16. Planck's Constant



16. Planck's ConstantGuided InquiryDriving Question | ObjectiveWhat is the value of Planck's constant and how can it be determined experimentally? Given the quantization of light energy and the relationship between photon energy and frequency, perform an experiment using the light emitted from monochromatic LEDs to determine the value of Planck's constant.Design and Conduct Your ExperimentIt is your group’s responsibility to design and conduct an experiment whose data will support your answer to the driving question above. Use the answers to the guiding questions below to help guide your experiment design. After you have answered the guiding questions, write an outline of the equipment setup and procedure you will use to collect data, identifying the steps in sequence and the points at which each piece of equipment will be used.Suggested Materials and EquipmentAlthough you have the freedom to design your procedure using any reasonable equipment at your disposal, the following equipment is recommended for your experimental setup.Data collection systemBattery, D-cell (2)PASCO Wireless Voltage Sensor1LED, blue (450–500 nm)4-mm banana plug patch cord with alligator clip1 (2)LED, green (501–565 nm)PASCO AC/DC Electronics Laboratory2LED, yellow/amber (566–620 nm)Wire leads2 (5)LED, red (621–750 nm)Resistor, 330-Ω2Spectrometer (optional)1ap41 2ap04PASCO WirelessVoltage SensorPASCO AC/DC Electronics LaboratorySafetyFollow these important safety precautions in addition to your regular classroom procedures:Do not stare at the LEDs when they are fully lit as this may be harmful to your eyes.Do not use LEDs that emit ultraviolet light, which can cause permanent eye damage.Do not apply voltages to the LEDs above approximately 2.8 V as this can cause permanent damage to the LEDs.right-36576000Voltage must only be applied to LEDs in the “forward-biased” orientation with current flowing from the positive lead to the negative lead. Connecting the LED incorrectly can damage it.Always connect the positive lead to positive voltage, and the negative lead to negative voltage. An LED's positive electrode lead is longer than the negative lead, and the negative lead has a flat spot on the side of the plastic LED housing. Guiding Questions1.What is the equation that relates the energy of a photon to its frequency? Write the equation and identify each variable with correct units.2.The semiconductor in a monochromatic LED will not emit light until the electrons within it are each given some threshold energy Eelectron = eΔV0, where ΔV0 is the threshold (turn-on) voltage applied to the LED (the potential difference required for an LED to just begin emitting light), and e is the charge of an electron (e = 1.60 × 10–19 C). When the LED just begins to emit light, each electron loses that threshold energy in the form of a photon.Assuming all of the threshold energy from each electron is converted into photon energy, what is the mathematical expression that relates the turn-on voltage ΔV0 of a monochromatic LED to the frequency of a photon emitted by the LED?3.In the expression established in your response to the previous question, which variables can be measured directly using tools available to you, and which variable must be measured indirectly? Identify the tools and techniques you would use to measure each variable.4.The color of the light emitted by a monochromatic LED is rarely specified by its frequency, but rather, by its wavelength. What is the equation that relates the wavelength of a photon to its frequency? Write the equation and identify each variable with correct units. Why is this equation important in your experiment?5.Assuming you choose a graphical data analysis method based on the variables identified in the previous questions, what will the dependent (measured) variable and independent (manipulated) variable on your graph be? Explain why you chose the variables that you did.6.How will you configure a simple LED circuit so that the independent and dependent variables can be manipulated and measured, as appropriate? Include in your description any voltmeters or other circuit measurement tools you may use.Experimental DesignYour goal is to experimentally determine the value of Planck's constant using monochromatic LEDs. Use the responses to the Guiding Questions to help finalize your procedure and equipment configuration.Once you are convinced that your procedure will accomplish the experiment's objectives, record your experimental setup and procedure in the following sections. SetupDraw and/or describe your experimental setup such that a third party could recreate the same setup in an attempt to reproduce your experiment.ProcedureOutline the procedure you will use in your experiment, listing all of the steps below. Your outline should be written such that a third party could follow the same procedure in an attempt to reproduce your experiment.Collect DataPerform your experiment and record all relevant data. Present your data below (or in an attached document) in a form that best suits the experiment format, such that a third party can understand your experimental results in an attempt to reproduce them.Analysis Questions1.What is your experimental value for Planck's constant, and how did you determine this value from your data?2.What are factors that might have caused error in your measured value for Planck's constant? Explain how each factor you list could have been avoided or minimized.3.The actual value for Planck's constant is h = 6.63 × 10–34 J?s. Calculate the percent error between your experimental value and the actual value.Synthesis Questions1.A solid-state laser emits light at 532 nm from the laser LED within it. What minimum potential difference applied across the LED is required for light to be emitted from the laser diode?2.A blue LED (λ = 472.2 nm) emits 3.89 × 1016 photons per second. In a few sentences, explain the process by which you would determine the power output in watts.3.The photoelectric effect is a process in which energized electrons are ejected from the surface of a metal when light strikes it. The maximum kinetic energy Kmax of each ejected electron is equal to the difference between the energy of one photon Ephoton incident on the metal and the minimum amount of energy needed to free the electron, known as work function φ:Assuming that the energy of an ejected electron is always positive and non-zero, below what wavelength must the incident light be for electrons to be ejected from an aluminum surface? Assume φaluminum = 6.54 ×?10–19 J. Show your work. ................
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