Group1_8_ch27-32

=Lab: Diffraction and Interference= toc Group: Pontillo, Listro, Hallowell, Dember Date: February 2, 2012

OBJECTIVE: The purpose of this experiment is to examine the diffraction and interference patterns formed by laser light passing through a single slit, diffraction grating and a double slit and verify that the positions of the minima or maxima in the resulting pattern match the positions predicted by theory. In addition, there will be a comparison between the diffraction and interference patterns formed by different wavelengths of laser light and different slit widths/spacing.

HYPOTHESIS: Our results should follow the equation: λ=(d*sinθ)/m which is derived from the equation: d*sin( θ)=m*λ. In these equations m is the integer of fringes the fringe is from the center one, λ is the wavelength of light, θ is the angle derived from the arctan of the fringe's distance and the length between the slit/diffraction grating and screen. The d will change for each method. It will represent the slit spacing in the double slit diffraction, the width in the single slit, and the difference in the lines of spacing in the diffraction grating. Our experimental wavelength should match with the theoretical wavelengths, and, as seen in the equation, red, which has the longest wavelength, should have the largest fringe lengths for each respective order of the integer.

METHODS/ MATERIALS: In order to perform this lab, we must first set it up by placing an optics bench on a flat surface with an optics screen on one end of the bench. Then we place a single slit on the opposite end of the bench. Once this is set up, shine a laser light through the single slit in the direction towards the screen. The patterns will then be produced on the screen. Upon shining the light, trace the patterns on a piece of paper, and record the measurements including the distance between the screen and the single slit, the wavelength of light, and the length of fringes. Using the single slit, we repeated this process using multiple lasers with varying wavelengths (different colors). After collecting data for the single slit, we replaced it with a diffraction grating, and upon completing our data collection for it, we performed the same experiment with a double slit diffraction.

DATA:



Analysis: We were able to see from our results, different patterns associated with these experiments. For the double slit interference: As (d) the slit spacing increased, the fringe distance decreased. Spacing was increased from .25 mm to .50 mm, and the fringe distance decreased from 2.1 mm to .9 mm. Also as wavelength increased (changing the color of the light) the fringe distance also increased. Violet 400 nm, Green 535 nm, and Red 650 nm, the fringe distance increased from Violet 1.2 mm to Green 2.1 mm to 2.5 mm.

For Diffraction Grating: As the grating lines/cm (a) increases the fringe distance decreases. When "a" was .0016 mm and increased to .0033mm, the fringe distance decreased from 29 mm to 16 mm.

For Single Slit: When single slit width is increased, the y (fringe distance) will decrease. When slit width is increased from .02 mm to .04 mm to .08 mm, the fringe distance decreases from 21 mm to 11.2 mm to 3.6 mm. Also as wavelength increased (changing the color of the light) the fringe distance also increased. Violet 400 nm, Green 535 nm, and Red 650 nm, the fringe distance increased from Violet 21 mm to Green 29.8 mm to 34.5 mm.

CALCULATIONS:

DISCUSSION QUESTIONS:

1. Qualitatively describe and compare the patterns produced by: >> >>
 * 1) The single slit
 * 2) It produced a central band with dimmer bands parallel to it on each side.
 * 1) The double slit
 * 2) It produced a central band with dimmer bands parallel to it on each side. Each band has light and dark spaces within it now.
 * 1) The diffraction grating
 * 2) This created dots on the screen on the same plane.

2. Make a chart to describe the changes that occur when: > >
 * 1) the double slit width is increased
 * 2) the double slit separation is increased
 * 3) the slit width of the single slit is increased
 * 4) the diffraction grating lines/cm is increased
 * 5) the wavelength of the light source is increased

CONCLUSION: Our hypothesis,that our results should follow the equation: λ=((w/d/a)*sinθ)/m which is derived from the equation: d*sin( θ)=m*λ. θ is the angle derived from the arctan of the fringe's distance and the length between the slit/diffraction grating and screen, was proven to be correct. We see that when the slit width, slit spacing, or the grating is increase, it also decreases the angle and the distance of the fringe. When the slit spacing increased from .25 mm to .50 mm in the double slit experiment, the 1stfringe distance decreased from 2.1 mm to .90 mm. We are able to show that we could use the two equations together to find theta then wavelength. Once finding the fringe distance and the distance between the slit and the screen, we were able to find the angle, to plug into λ=((w/d/a)*sinθ)/m.

