest mass of the target particle from which the photon scatters. What kind of particle is it? Warning: this experiment will require long accumulation times and a careful treatement of background and calibration. The Charge to Mass Ratio of an ElectronBackground: The cyclotron radius of a charge moving in a magnetic field is R = mv/qB. Task: Use the Helmholtz coil apparatus to measure R for different values of v and B. The knobs on the device control the potential across two plates that are used to accelerate the electrons (KE = qV) and the current flowing through the Helmholtz coils that will generate B. You will have to look up (or derive) the formula for the B field at the center of a pair of Helmholz coils, and measure the properties of the device in order to convert this current into a value for B. By plotting R vs. the right combination of V and B, you should get a curve that you can fit to get an estimate for q/m for the electron. Think carefully about uncertainties on this one. If you already did the Millikan Oil Drop experiment, you should also report an estimate for the mass of the electron. The Millikan Oil Drop ExperimentBackground: Read the manual for the PASCO apparatus. Particularly the historical material at the end will be of interest to give you some background on the experiment. This is a Nobel Prize winning experiment that, if you do it carefully, you should be able to get an accurate result to better than 5%. Task: Measure the charge on the electron. If you did the charge to mass ratio of the electron experiment, you should also report the mass of the electron. Pay close attention to uncertainties. |