Group3_8_ch27-32

Allison Irwin, Eric Solomon, Phil Litmanov, Sam Fihma
flat =Lab Atomic Spectra=


 * Objective:** We will attempt to measure the wavelengths of light emitted from three different elements through this experiment. We will then construct three different electron energy level diagrams from this information.


 * Hypothesis:** We should be able to use a diffraction grating in order to observe the lengths at which the emitted wavelengths from the different elements. These lengths should correspond with the wavelengths using the equation asin(theta)=mλ. These experimental wavelengths should conform with the actual wavelength values. We believe that this is true because of the principles of photons and electrons within a specific element absorbing only discrete photon wavelengths. These absorbed wavelengths should correspond to jumps between energy levels of the electrons within the atom's orbital due to contemporary views of atomic physics.

See Hypothesis See Hypothesis See Materials and Procedure See Data A continuous spectrum is one defined by viewing the emission spectrum of white light. White light emits every single wavelength, so if we were to view the emission spectrum of it, we would see basically a horizontal rainbow. There are an infinite number of wavelengths associated with it. A discrete spectrum, on the other hand, deals with specific, integer values of wavelengths associated with it. This generally is associated with viewing the emission/absorption spectra for a specific element. Measured in nm Hydrogen: 390 (violet), 410 (violet), 435 (indigo), 485 (teal), 657.5 (red) Helium: 405 (violet), 447.5 (blue), 470 (teal), 505 (green), 587.5 (yellow), 667.5 (red) Mercury: 405 (violet), 435 (violet), 545 (green), 575/577.5 (yellow), 615 (orange), 652.5/672.5/690 (red)
 * Prelab:**
 * 1) The objective is stated in the title. What is your hypothesis?
 * 1) What is the rationale for your hypothesis?
 * 1) How do you think you might test this hypothesis?
 * 1) Read through the procedure notes. Make any tables in order to organize your data and calculations.
 * 1) What is a continuous spectrum? A discrete spectrum? What type of light source produces each?
 * 1) Go to [] and record estimated wavelengths and colors for the emission lines for Hydrogen, Helium and Mercury.
 * 1) Go to [|http://astro.u-strasbg.fr/~koppen/discharge/] to see images of the emission spectra.


 * Materials and Procedure:** First, we must prep for this experiment before actually beginning. We must cover all of the windows and other light sources in the lab room so that there will be no residual light. All that we can see must be the light from the emission tubes so that we will only be measuring the emission wavelengths of the desired sources. After darkening the room completely, we must keep the lights on for a short time more. We must set up an optics bench with known length measurements. We must place the diffraction grating on the bench a known distance from the spectral tube power supply. Now, we must place in the first emission tube and darken the room. Then, we will look through the grating. A meter stick will be set up at the same point as the power supply. Another person will stand behind the power supply. The observer will shine a laser pointer at the meter stick to determine the length that the emission wavelengths are from the center. We will continue this for all three emission tubes and then the incandescent bulb (where we will measure where each individual color begins and ends). Then, after this experiment, we must measure the lines/mm of the diffraction grating. We will use the same equation asin(theta)=mλ as in the last part of the lab. We will set up the experiment in a similar manner with the exception of a viewing screen in place of the power supply. We will measure the space between the diffraction patterns and from this, determine the lines/mm of the diffraction grating.



http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/atspect2.html (amongst other sources) **Fihma sucks**
 * Data:**