The lab did have error along with it. Our error ranged from 5-20% The actual measurements were hand-drawn and it was very difficult to draw the light exactly because every time we would try to draw the bands a hand would block the light a bit. This error came mostly from the small measurements we were taking. The values were rough estimates compared because of the small spacing in between these points. We had to keep re-measuring to make sure our measurements were accurate in accordance within our equation.

This lab shows the property that light can behave like wave and it is not only behaving particle. This is the basic principle behind wave- particle duality, which can be used in electron microscopy, where the small wavelengths associated with an electron can be used to see objects smaller than what’s visible using light. The double slit experiment which we performed is also a basis to quantum mechanics.

=Lab: Photoelectric Effect and Planck's Constant= 2/9/12 Hallowell, Listro, Pontillo, Dember

OBJECTIVE: Determine Plank's Constant using stopping potential.

HYPOTHESIS: As the frequency of a light in a circuit increases, the kinetic energy in the circuit will increase directly at rate of Plank's constant. It comes from the equation KE (max)= hf- work function. As the frequency changes the Energy will change at a constant rate of plank's constant.

METHODS/MATERIALS: In order to begin this lab, we must first set up a variable power supply connected with wires; we must then connect an ammeter to the circuit in series to the diode in order to find the minimum amount of current flowing through the circuit. Once this value if found, we place a voltmeter in parallel to the diode. Starting from zero volts, we slowly increase the amount of voltage running through the circuit until diode just lights. The voltage at this instance, as measured with a voltmeter, equals kinetic energy once it is multiplied by the charge of an electron. We repeated this process of finding the KE for different colored diodes (because of the different wavelengths of light). Since we knew the wavelengths of each light, we could solve for the frequency of each by dividing the speed of light by the given wavelength. We ended up graphing these different frequences v. KE values. Since kinetic energy equals planck's constant times frequency minus the work function, the slope should be equal to Planck's constant and the y-intcercept should be equal to the work function.



DATA: GRAPHS: ANALYSIS: The x intercept on the graph should be equal to the stopping potential. The y- intercept is the work function, -1.73 x 10^-19. The coefficient of x should be Plank's constant, but from our data, the constant came out to be 8.60 x 10^-34.

CALCULATIONS: ANALYSIS QUESTIONS:
 * 1) Plot the graph of Energy (Joules) vs. Frequency (Hz). **Shown Above.**
 * 2) Interpret the best-fit line of the graph. **The slope represents Planck's constant and the y-intercept value is equal to the work function. We got this from the equation** **KE (max)= hf- work function, just as we stated in our hypothesis. Also, the x-intercept (not shown on graph) is the threshold frequency, when the stopping potential equals work function.**
 * 3) Calculate a percent error using the accepted value. **Shown in calculations.**
 * 4) Which LED has the highest work function ( ** Ψ ** )? Explain what this means.  **The work function is constant throughout the graph, so technically none of them have the highest work function.**
 * 5) Add columns to your data table.
 * 6) Calculate the final velocity of an electron as it travels across the LED point gap. **Equation: [[image:Screen_shot_2012-02-12_at_1.01.14_PM.png]]** [[image:Screen_shot_2012-02-12_at_12.43.55_PM.png width="187" height="96"]]
 * 7) How does this velocity change with color? Explain. **The colors with a shorter wavelength, and therefore a higher frequency, will have a larger maximum kinetic energy, and will therefore have a larger velocity.**
 * 8) If the point gap approximates 1.0 mm, calculate the acceleration of the electron and the time t to cross the gap. **Equations: [[image:Screen_shot_2012-02-12_at_1.10.19_PM.png width="118" height="37"]]and [[image:Screen_shot_2012-02-12_at_1.10.23_PM.png width="89" height="21"]](in each case initial velocity was equal to zero and final velocity derived from what is labeled (velocity of electron) on the middle column) [[image:Screen_shot_2012-02-12_at_1.10.03_PM.png width="322" height="98"]]**
 * 9) What vector field supplies the accelerating force? **Electromagnetic Force.**

