Phenomena of the Photoelectric Effect - Lab Report Example

Photoelectric Effect Background Under right conditions, light can be used to free electrons pushing them from surface of the solid. This phenomenon is referred to as photoelectric effect or photoemission or photoelectric emission. A material exhibiting the photoelectric effect is said to be photoemissive, and the electros ejected are referred to as photoelectrons. These electrons are not distinguishable from other electrons since all electrons are identical and have same mass, magnetic moment, charge and spin. The photoelectric phenomena was first demonstrated by Heinrich Hertz. Hertz generated a spark between two metal spheres in a transmitter, which induced a similar spark between the first and second metal spheres in a receiver. However, it proved difficult working with a spark-gap generator. To further improve on this, Philipp Lenard, Hertz’s assistant, used metal surfaces that had been cleaned and held under vacuum condition to ensure the photoelectric effect is studied on a metal alone but not affected by surface oxidation or contamination. In this experiment, an evacuated glass tube was used to house the metal sample. The second metal plate was mounted at the other end. The tube was constrained or positioned in a way that light could only shine on the metal plate made out of a photoemissive material. This tube was called a photocell. The photocell was connected to the circuit with a micrometer, voltmeter, and variable power supply. The photoemissive surface was then illuminated with light of differing intensities and frequencies. Electrons were knocked free from a photoemissive plate and which gave some slight positive charge. Connecting the second plate to the first plate by wiring the circuit made it positive too. This attracted free floating photoelectrons via a vacuum where the electrons landed and bounced back to the initial plate that they had started. This experiment did not create photoelectrons out of the light. It instead it used light energy to push electrons that were already around the circuit. This means generated a very small photoelectric current, but the microammeter could measure it. The microammeter could measure the rate at which electrons were ejected from the photoemissve material surface. The power supply was wired into the circuit with the negative end of the power supply connected to the plate that was not illuminated. This set up the potential difference that could push photoelectrons into the photoemissive metal surface. When power supply was set to a very low voltage, it trapped the electrons with the least energy. This reduced current via the micrometer. Increasing the voltage drove more energy photoelectrons back until none of these electrons could leave the surface if the metal with the microammeter reading zero. This potential at which this happened was referred to as the stopping potential. Stopping potential measures the maximum kinetic energy possessed by the ejected phoelectrons due to the photoelectric effect. In this experiment, Lenard demonstrated that the maximum kinetic energy associated with the photoelectrons is not affected by the intensity of light incident to the metal surface. Lenard found that photoelectrons emitted from exposure to bright light had equal energy to those photoelectrons emitted from exposure to dim light of similar frequency. However, as provided by the law of conservation of energy, more photoelectrons were emitted by a bright light source compared with the dim source. In later experiments, Robert Millikan demonstrated that light with frequencies much below the threshold frequency (below the cutoff value) would not emit electrons from a metal surface irrespective of whether the source was dim or bright. In this experiment the focus was on photoelectric effect. Objectives of the experiment The objectives of the experiment involved to study the effect of intensity of light on photoelectric experiment, to estimate the plank’s constant, through the simulation, to explain how the photoelectric effect experiment works and why a photon model of light is necessary to explain the results, and to calculate the wavelength of light, the work function of the metal or the stopping potential, if given the other two. Procedure Starting with the plate made up of sodium all the parameters were kept constant except the colour (wavelength). The light source was turned on at every low intensity and battery set to zero volts. The wavelength of light source was varied from Infra Red to Ultra Violet until electrons just begin to be ejected from the sodium surface. The instructions were then repeated to allow