__Wavelength Experiment__ __Diffraction Grating Experiment__
 * ||  |||||||| Position (cm) ||   ||   ||   ||   ||   ||
 * Element || Color || Trial #1 || Trial #2 || Trial #3 || Average || Distance (cm) || a || Wavelength (m) || Theo Wavelength || Percent Error ||
 * Hydrogen || Red || 47.4 || 47.2 || 47.5 || 47.4 || 121 || 0.0162 || 6.342E-07 || 6.575E-07 || 3.55 ||
 * ^  || Turquoise || 34.0 || 33.5 || 34.0 || 33.8 || 121 || 0.0162 || 4.530E-07 || 4.850E-07 || 6.60 ||
 * ^  || Blue || 30.3 || 29.5 || 29.5 || 29.8 || 121 || 0.0162 || 3.985E-07 || 4.350E-07 || 8.38 ||
 * Mercury || Red #1 || 50.0 || 49.9 || 50.2 || 50.0 || 121 || 0.0162 || 6.699E-07 || 7.200E-07 || 6.96 ||
 * ^  || Red #2 || 49.3 || 49.4 || 49.3 || 49.3 || 121 || 0.0162 || 6.605E-07 || 6.840E-07 || 3.44 ||
 * ^  || Red #3 || 46.0 || 46.0 || 45.8 || 45.9 || 121 || 0.0162 || 6.150E-07 || 6.550E-07 || 6.11 ||
 * ^  || Orange #1 || 43.7 || 44.4 || 44.0 || 44.0 || 121 || 0.0162 || 5.895E-07 || 5.790E-07 || 1.82 ||
 * ^  || Orange #2 || 42.5 || 43.4 || 42.9 || 42.9 || 121 || 0.0162 || 5.748E-07 || 5.770E-07 || 0.38 ||
 * ^  || Orange #3 || 41.6 || 42.3 || 41.9 || 41.9 || 121 || 0.0162 || 5.614E-07 || 5.460E-07 || 2.82 ||
 * ^  || Blue/Turquoise || 33.6 || 33.0 || 33.2 || 33.3 || 121 || 0.0162 || 4.454E-07 || 4.910E-07 || 9.29 ||
 * ^  || Blue || 30.9 || 31.0 || 31.3 || 31.1 || 121 || 0.0162 || 4.159E-07 || 4.350E-07 || 4.38 ||
 * ^  || Purple #1 || 28.7 || 28.5 || 28.2 || 28.5 || 121 || 0.0162 || 3.811E-07 || 4.070E-07 || 6.36 ||
 * ^  || Purple #2 || 27.0 || 27.4 || 27.2 || 27.2 || 121 || 0.0162 || 3.642E-07 || 4.040E-07 || 9.86 ||
 * Helium || Red #1 || 49.9 || 50.1 || 50.0 || 50.0 || 121 || 0.0162 || 6.694E-07 || 6.680E-07 || 0.21 ||
 * ^  || Red #2 || 47.7 || 47.9 || 47.8 || 47.8 || 121 || 0.0162 || 6.400E-07 || 5.870E-07 || 9.02 ||
 * ^  || Orange/Yellow || 41.5 || 41.3 || 41.3 || 41.4 || 121 || 0.0162 || 5.538E-07 || 5.040E-07 || 9.89 ||
 * ^  || Green || 34.6 || 35.0 || 34.8 || 34.8 || 121 || 0.0162 || 4.659E-07 || 4.710E-07 || 1.08 ||
 * ^  || Green/Blue || 33.8 || 34.2 || 34.0 || 34.0 || 121 || 0.0162 || 4.552E-07 || 4.470E-07 || 1.84 ||
 * ^  || Blue #1 || 32.3 || 32.8 || 32.5 || 32.5 || 121 || 0.0162 || 4.356E-07 || 4.380E-07 || 0.55 ||
 * ^  || Violet || 30.6 || 30.9 || 30.8 || 30.8 || 121 || 0.0162 || 4.119E-07 || 4.030E-07 || 2.21 ||
 * Color || Distance (m) || Wavelength || m || Y (m) || Tangent || a ||
 * Red || 0.15 || 0.00065 || 1 || 0.0059 || 0.039 || 0.0165 ||
 * ^  ||^   ||^   ||^   || 0.0060 || 0.040 || 0.0163 ||
 * ^  || 0.2 ||^   || 1 || 0.0081 || 0.041 || 0.0160 ||
 * ^  ||^   || 0.0081 ||^   ||^   || 0.040 || 0.0161 ||
 * ||  ||   ||   ||   || Average a - || 0.0162 ||

