Determine Planck constant using the photoelectric effect.
- 1. 1 DETERMINE PLANCK CONSTANT USING PHOTOELECTRIC EFFECT . INTRODUCTION : In 1887, Hertz was the first to discover that a metallic surface, when illuminated by light of sufficient frequency, may emit electricity. This ‘photoelectric effect’ was unexplained until Einstein connected this experimental curiosity with Planck’s idea that radiation comes in small packets, or quanta. He proposed that the energy of the ejected electrons is proportional to the energy of the incident light with a constant offset that is unique to the metal, referred to as the work function. This phenomenon was a crucial precursor to the formulation of quantum mechanics as it was one of the first to show the wave-particle duality of light. We will examine this effect, test the hypothesized linear relation, and extract values for Planck’s constant and the effective work function. DISCUSSION OF APPARATUS : o Welch photoelectric tube apparatus o filters with known cut-off frequencies o voltmeter o incandescent light source o galvanometer o power supply o 6 leads
- 2. 2 THEORY AND BACKGROUND OF EXPERIMENT : An electron in a metal can be modelled as a particle in an average potential well due to the net attraction and repulsion of protons and electrons. The minimum depth that an electron is located in the potential well is called the work function of the metal, Φ . In other words, it is a measure of the amount of work that must be done on the electrons (located in the well) to make it free from the metal. Since different metal atoms have different number of protons, it is reasonable to assume that the work function (Φ) depends on the metal. When light strikes a metallic surface, electrons are emitted from the surface. This effect is called the photoelectric effect. The emitted electrons, called photoelectrons, have varying kinetic energies that are primarily dependent upon the frequency of the light that strikes the surface. A phototube consists of two electrodes in an evacuated glass tube. One electrode has a large photosensitive surface and is called the cathode or emitter. The other electrode is in the form of a wire and is the anode or the collector. In normal operation the anode is held at a positive potential with respect to the cathode. When the cathode is exposed to light, electrons are emitted from its photosensitive surface. These electrons are attracted to the positive anode and form a current that can be measured with an ammeter or galvanometer. The kinetic energy of the emitted electrons is dependent upon the frequency of light striking the phototube, and the quantity of emitted electrons is dependent on the intensity of the light.
- 3. 3 PERFORMANCE : a) Connect the voltmeter, galvanometer, and power supply to the phototube connections. b) Plug in the galvanometer and adjust the index on the galvanometer to some convenient reading on the scale with one lead to the galvanometer disconnected. c) This reading on the galvanometer corresponds to the situation where no current flows through the galvanometer. d) Now reconnect the lead to the galvanometer. e) Plug in and turn on the light source. f) Place the light source directly in front of the opening to the phototube. g) Note the wavelength of the filter and insert it in the slot above the phototube. h) Adjust the potentiometer on the phototube apparatus until the voltmeter reads as close to zero as possible. Record the galvanometer reading. i) Adjust the potentiometer until the voltmeter read 0.05 volts. j) Record the galvanometer reading. Continue in the above fashion at 0.05 volt intervals until a voltage of 1.00 volts is -reached. k) Change the filter and repeat steps (g) through (k). Repeat for the remaining filters. OBSERVATIONS AND CALCULTIONS : h f Wf K max Where h is Planck's constant, f is the frequency of the incident light, and W , is the work function of the metallic surface, i.e., the energy needed to dislodge the electron from the surface. At frequencies above the threshold frequency, electrons will be emitted. Therefore, Wf h fo
- 4. 4 h f h fo K max At the voltage called the "stopping potential," Vs, the electron current from the cathode to the anode will cease to flow. At this voltage the maximum kinetic energy of the electrons is K e V eVS = h f - Wf where e = the electronic charge 1.602 x 10-19 C and Vs is the stopping potential. By experimentally determining the stopping potential for several values of the frequency of the incident light and using above equation, Planck's constant can be determined. RESULT ANALYSIS : VS = ( h / e ) f - Wo / e This equation shows a linear relationship between the stopping potential Vs and the light frequency f, with slope h/eh/e and vertical intercept −W0/e. If the value of the electron charge e is known, then this equation provides a good method for determining Planck's constant h. In this experiment, we have measured the stopping potential with modern electronics.
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