light to shine on the metal for a relatively longer time before varying the wavelength. After this, the instruction was repeated again but with varying the intensity of light. The wavelength needed in starting the flow of current when the voltage of the battery was set to zero and an intensity of five percent was recorded. The battery was then adjusted to a voltage of 8.00volts and shined a 100nm bright light of 100% intensity on the surface of sodium. The battery voltage was reduced to about -8.00V. The collected results were recorded in tables under the result section of this paper. Results Table 1: Required wavelength in starting the flow of current (5% intensity) Surface Wavelength Sodium 491 Zinc 270 Copper 248 Platinum 185 Calcium 397 Element x 312 Table 2: Sodium Volts Wavelength Frequency(Hz) Photon energy Work Function Kray 0 540 5.57x 3.69 2.31 0 -0.2 497 6.03x 4.01 2.30 -0.2 -0.4 458 6.55x 4.34 2.31 -0.6 -0.6 428 7.0x 4.64 2.31 -0.6 -0.8 397 7.55x 5.01 2.30 -0.8 Table 3: Calcium Volts Wavelength Frequency(Hz) Photon energy Work Function Kray 0 427 7.02x 4.63 2.0 0 -0.2 400 7.5x 4.97 2.9 -0.2 -0.4 375 8.0x 5.30 2.9 -0.6 -0.6 353 8.49x 5.63 2.9 -0.6 -0.8 333 9.01x 5.97 2.9 -0.8 Calculations The maximum kinetic energy for sodium was given as; KEmax= 1.3 x 10 The maximum kinetic energy for calcium was given as; Calcium = 3.2 x 10. The discrepancy percentage between the obtained and the real value was given by; F= 1.5 x 1015, electron energy was 4eV Therefore 4eV = h (1.5 x 1015) + Wo In the case of f = 3.0 x 10 15 Hz and electron energy equal 10eV, 10eV = h (3.0 x 10 15) + Wo Subtracting the two equations we get (6.4 x 10-34-1.5 x 1015) h = (|6.626-6.4|x 10 -34) / (6.626 x 10-34) = 3.41% In this case, the percentage discrepancy would be 6.626 x 10-34 Discussion According to the collected results the corresponding frequency was 7.59 x 10 14 and 8.11 x 10 14 Hz. This was referred to as the threshold frequency since it was the minimum frequency required for the photoelectric to take place. After this, the light was allowed to shine for a lengthy duration of time before varying the wavelength. The wavelength was found to be 200nm. The more the light shines on a metal, the more the photons to provide energy to the metal electron (Willett, 2004). In this case, when the wavelength for the light source shortened the speed of the electron increased when the high energy is transferred towards the electrons. The study also showed that platinum was the least element in terms of the optical sensitivity (Greiner, 2001). Platinum is followed by copper and zinc in the optical sensitivity ladder. This means that element x could be sodium or calcium. It is assured that element X is a material whose work functions in between zinc, calcium, magnesium, and gold. The study showed that photoemission is depended on the frequency or wavelength of the source of light source such that a short wavelength will lead to high electron energy emitted using the frequency ,considered being different for various materials (Willett, 2004). Additionally, the study noted that the intensity increase slightly increased the required wavelength for the emission of photo electricity hence increasing the circuit current (DuBridge, 2008). The stopping voltage is not depended on the light incident intensity. The estimated value for the planks constant was 6.1 x 10-34Js. This value is smaller than the real value. The simulation of the experiment provided accuracy through the provision and simulation of the vacuum and giving the electron movement view on two metal surfaces (Hughes and Alvin, 2006). Conclusion The objectives that were set for this study were realized. The obtained values were slightly different from the theoretical values because of the experimental errors. Some of the experimental errors were due to parallax, wrong calculation, faultiness of the apparatus, and air resistance (Leigh, 2012). The experimental errors can be corrected by having the experiment done in a room with vacuum conditions, performing the experiment three times and obtain the average in order to avoid parallax, and checking the apparatus before the experiment to ascertain their accuracy. References Leigh, P., 2012. Photoelectricity. Cambridge: Cambridge University. DuBridge, A., 2008. New Theories of the photoelectric effect. New York: Hemann & Cie. Willett, E., 2004. The Basics Quantum Physics: Understanding photoelectric effect and line spectra. New York: The Rosen publishing group. Greiner, W., 2001. Quantum mechanics: An introduction. Oxford: Oxford University press. Hughes, L., and Alvin, L., 2006. Photoelectric: My phenomena. New York: McGraw Hill Book. Read More