Experimentally Verifying Plank’s Constant
Plank’s constant is one of those mysterious constants in nature. Just like π, this constant appears in nature as some higher truth. Max Planck first used the constant later named after him to solve the ultraviolet catastrophe. Einstein later used it to describe the photoelectric effect, and it is now a fundamental constant used to describe the transfer of energy in discrete packets on a quantum scale.
Experiment
A Light-emitting diode contains a semiconducting material that releases electromagnetic radiation in or near the spectrum of visible light. The semiconducting material is receptive to incoming electrons, but only when the quantized energy goes above a level that can cross the bandgap. Before the diode passes a specific potential where the step function of the material, hc/λ, is overcome, the potential across the LED will be constant after the voltage is more than the bandgap, the potential across the LED will increase exponentially.
This picture shows the functionings of a LED. http://upload.wikimedia.org/wikipedia/commons/d/d7/PnJunction-LED-E.svg
The LED lights used in this experiment produce wavelengths of 590, 665, 635, and 950 nanometers. Wired into a circuit are a resistor substitution box, one at a time, and a direct current from a 6-volt source.
This picture is a circuit diagram of the circuit used in the experiment.
http://physics.ua.edu/lab10x/ph102/PDF/Plank %27s_Constant_LAB.pdf
We varied resistance on the substitution box from 4M Ω to 1Ω, then measured the voltage over the resistor and the LED.
Procedure
The LED lights are wired into the circuit described above, with the voltmeters wired across the variable resistor and the LEDs. As we varied the resistance, the readings on the voltmeters never settled to one value. Instead, the voltmeters would continuously increase; we recorded the voltage as soon as we varied the resistance to minimize discrepancies in the data.
Data
We collected data from several of the LEDs, with as little as 0.9% error at times. The LED with a wavelength of 635 nanometers produced a curve closest to what was to be expected.
The LED that produces electromagnetic radiation of wavelength 635 nm. The graph is current in (mA) vs. LED voltage (v) while another of the LEDs with a wavelength of 590 nm produced an erratic graph. Because the chart was not close to the other graph, it was assumed to be because of an error that occurred, and the data reflects something going wrong, possibly a mistake with the voltmeter or based on human error. For this data we could not find an experimental value for Planck’s constant, as the value for the knee of the curve could not be defined clearly. However, for the rest of the data, the experimental value for Planck’s constant was determined to be 0.90% for the LED that omits 635 nanometer lights, to as high as 3.0% for the LED that emits 950 nanometer electromagnetic light, which is not in the visible spectrum.
The graph for the LED with 590 nm light appeared to give erratic results. It is a graph of current in mA vs. LED voltage in v.
Analysis
We determined the value for Planck’s Constant from the experiment by taking the voltage across the resistor when the current vs. the LED voltage graph was most rapidly changing from linear to exponential. We found Planck’s Constant by the equation hc/λ=eVo solved for h, for wavelengths 950, 560, 665, and 635 nanometers, the data for the 590 nanometers was inconclusive, and some experimental error must have occurred. Solving for Planck’s Constant for each wavelength and calculating the average h equals 4.49x10–34 joules seconds with a standard deviation of 0.9x10–34 joules seconds. This result yields a percent error of 27%.
Happy Experimenting
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