__Rainbow Experiment__
 * || Position ||  ||   ||   ||   ||   ||
 * Color || Trial #1 || Trial #2 || Average || Distance || a || Wavelength ||
 * Red || 49 || 49.6 || 49.3 || 106.5 || 0.0162 || 7.49915E-07 ||
 * Orange || 39.9 || 39.7 || 39.8 || 106.5 || 0.0162 || 6.05408E-07 ||
 * Yellow || 36.6 || 37.2 || 36.9 || 106.5 || 0.0162 || 5.61296E-07 ||
 * Green || 32.9 || 31.7 || 32.3 || 106.5 || 0.0162 || 4.91324E-07 ||
 * Blue || 26.8 || 25.5 || 26.15 || 106.5 || 0.0162 || 3.97775E-07 ||
 * Purple || 22.6 || 23.7 || 23.15 || 106.5 || 0.0162 || 3.52141E-07 ||


 * Calculations:**



**Analysis:**
 * 1) Calculate the wavelengths of hydrogen, helium, and mercury and evaluate your results.
 * 2) 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.
 * 3) Determine the wavelength corresponding to the various points in the spectrum that were located on the continuous spectrum.
 * 4) 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.

**Discussion:**
 * 1) 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?
 * 2) If we used a grating that had more lines/mm, a would have been smaller as a result. By decreasing a, we also decrease the calculated wavelength based on the equation a*sin(theta) = m(lambda). Our results would be worse because as it is most of our calculated wavelengths are already lower than the theoretical ones.
 * 3) 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.
 * 4) asin(theta) = m(lambda)
 * 5) 2000x10-9*sin(theta) = 1*492.5x10-9
 * 6) theta = 14.26 degrees
 * 7) 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?
 * 8) Yellow -- 5.61296E-07m to 6.05408E-07m
 * 9) Orange -- 6.05408E-07m to 7.49915E-07m
 * 10) These values are close to known values but not exact. They are greater than the actual values.
 * 11) <span style="font-family: Arial,Helvetica,sans-serif;">The middle of the visible spectrum according to our measured values is around 5.3E-07m.

When we began this experiment, we asserted that through the usage of a few simple measuring apparatuses (albeit with the exception of the actual element tubes and the power supply), we could actually visualize and accurately observe the visible light atomic emission spectra for various elements, namely hydrogen, helium, and mercury. Much to my pleasant surprise, this actually worked. I had not expected to achieve such accurate and precise results with the relatively low-tech (compared to the great science labs and measuring tools used for professional experiments) equipment that we were given. We were able to calculate the emission spectra of the lines with high enough intensity to within a few percentage points of their actual values. This error derived from a number of sources, but mainly, as mentioned previously, the imprecise measuring tools that we were supplied with. We were given a ruler that had to be placed manually atop the power supply so that the power supply would hypothetically bisect the ruler perfectly. We were given a laser pointer to be shone upon the ruler with, needless to say, a lack of surgical precision. And lastly amongst the important sources of imprecise measurement, we were shown spectra containing countless colored lines of varying intensities. It was up to our high-school level discretion to pick which lines were worth measuring and which were to be considered insignificant. But despite all of this adversity, our results ranged from effectively no error according to our theoretical values up to a still viable less than 10%. This experiment fits within the realm of contemporary views of atomic physics. Essentially, what we accomplished through this lab was further proof of the plausibility of the modern views on the atom. According to these theories, specific atoms can absorb and emit discrete wavelengths of photons. The energy provided by these photons will allow for the electrons within the atom to jump up to energy levels. And when the electrons fall back down, they emit photons of certain energies corresponding to wavelengths of light. The wavelengths of light that are visible make up these visible light atomic emission spectra. The emission wavelengths have been experimented and theorized, and our results depicting very similar wavelengths for each of these emissions is only more backing of these hypotheses.
 * Conclusion:**

P.S. Eric sucks

= = =Lab: Width of Human Hair=


 * Objective:** We will attempt, through this experiment, to find the width of a single human hair. This will basically react as would an example of single-slit diffraction. In such an example, we would be able to find the width of the slit. And in this case, the slit would be the width of the hair.


 * Hypothesis:** Using a laser and our knowledge of diffraction and interference, we can figure out the width of a single human hair. By treating this experiment as one would an example of single-slit diffraction, we can apply all of the same data and equations to find the width of the hair.


