Planck's Constant

From MariachiWiki

by, Ted, Jeremy, Tom, Christian, Alan, Helio

1 Introduction
2 Experimental Setup
3 How to perform the experiment
4 How to view the infrared light
5 Example
6 Classroom Example
7 References

Introduction

Planck's constant is one of the fundamental constants in modern physics. It relates the energy of a photon to its frequency. To determine this constant we use Light Emitting Diodes (LED). Diodes today come in a variety of colors. Each color is achieved by having a slightly different semiconductor material. This experiment has being carried out in many manners with a variety of recipes. We chose to do the experiment using a number of LEDs, with different colors including infrared and ultraviolet.

The experiment is based on the fact that the energy of the photon relates to its frequency as:

$E= h\nu \,$

When the diode first emits light the voltage across the diode, $V d$ , is just enough to give energy to electrons to jump between two energy levels. Therefore

$V_d \times e = h\nu$

where e is the electron charge. Therefore by measuring the voltage across the diode when the first light is observed for a number of diodes a graph of $V d$ vs $ν$ can be made. The slope of this graph is equal to (h/e).

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Experimental Setup

This setup uses 5 LEDs, all from SuperBrightLed. They are made of different materials and the color is determined by the radiative wavelength. Unfortunately for an LED the line is not monochromatic, i.e. single wavelength. Most likely it is a distribution of wavelengths around a central spectral line. Reputable manufacturers publish such spectra and can be obtained from the company's web site. Another way to determine the wavelength is to use a spectrometer. Inexpensive grating spectrometers can be purchased, for example from Starlab.

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How to perform the experiment

To begin the experiment, a simple series circuit consisting of the LED and a resistor is connected to a variable power supply. The value of the resistor is not critical for the experiment. Any resistor over 300 ohms will work.

In a dark room, slowly increase the potential on the power supply until the LED just starts to emit light. The light will be very faint and easiest to view from above. Record the value of the potential difference across the LED using a voltmeter. Turn the variable power supply up so that the LED glows brightly. Using a calibrated spectrometer, identify the wavelength of the LED. (Note: if a spectrometer is not handy you should be able to look up the wavelength from the distributor). Turn off the voltage, replace the LED with a new color and repeat.

The key to achieving a highly accurate value for Planck’s Constant is to include a wide range of frequencies in the data. The ultraviolet LED should be viewable with the naked eye, however, the infrared LED is not. One way to get the data for this point is to use a digital camera that will “convert” infrared light to visible light. The camera on most cell phones will work well. Hold the camera over the LED and slowly increase the potential on the power supply. When the LED begins to emit light you will be able to view the light through the camera’s display. Having these two points in the data will greatly improve the value of Planck’s Constant.

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How to view the infrared light

To view the infrared led use a cell phone camera. To test if your cell phone camera is sensitive to IR leds use a remote control (TV for example) and while pushing a button look at the LED (usually in front of the remote control unit).

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Example

The table below show an example measurement performed as decribed in previous sections.

Data for Planck's Constant Experiment
potential (V)	color	wavelength (nm)	frequency (Hz)
2.195	blue	465	6.452E+14
1.545	yellow	590	5.085E+14
1.446	orange	610	4.918E+14
1.463	red	630	4.762E+14
0.946	IR	945	3.175E+14
2.737	UV	405	7.407E+14
1.980	green	520	5.769E+14

To analyze the data we remember that

U E = E γ

$V_d \times e = h\nu$

$\frac {V_d}{\nu} = \frac{h}{e}$

A graph of $V d$ vs $ν$ will yield a slope of $\frac {h}{e}$ . Therefore, multiplying the slope by the charge of the electron, e, Planck's constant can be found.

$h = slope \times e$

The resulting graph is shown below. In this example the straight line is the result of Excel's Trendline.

A quick analysis results in:

$(4.308 \times 10^{-15}(\frac{V}{Hz}) \times (1.602 \times 10^{-19}C) = h$

$h = 6.96 \times 10^{-34}J \times s$

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Classroom Example

Using the following materials the students constructed the aforementioned circuit.

Power supply (Sargent-Welch)
Ultra bright LEDs
Resistors (200 Ohm)
Aligator Clips and wires
Spectroscopes
Multimeters

The students easily constructed the circuit which took up very little time. The voltage measurements were also easily obtained. The only difficulty associated with the experiment were the wavelenght measurements taken with the spectroscopes. The spectroscopes were not calibrated properly and there was some light contamination comming into the room (from lights and the sun), both of which interfered with our measurements. By using the LED manufacturer specifications, the students were able to obtain a very close value to Plancks constant. Overall this was a great experiment and the students enjoyed it very much.

The template used for the class was the following:Template

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