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A historical perspective on the development of Planck's constant, a fundamental concept in quantum physics. It also includes a description of an experiment designed to measure Planck's constant using light emitting diodes (LEDs). the physics theory behind the experiment, the procedure for conducting it, and the apparatus required.
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By Martin Hackworth
Historical Perspective and Physics Theory
Max Planck (1858-1947) was born in Kiel Germany and attended schools in Munich and Berlin. Planck was an early pioneer in the field of quantum physics. Around 1900 Planck developed the concept of a fundamental unit of energy, a quantum , to explain the spectral distribution of blackbody radiation. This idea of a basic quantum of energy is fundamental to quantum mechanics of modern physics. Planck received a Nobel Prize for his work in the early development of quantum mechanics in 1918. Interestingly, Planck himself remained skeptical of practical applications for quantum theory for many years.
In order to explain blackbody radiation, Planck proposed that atoms absorb and emit radiation in discrete quantities given by
E =n hf
where:
Planck named these discrete units of energy quanta. The smallest discrete amount of energy radiated or absorbed by a system results from a change in state whereby the quantum number, n, of the system changes by one.
In 1905 Albert Einstein (1879-1955) published a paper in which he used Planck's quantization of energy principle to explain the photoelectric effect. The photoelectric effect involves the emission of electrons from certain materials when exposed to light and could not be explained by classical models. For this work Einstein received the Nobel Prize in Physics in 1921.
Niels Bohr (1885-1962) used Planck’s ideas on quantization of energy as a starting point in developing the modern theory for the hydrogen atom. Robert Millikan made the first measurement of Planck’s constant in 1916. The best current value for Planck's constant is 6.62607554 x 10-34^ J · s.
In this experiment, you will use light emitting diodes (LED’s) to measure Planck's constant. You should be familiar with semiconductors and diodes from Modern Physics. To review: LED’s are semiconductors that emit electromagnetic radiation in optical and near optical frequencies when a voltage is applied to them. LED’s emit light only when the voltage is forward biased and above a minimum threshold value. This combination of conditions creates an electron hole pair in a diode. Electron hole pairs are charge carriers and move when placed in an electrical potential. Thus many electron hole pairs produce a current when placed in an electric field. Above the threshold value the current increases exponentially with voltage.
A quanta of energy is required to create an electron hole pair and this energy is released when an electron and a hole recombine. In most diodes this energy is absorbed by the semiconductor as heat, but in LED’s this quanta of energy produces a photon of discreet energy E = hf. Because multiple states may be excited by increasing the voltage across a diode, photons of increasing energies will be emitted with increasing voltage. Thus the light emitted by an LED may span a range of discrete wavelengths that decrease with increasing voltage above the threshold voltage (shorter wavelength = higher energy). We are interested in the maximum wavelength that is determined by the minimum energy needed to just to create an electron hole pair. It is numerically equal to the turn on voltage of the LED. The relation between the maximum wavelength, λ , and the turn on voltage, V 0 , is
eV 0 E = hf = hc = λ where:
The maximum wavelength of the LED can be measured to a resolution of a few nanometers with a good spectrometer. If the turn on voltage, V 0 , is measured for several diodes of different color (and different maximum wavelength, λ ), a graph of V 0 vs. 1/ λ should be linear with a slope of hc / e. An experimental value of Planck's constant may then be determined by using the known values of the speed of light, c , and the charge of an electron, e , and computing h.
- 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0. Apparatus
PC Pasco 750 interface Voltage probes Breadboard 1000 Ω ½W resistor 5V DC regulated power supply 10kW potentiometer large LEDs (blue, green, red, yellow) infrared LED of known wavelength (if available) connecting wires Gratner spectrometer with grating.
Data
Slope of turn on voltage versus 1/ λ graph __________ V· m Experimentally determined value for h _______× 10 -34^ J· s
Calculations