 * Materials and Procedure:** In this lab, we will require only a few materials. We need, first, a human hair (or an equally thin substitute wire). Next, we need a hollowed out bracket on which to mount the hair. We will mount the hair in the direct center of this bracket in a direct vertical fashion. We require a laser of known wavelength as well. We will place this laser behind the hair and shine it directly onto the hair, hitting it at an angle exactly perpendicular to the surface of the hair. Also, we will need a blank screen. We will place the blank screen some known distance from the hair. We will then be able to see the projection of the laser onto the paper. It will appear as a diffraction pattern. We will require some sort of measuring apparatus (ruler, meter stick, etc.). We will measure the distance of the outer diffraction patterns from the central pattern as per norm.


 * Data:**

Our hypothesis was correct, like usual. We shone a laser at a strand of human hair and by doing so, we created a single slit diffraction experiment as evidenced by our patterns on the white screen. We measured how far apart each fringe on our pattern was and the distance between the screen and hair. Using these two values, we calculated x, the width of the slit. Because one result would not suffice, we varied the distance between the hair and screen, getting multiple values for our width of the hair. We averaged all of these experimental values together and got an answer of 0.061 mm. The great thing about our experiment was how consistent our results were and how the average was just in line with the normal range. We found percent difference of each of our trials, comparing the experimental value to the average. Our highest percent difference was ten, showing that our results were relatively close together. Also, we found the actual range of human hair to be in between 18 and 180 micrometers and our answer was 61! It seems like we did a good job, but of course there was some error in this lab. The biggest source of error stemmed from measuring the fringes. Putting a dot on exactly the center of each fringe was tough as was measuring the exact value for the distance between. Because of these two things, our answers were not as consistent as we would have liked. Nevertheless, we found a great value for the width of hair and performed our experiment successfully!
 * Calculations:**
 * Conclusion:**

=Lab: Diffraction and Interference=


 * 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, you will compare the diffraction and interference patterns formed by different wavelengths of laser light and different slit widths/spacing.


 * Hypothesis:** What we are setting out to prove here is the equation<span style="font-family: Arial,Helvetica,sans-serif;"> λ=(d*sinθ)/m (the d is an interchangeable variable representing distance between slits in double slit, width of slit in single slit, and distance between slits in diffraction grating. Through this experiment, we will change wavelengths and possibly length to screen if we need to. This will change the value of d/w/a. Through our experimental knowledge of d/w/a,<span style="font-family: Arial,Helvetica,sans-serif;">θ, and m, we should be able to figure out an experimental value of λ equivalent to the theoretical value. We predict that increasing d/w/a will increase our experimental value of λ through the application of the above equation.


 * Procedure:**

In this lab we needed an optics bench to secure the laser, screen, single slit disk, double slit disc, and diffraction grating. We used the ruler on the optics bench to measure the location of each of the other materials. We needed the three different discs in order to compare the patterns produced by each. For the lasers, we used three different colors, red, violet, and green. We used clamps to secure the lasers so that they would be pointed at the screen. We needed three to compare the tests using different wavelengths. We also required white paper, a pencil, and a ruler to trace and measure the patterns produced by the discs. We used the optics bench to secure the other materials. We placed the laser at one end of the optics bench and the screen at the opposite side. In between we placed the disc/diffraction grating. This setup can be seen in the above image and photograph. We first started with the single slit diffraction grating. We set the screen at a known location and pointed the green laser through the diffraction disc. We used the pencil and paper to trace the pattern that was produced on the screen. We then used the ruler to measure this pattern (find the experimental y values). We then repeated this process with the other two lasers (red and violet). We then switched to the double slit interference disc and then again with the diffraction grating. We continued to test all three lasers.
 * Materials:**
 * Methods:**

Additional data collection provided by: Group 1 (Ross Dember, Bret Pontillo, Chris Hallowell, and Ryan Listro)
 * Data:**


 * Sketches:**

__Diffraction Grating__

















__Single Slit__







__Double Slit__













Patterns that we observed: __Single Slit Diffraction-__
 * Analysis:**
 * 1) As w decreased, y increased (the fringe spread out, so we had fewer data points because we could see less nodes).
 * Ex:[[image:Screen_shot_2012-02-11_at_7.44.39_AM.png]]
 * 1) As wavelength increased, y increased.
 * Ex:[[image:Screen_shot_2012-02-11_at_7.50.02_AM.png]]

