Redlands Unified School District



The Experimental Determination of Planck’s ConstantIntroduction?Planck’s constant (h), a physical constant was introduced by German physicist named Max Planck in 1900. The significance of Planck’s constant is that ‘quanta’ (small packets of energy) can be determined by frequency of radiation and Planck’s constant. It describes the behavior of particle and waves at atomic level as well as the particle nature of light.??An LED is a two terminal semiconductor light source. In the unbiased condition a potential barrier is developed across the p-n junction of the LED. When we connect the LED to an external voltage in the forward biased direction, the height of potential barrier across the p-n junction is reduced. At a particular voltage the height of potential barrier becomes very low and the LED starts glowing, i.e., in the forward biased condition electrons crossing the junction are excited, and when they return to their normal state, energy is emitted. This particular voltage is called the?threshold voltage. Once the threshold voltage is reached, the current may increase but the voltage does not change. Until the threshold voltage is reached, there is no current and the LED does not produce any light.The light energy emitted during forward biasing is given as ,?? ? ?(1) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Wherec = Velocity of light.h = Planck’s constant.λ = Wavelength of light.?If V is the forward voltage applied across the LED when it begins to emit light (the threshold voltage), the energy given to electrons crossing the junction is:??? ? ? ?(2) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ???Setting these equations equal to each other gives:? ? ? ?(3) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?The threshold voltage V can be measured for LED’s with different values of λ (wavelength of light).? ? ? ?(4) ? ? ? ? ? ? ? ? ? ? ? ? right000Now from equation (4), we see that the slope s of?a graph of V on the vertical axis versus 1/λ on the horizontal axis is? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ??? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? To determine Planck’s constant “h”, we take the slope s from our graph and calculate?using the known value???Alternatively, we can write equation (3) as??and calculate h for each LED, and take the average of our results.I.)PURPOSE?To experimentally determine Planck’s constant by using the slope and direct calculation methods?II.)MATERIALS?Variable power supply (set at 9.0V), LabQuest with Current and Voltage probes, Planck’s Constant Determination Box with six leads.III.) PROCEDUREA.) Carefully examine the Planck’s Constant Determination Box. Connect one pair of leads between the Variable Power Supply and the Planck’s Constant Determination Box (the correct location on the Box is across the “DC 9V” label). Use two additional sets of leads to connect the Current (A) and Voltage (V) Probes to the Box, then plug both probes into the LabQuest. Turn the black knob all the way counterclockwise (on the 470 nm LED), and turn the red knob all the way counterclockwise as well.Preliminary Questions on Setup of Apparatus?1.) Is the Voltage probe connected in Series or Parallel with the LED? Why? What would it read if it was connected incorrectly?2.) Is the Current probe connected in Series or Parallel with the LED? Why? What would it read if it was connected incorrectly?3.) Clearly explain the purpose of the black knob.4.) Clearly explain the purpose of the red knob.Why do we start with the red knob turned all the way counterclockwise?5.) Why is there a 220Ω resistor wired in series with our circuit? What would happen if it was not there? What would happen if it burned out, and did not allow any current to flow?6.) Draw a schematic of the circuit in the Planck’s constant Determination Box, the power supply and the instrumentation attached to the LabQuest (you may simplify it by showing only one LED), and provide a brief explanation of how it works. B.) Turn on the LabQuest, power supply and the Planck’s constant Determination Box. Set the power supply voltage to 9.0V and zero both LabQuest probes.C.) Place one end of the viewing tube over the 470 nm LED, and look into the other end at the LED. The purpose of the viewing tube is to make faint light easier to see.D.) Slowly turn the red knob clockwise to increase the voltage supplied to the LED. Stop turning the knob when the LED begins to glow, and the Current Probe begins to register a nonzero amperage.E.) Record this minimum voltage measured by the LabQuest Voltage Probe in your data table; also record the wavelength of the LED (4.70 X 10-9 meters).F.) Repeat steps A-E for each LED. Note that the last two LEDs do not emit a visible wavelength of light, but will still register a non-zero amperage when they begin to emit light.IV.) DATAWAVELENGTH (meters)VOLTAGE (V)“h” calculated (J.sec)V.) CALCULATIONSMethod #1:1.) Calculate “h” for each given wavelength using the equation from the introduction of this lab. Show all work and units for the 470 nm LED, including substitution and canceling of units. Record these values in your data table.2.) Calculate the average value for your calculated values of “h”, and use a percent error calculation to compare your value to the accepted value of h (h = 6.63 X 10-34J.sec).Method #2:1.) Use a graphing calculator or spreadsheet to calculate the slope of a graph of the inverse of the wavelength 1/λ (1/m) on the X axis versus the Threshold Voltage (V) on the Y axis. This slope is equal to hc/e, where e is the elementary charge (1.6 X 10-19 C) and c is the speed of light (3.00 X 108 m/sec). Compare this slope to the accepted value of hc/e. VI.) QUESTIONS1.) Explain why the numerical value of h is so tiny. What energy changes does h measure in this experiment?2.) In what way is Method #2 better than Method #1 for estimating h?3.) In 1895, Planck proposed that energy was quantized. In what way did Einstein improve upon Planck’s hypothesis in 1905, and what did Einstein call Planck’s quanta? (Einstein won a Nobel Prize for this).4.) Are the results of this experiment evidence of the Wave or Photon Theory of light? Explain.VII.) DISCUSSION OF ERRORExplain why the results of this lab have relatively high rates of error. You will need to do some research to accomplish this.VIII.) CONCLUSION1.) Claim: What is your estimate of the value of Planck’s Constant?2.) Evidence: Clearly and concisely explain how you arrived at your estimate.3.) Reasoning: Why do you think that this method was effective? What did you measure, and why?4.) Connections to the Real World: How are LEDs used in technological applications? 5.) Future Experiment: Suppose that you only had one LED of known wavelength, and all other equipment used in this lab. Research how a single LED can be used to provide an estimate of Planck’s Constant. Describe the experiment you would do in enough detail that someone could follow your instructions. ................
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