CONCLUSION: Our hypothesis was proven correctly. Looking at our graph, our trend line had a constant slope, and a negative y-intercept, just as we explained in our rational. Furthermore, the maximum kinetic energy increased directly and proportionally with our frequency, showing a direct relationship in terms of our slope, which represented Planck's constant. Thus, our results followed the equation: KEmax = hf - work function.

This lab had a decent amount of error in it, nearly 30% to be exact. However, there were many areas where this error could have, and did, come from. First, our procedure called for us to make the smallest current possible, so given the inexact readings of the multimeter and unaccounted for current, our results would be higher than the expected value. Furthermore, given the sensitivity of the measurements and possible flaws in the measuring tools (such as internal frequency in the multimeter), it is very much possible that more precise and advanced measuring tools would have yielded better results.

The photoelectric effect has many advanced and practical uses, most importantly that involving LED lights. This lab used LED lights as one of the materials. These are found in televisions and cell phones, and they are much better than traditional light bulbs. Relying on transmitting light particles instead of heating up a filament, LEDs use less energy and lasts exponentially longer than traditional bulbs. They release only portions of energy in photons instead of a traditional stream-line of electrons, and the energy of these photons is represented by KEmax = hf - work function, which, of course, was at the heart of our lab.

=Lab: Width of a Human Hair= 3/1/12 Chris Hallowell, Ryan Listro, Ross Dember, Bret Pontillo

OBJECTIVE: The purpose of this lab is to determine the width of a single human hair. Because of the very small value, we will have to use the same ideas used in our single slit diffraction unit. Instead of finding the width of the slit, we now have to find the width of a human hair.

HYPOTHESIS: Using the ideas of single slit diffraction and the two equations used for constructive and destructive interference, we will be able to find the width of a single human hair. We may also need to use a laser and some paper in order to properly obtain our value.

METHODS/MATERIALS: In order to perform this experiment, we must first set it up using a ring stand, piece of paper, a small white board, a laser, an optics bench and a human hair. The ring stand will hold the laser in the air while we suspend the human hair in the path of the laser beam. We will then draw what we see on the sheet of paper, which is connected to the board on the optics bench. This pattern should resemble something similar to single slit diffraction, which is characterized by a central maximum that is twice as wide and twice as bright as the fringes. While drawing the patterns, make sure to measure the distance between the screen and the hair. After drawings are made for three different distances, perform the same steps for a different color laser. Finally, when all drawings are done and when all distances are measured, you must measure the distance between the fringes of each drawing. This value will be used, along with the distance between the screen and hair, to determine theta. To determine the width of the hair, you must use the equation wsin(theta)=(m+.5)(lambda). Plug in the angle you solved for, the wavelength of the laser light, and 1 for m. After this, you will be able to solve for the width of the hair.

PHOTO OF SET-UP:

DATA: CALCULATIONS:

CONCLUSION: After performing the lab, I can conclude that what I stated in my hypothesis was correct. After using two different colored lasers in our experiment and using the single slit diffraction ideas, we were able to perform several trials for both colors to obtain our values. We decided to move the distance of the screen for each trial in order to obtain widths that we could average together at the end. This provided an opportunity to get a nice sampling of data for both laser colors.

Although the lab seemed to be successful, there was still some difference between the values. We calculated an average of 8.83% difference throughout our lab. This imperfect value could have been caused from a few different sources. First, it was difficult for our drawer to draw the exact edges of each little section of light on the paper. Some of the drawings had blobs that were not exactly perfect and this would have caused some slightly inaccurate values. Another source was when we measured the distances of each quanta. Although we had a ruler, it was still very tough to get the exact distances of the very small spaces on the paper.