__Double Slit Interference-__ __Diffraction Grating-__
 * 1) As d decreased, y increased (the fringe spread out, so we had fewer data points, because we could see less nodes).
 * Ex: [[image:Screen_shot_2012-02-11_at_7.58.39_AM.png]]
 * 1) As wavelength increased, y increased.
 * Ex: (this requires 2 examples because the variable L was not consistent throughout)
 * [[image:Screen_shot_2012-02-11_at_7.55.26_AM.png]]
 * 1) As a decreased (more slits), y increased (the fringe became closer together, so we had more data points, because we could see more nodes).
 * Ex: [[image:Screen_shot_2012-02-11_at_8.05.02_AM.png]]


 * Sample Calculations:**


 * Discussion Questions:**

1. Qualitatively describe and compare the patterns produced by:
 * 1) The single slit
 * 2) Single slit diffraction produced lines of varying length on the screen.
 * 3) The double slit
 * 4) Double slit interference produced lines of varying length on the screen and dots or points within those lines of varying distance from each other.
 * 5) The diffraction grating
 * 6) Diffraction grating produced precise points or dots on the screen,

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:**

Having analyzed our results through both the equation <span style="font-family: Arial,Helvetica,sans-serif;">λ=(d*sinθ)/m as well as the equation y=(mλL)/d, we have proven our hypothesis. First of all, we have proven that when the value of d/w/a increases, the wavelength will increase. Our results have backed this up. We have also shown that the changes in the y value from the latter equation corresponded with both our theoretical and experimental data. This is further validation of our experiment. The y values showed either a general trend of increasing or decreasing depending upon whether the slit width/amount of lines per cm/slit length/wavelength increased or decreased. I would love to say that this lab had very little error behind it. Unfortunately, I can not say this. The bulk of this error came mostly from inexactitude. Our theoretical values for wavelength were so miniscule that even the tiniest of changes in any of the other variables could have been extremely volatile. The actual measurements were hand-drawn, and due to the fact that light can't shine through hands (which were attempting to trace certain points of interference/diffraction), much of the values were rough estimates compared to the relatively small spacing in between these points. This was a major hindrance in the process of analysis and calculation. And it initially led to a very high percentage of error, but once we figured out what was wrong (and admittedly re-did some of the tests), we had obtained a relatively good percentage of error hovering around the 0-15% mark. One important quality of light that this experiment has shown is its property as a wave and not explicitly as a particle. What makes up the patterns of interference? Well of course these patterns are composed of the crests and troughs of light interacting with one another. We have seen why certain scenarios of light interacting with certain surfaces leads it to act the way that it does. Also, this has shown how light can be spread and manipulated. Each differing value for d/w/a had affected the incoming light differently and had caused the ensuing pattern to look as it did. Otherwise, the pattern would always show the same at the same screen length no matter what was placed in the way of the light. However, Young (from the titular Young's Experiment) had correctly predicted that light waves would maneuver around and through slits that may be in the path of travel. = Lab: Photoelectric Effect and Planck's Constant =
 * Objective:** Determine Planck's constant using stopping potentials.

If we calculate the kinetic energy using electron charge and voltage, while also calculating the frequency of each diode, we should get a linear fit for a graph with an equation that looks like the one below. H is planck's constant and should be close to 6.626x10^34. The "trident" is the work function value for the specific materials we are using.
 * Hypothesis:**

In this lab we used four different LED's. We needed four (red, yellow, blue, and blue-green) in order to test different wavelengths. We used a variable power supply because we needed to change the voltage of the circuit. The power supply was easier and more accurate than any other power supply (ie. batteries, genecon, etc.) because we were measuring the current in milliamps. We also used 2 digital multimeters to measure the current (ammeter) and voltage (voltmeter). Finally, we used wires to connect the circuit because they have no resistance.
 * Procedure:**
 * Materials:**

First we set up the above circuit using the wires, power supply, ammeter, voltmeter, and red LED. We supply the smallest amount of voltage to the circuit that would allow the diode to light. We used the ammeter to insure that there was current in the circuit. We used the voltmeter to measure the voltage. We then shut the power supply off and repeated this process for 4 trials. We then repeated this process with the other three LED's (yellow, blue, blue-green). We used the measured voltage to calculate the maximum KE. We used the known wavelength of the diodes to calculate the frequency. We then made a graph of KE vs. F to determine Planck's constant.
 * Methods:**


