Quantum and Thermochemical Structure - Assignment Example

?Laboratory Photoelectric Effect The obtained value for the work function (k1) of Cesium was 3.3448 x 10-19 Joules which matches the literature equivalent of 3.4286 x 10-19 Joules. The k2 constant calculated having a value of 8.3632 x 10 -34 J-s, however, was not as close to the expected Planck’s constant of 6.626 x 10-34. Introduction: The emission of electrons from metals irradiated by light was first observed by Becquerel in 1839. Under a classical model of light, one would expect the energy of the ejected electrons to be related to the intensity of the light waves used, and also that light waves of any frequency would be effective in ejecting electrons. Because of the difficulty of maintaining clean metal surfaces under vacuum, quantitative measurements of the photoelectric effect could not be made for many decades. However, as technology improved, it became evident that the energy of ejected electrons was not related to the intensity of the light waves used, and also that below a certain light frequency - for a given material - no electrons at all could be ejected. Eventually it became possible to determine the relationship between the kinetic energy of the ejected electrons and the frequency of light used to eject them, and this was one of the major factors leading to the development of the quantum model. The kinetic energy of photoelectrons (E) can be measured by determining the voltage required to just stop the ejection of electrons (V) and multiplying this by the charge on an electron (e). Equation 1: V (J C–1) x e (1.602 x 10–19 C) = E (J) Experimentally, the dependence of E on frequency turned out to be: Equation 2: E (J) + k1 (J) = k2 (Js) x ? (s–1) Where k1 was different for every metal and k2 was exactly the same for every metal. What’s more, k2 was exactly the same as a ‘fudge factor’ that had been introduced into a theory developed a few years earlier to explain a completely different phenomenon. In this experiment you will carry out solo measurements to determine k1 and k2. Unlike early 20th century researchers, you will not need to spend several years constructing your apparatus from scratch, but will use a demonstration apparatus designed to measure the stopping voltage of electrons ejected from Cs3Sb in a vacuum. Experimental: The EP-05 photoelectric effect apparatus was used to measure the stopping voltage of light at 8 different wavelengths. A modified spectrometer was used t o provide UV-visible light. The wavelengths tested were 400 nm, 425 nm, 450 nm, 475 nm, 500 nm, 525 nm, 550 nm, and 575 nm. The photoelectric apparatus was set up such that the aperture in front of the photodiode was positioned near the light source. The dials with labels “zero” and “voltage” was set to minimum before the shutter was closed. The plotting was initiated using the Lab View window. The voltage dial was set to maximum while the other dial was turned until nanoampere readings reached zero. The voltage dial was set back to minimum before the shutter was opened to increase the nanoampere reading to 10. The voltage dial was maximized once again to recheck that the “zero” dial was adjusted properly. Once everything was set, the stopping voltage was minimized and the plotting of nanoamperes versus stopping voltage was reset and started at the Lab View window. The output current in nanoamperes were determined by slowly turning the voltage dial. The measured current was recorded and then plotted according to its stopping voltage reading. The measurement is ended when the critical value for stopping voltage where there is minimal change in nanoamperes with respect to voltage is achieved. The whole procedure was done for each of the 8 chosen wavelengths. Results: The experiment was done properly and all the needed data were acquired. The numerical values obtained from the use of the apparatus can be found at the attached document. The plot of the graph and the summary of the derived values are the following: Figure1. Compiled plots for output current versus stopping voltage of the eight wavelengths. Table 1. The estimated stopping voltage based on the plot and the corresponding Energy and frequency calculated for each wavelength. Wavelength (nm) Stopping Voltage (V) Energy (Joules) Frequency (s-1) 400 1.96 3.14026591E-19 7.500000000E+14 425 1.45 2.32315591E-19 7.058823529E+14 450 1.35 2.16293826E-19 6.666666667E+14 475 1.23 1.97067708E-19 6.315789474E+14 500 1.07 1.71432884E-19 6.000000000E+14 525 0.88 1.40991531E-19 5.714285714E+14 550 0.73 1.16958884E-19 5.454545455E+14 575 0.69 1.10550178E-19 5.217391304E+14 Discussion: The stopping voltage were estimated based on the graphs per wavelength by picking the voltage at which the output current started to remain constant as voltage is increased. Based on equation 1, the constant e with the value of 1.602 x 10-19 Coulombs was multiplied to the voltage value to get the Energy equivalent in Joules. The frequency of each wavelength was then computed by dividing the wavelength in meter from the speed of light of 3 x 108 m/s. Rearranging equation 2 would result to a linear equation where energy would be y and frequency would be x with k2 as slope and -k1 as y-intercept. Because of this, the energy calculated was plotted against respective frequency. Linear regression was done which resulted to a fit with an R2 equal to 0.9632. The constant k1 , technically known as the work function, can be computed as the negative of the y-intercept of the linear regression of the obtained values. It is different for each metal making it useful in the identification of metals. It represents the amount of energy required to eject electron from a surface. For example, the work function of Cesium is smaller than that of Gold since it requires less energy to eject electrons as a cause of its high reactivity (chemicool.com, 2012). The obtained value of 3.3448 x 10-19 Joules is a very close match to the literature value of 2.14 Volts (environmentalchemistry.com, 2012) equivalent to 3.4286 x 10-19 Joules.Any difference can be attributed to the estimation of the stopping voltage. Improper use and calibration of the equipment use could also produce erroneous data. Unlike the work function, the k2 value obtained from the slope of the linear equation is not as close a match to the Planck’s constant. The value was 8.3632 x 10-34 compared to the target of 6.626 x 10-34. The estimation of the stopping voltage, improper use and calibration of apparatus and human error are also possible sources of error for k2. ______________________________ References: 1 www.environmentalchemistry.com, 2012, 2 http://www.chemicool.com/elements/cesium.html, (2012) 3 Tipler, Llewellyn, Modern Physics, (Tipler & Llewellyn, 4th ed.) Chapter 3, pp. 141–147. Read More