This was a very interesting lab to do because it took a concept that we have learned about in class and brought it to the real-world with our hair. It was interesting to see how single slit diffraction could help us out figure out the width of our hair. I feel that in the future, it would be cool to do this lab with other types of hair as well (animals) and compare it to the widths of ours.

=Lab: Atomic Spectra= Group: Ryan Listro, Bret Pontillo, Chris Hallowell, and Ross Dember Due: March 16, 2012

PRE-LAB: > We will use a diffraction grating to observe the lengths at which the emitted wavelengths are located from the different elements. These lengths should correspond with the wavelengths using the equation asin(theta)=mλ. > Hydrogen: 3900 (violet), 4100 (violet), 4350 (indigo), 4850 (teal), 6575 (red) > Helium: 4050 (violet), 4475 (blue), 4700 (teal), 5050 (green), 5875 (yellow), 6675 (red) > Mercury: 4050 (violet), 4350 (violet), 5450 (green), 5750/ 5775 (yellow), 6150 (orange), 6525/ 6725/ 6900 (red) > >
 * 1) The objective is stated in the title. What is your hypothesis?
 * 1) What is the rationale for your hypothesis?
 * 2) We were able to develop this hypothesis based on our past knowledge of diffraction grating and our current knowledge of the atomic spectra. This equation seen in the answer above was from our past unit.
 * 3) How do you think you might test this hypothesis?
 * 4) We think we will test this hypothesis using a similar set-up to our lab from earlier in the year involving diffraction grating, double slit interference, etc. This will include an optics bench, diffraction grating lens, and a meter stick. In addition, for this lab, we will probably have to use some sort of power source that will light up these different elements so we can view their spectrums.
 * 5) Read through the procedure notes. Make any tables in order to organize your data and calculations.
 * 6) What is a continuous spectrum? A discrete spectrum? What type of light source produces each?
 * 7) A continuous spectrum is a spectrum having no lines or bands. It is a range of wavelengths that is uninterrupted. White light and the sun create continuous spectrums. A discrete spectrum is an emission or absorption spectrum for which there is only an integer number of intensities. These can be created from any type of element.
 * 8) Go to [] and record estimated wavelengths and colors for the emission lines for Hydrogen, Helium and Mercury.
 * 1) Go to [] to see images of the emission spectra.

OBJECTIVE: To measure the wavelengths of light emitted from several different atoms with high accuracy, and then construct an electron energy level diagram.

HYPOTHESIS: We will use a diffraction grating to observe the lengths at which the emitted wavelengths are located from the different elements. These lengths should correspond with the wavelengths using the equation asin(theta)=mλ. Our reason for believing this involves the principles of photons and electrons. this suggests that elements will only absorb certain photon wavelengths, which will correspond to electrons jumping up energy levels in an element's orbitals.

METHODS AND MATERIALS: To begin this lab, we must first prepare our lab area by covering all sources of light (i.e. windows, lights). By taking this measure, this will prevent any residual light from interfering with our data, therefore allowing us to only see the light from the emission tubes. After this is done, we must then start our setup for the lab by placing a diffraction grating at one end of an optics bench and a spectral tube power supply at the other end. On top of the power supply, we taped a centered meter stick in order to measure the y-lengths of the diffraction pattern. After this, we can now begin our experiment by placing our first emission tube in the power supply and turning off the lights. One person from the group will look through the diffraction grating while another person will be at the other end of the optics bench. While looking through the diffraction grating, the observer will use a laser pointer to show the locations of the emission wavelengths. The person opposite the observer will read the distances the laser point (or wavelengths from the observer's view) are from the center light. To provide another perspective, the observer and person reading the lengths will switch positions and perform the same task. We will then perform this same experiment for all three emission tubes (hydrogen, helium, mercury) and the incandescent bulb (where we will measure where each individual color ends). After this, we must then determine the lines/mm of the diffraction grating. Our setup will be the same, with the exception of a viewing screen being in place of the power supply. We will shine a laser pointer of known wavelength through the grating and trace the pattern that appears on the screen. Using the equation asin(theta)=mλ, we can determine the diffraction grating.