 * Data:**


 * Colors || Average KE (J) || Velocity (m/s) ||
 * Red || 2.30E-19 || 7.11E05 ||
 * Yellow || 2.48E-19 || 7.38E05 ||
 * Blue || 3.70E-19 || 9.01E05 ||
 * Blue-Green || 3.396E-19 || 8.63E05 ||




 * Analysis: **


 * Sample Calculations:**


 * Discussion Questions:**


 * 1) Plot the graph of Energy vs. Frequency
 * 2) Interpret the best-fit line of the graph.
 * 3) In order to not repeat ourselves, this is thoroughly explained in our conclusion.
 * 4) Calculate a percent error using the accepted value.
 * 5) Calculated above.
 * 6) Which LED has the highest work function? Explain what this means.
 * 7) None. The work function is constant in our graph so none of the LEDs have the highest work function.
 * 8) Add columns to your table
 * 9) Calculate the final velocity of an electron as it travels across the LED point gap.
 * 10) Calculated Above (below colored data table is a non-colored extension to the table)
 * 11) How does this velocity change with color? Explain.
 * 12) We used the equation KE = (1/2)mv^2The velocity increases as the wavelength decreases. From red to blue, the velocity steadily increases by a square root proportion. As shown in the equations and table above, the KE increases as wavelength decreases. Using simple mathematics, we can derive that this greater KE produces a greater velocity because of the constant value for mass.
 * 13) If the point gap approximates 1.0 mm,
 * 14) calculate the acceleration of the electron and the time to cross the gap.
 * 15) v(i)=0 for all and v(f) was calculated above)
 * 16) v(f)^2=v(i)^2+2ad
 * 17) Red: a=4.21E05 m/s^2
 * 18) Yellow: a=4.29E05 m/s^2
 * 19) Blue: a=4.74E05 m/s^2
 * 20) Blue-Green: a=4.64E05 m/s^2
 * 21) Δ d=v(i)t+(1/2)at^2
 * 22) Red: t=6.89E-05 s
 * 23) Yellow: t=6.83E-05 s
 * 24) Blue: t=6.50E-05 s
 * 25) Blue-Green: t=6.57E-05 s
 * 26) what vector field supplies the accelerating force?
 * 27) Electromagnetic Force.

After performing this experiment, we can conclude that our hypothesis was correct. We first found the kinetic energy by multiplying the electron charge with the voltage (described in our method) and then found the frequency by dividing velocity by wavelength. This allowed us to graph the kinetic energy vs. the frequency of LEDs. According to our hypothesis, the equation it should follow is shown below. Kinetic energy is on the y axis, while the frequency is on the x axis. The slope of the linear fit is Planck's constant. We found our experimental value of this number to be 8.96x10^34 compared to the actual value of 6.626x10^34. This turned out to be a 35% error. The trident in the equation shown below is the work function of the diode. We got a value of 1.99x10^-19 and do not have a theoretical value to compare it to. This work function is the energy subtracted from the energy when multiplying frequency and planck's constant and it differs for every material. To define it, work energy is the minimum amount of energy needed to remove an electron from a particular solid to a point immediately outside of this solid. Since it is being subtracted, the y-intercept has a negative value. When there is just barely any movement inside the diode (KE is basically zero), there is the threshold frequency, which is the minimum frequency of radiation that will still produce a photoelectric effect. We got a percent error of 35%, which for this lab is not that terrible, but it is still a bit of error. The error probably came from calculating kinetic energy. The reason it was not from frequency is because we used set values to calculate it. The speed of light and the wavelength of each LED might be a bit different from the numbers we used, but the error was probably miniscule. Still, one source of error could have been from the velocity not being 3x10^8, because that is the value in a vacuum and we did not perform this experiment in one. Kinetic energy could have been off because of the way we calculated voltage. It was tough to determine just exactly when the light turned on. As a result, our voltage readings could have been a little off. Also, we took the average kinetic energies to use as points in our graph. One voltage reading that was not as accurate as another could have changed the average kinetic energy for a particular color. All of these errors contributed to our 35% error, but overall we proved the equation below to hold true.
 * Conclusion:**