PHOTO OF SET-UP: DATA:

ANALYSIS:
 * 1) Calculate the wavelengths of hydrogen, helium, and mercury and evaluate your results.
 * 2) Seen in graph above.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">Use these wavelengths of the emitted photons to draw an energy level diagram for each atom. This must include quantum numbers, the transitions, associated energies, and write the color of the observed line next to its transition on your energy level diagram.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif;">Determine the wavelength corresponding to the various points in the spectrum that were located on the continuous spectrum.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif;">You probably couldn’t see the violet lines of mercury. Using the actual values from the Internet (restate source), calculate the expected position of the lines. If possible, go back to the set-up to see if you can find them now that you know where to look. Describe your results.

CALCULATIONS:

<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">DISCUSSION: > If the grating had more lines/ mm than calculated in part 1, the wavelengths would be larger. From the equation asin(theta)=m(lamda), when a (diffraction grating) is increased, wavelength (lamda) increases. This would create worse results because the fringes would be located much farther away from the source than it did in the original experiment. > <span style="font-family: Arial,Helvetica,sans-serif;">asin(theta) = m(lambda) > <span style="font-family: Arial,Helvetica,sans-serif;">2000x10-9*sin(theta) = 1*492.5x10-9 > <span style="font-family: Arial,Helvetica,sans-serif;">theta = 14.26˚ > > <span style="font-family: Arial,Helvetica,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Yellow: 5.61296E-07m to 6.05408E-07m >>> <span style="font-family: Arial,Helvetica,sans-serif;">Orange: 6.05408E-07m to 7.49915E-07m > <span style="font-family: Arial,Helvetica,sans-serif;">These values are close to known values but not exact. They are greater than the actual values. > <span style="font-family: Arial,Helvetica,sans-serif;">The middle of the visible spectrum according to our measured values is around 5.3E-07m.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">If the grating actually had more lines/mm than you calculated in Part I, what effect would that have on the calculated wavelengths? Would the results be better or worse?
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">A diffraction grating with d = 2000 nm is used with a mercury discharge tube. At what angle will the first-order blue-green wavelength of mercury appear? What other orders can be seen, and at what angle will they appear? If the distance between the grating and the screen is 50.0 cm, at what distance from the center will the first-order image for blue wavelength appear? Show your work.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">In the continuous spectrum what is the range of yellow wavelengths? Orange? Do these agree with known values? What is the middle of the visible spectrum according to your measured values of the range of the visible spectrum?

CONCLUSION: Our hypothesis that the lengths correspond with the wavelengths using the equation asin(theta)=mλ was proven correct. We were able to see the visible light spectrum of hydrogen, helium and mercury by looking through the diffraction grating. For hydrogen we were able to see VIolet, blue, turquoise, and red. We were able to measure our results with great precision and get an error of around 5%.

This showed that the equation used asin(theta)=m(wavelength) is accurate in finding the wavelength in the visible light spectrum. There is error within the lab though. Using the laser to point out the distance the visible light was away from 0, the person who was measuring the light adjacent to the ruler could not see where the light was, because only the person who was looking through the diffraction grating could see it. They might not have been pointing the laser exactly at the right position which could have caused error. This could be fixed if there was a larger grating where everyone is able to see closer to the ruler. Although the room was real dark, there were three bulbs on at once with some ambient laptop brightness. If these were cut out, the spectrum might have been more precise unlike what it was (a bit blurry at times with colors other than orange and yellow).

In real life, by knowing the visible light spectrum of elements, one would be able to tell if small amounts of the element are in different things. Energy spectra are also used in astrophysical spectroscopy. Spectroscopy is the study between matter and radiated energy.