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Determination of Planck’s constant using LEDs
The purpose of this lab activity is to determine Planck’s constant by measuring the turn-on
voltage of several LEDs
- Introduction
Light-emitting diodes (LEDs) convert electrical energy into light energy. They emit radiation (photons) of visible wavelengths when they are “forward biased” (i.e. when the voltage between the p side and the n-side is above the “turn-on” voltage). This is caused by electrons from the “n” region in the LED giving up light as they fall into holes in the “p” region.
The graph below shows the current -voltage curve for a typical LED. The 'turn-on' voltage Vt times e (electron charge) is about the same as the energy lost by an electron as it falls from the n to the p region, and this is also approximately equal to the energy of the emitted photon.
If we measure the minimum voltage Vt required to cause current to flow and photons to be
emitted, and we know (or measure) the wavelength of the emitted photons and use it to calculate the photon energy hf, we always find that eVt < hf. Some of the
photon energy is supplied by thermal energy.
- Procedure:
Light-emitting diodes require a series load resistor to prevent thermal runaway - unlimited forward current - from destroying them. Our experiment is conceptually as shown above, with some modification: we use AC voltage rather than DC, so the voltage keeps varying periodically, and the LED lights up whenever the voltage is large enough to overcome the depletion barrier. Then also a current flows across the junction (through the diode). We measure the applied voltage with an oscilloscope which allows visualization of time dependent electric signals. We measure the current by measuring the voltage across the 100 resistor. By measuring the voltage Vt at which the LED “turns on”, i.e. at which current flows (current >0), we can determine the energy of the photons (it is eVt ). This voltage is different for the LEDs of different color. We know the wavelength of the light emitted by the different LEDs (and therefore the frequency). By using the equation eVt hf, we can determine Planck’s constant h. This is only approximate, since, as mentioned above, eVt < hf , because some of the energy can be supplied by thermal motion. A better method is therefore to plot Vt vs frequency and determine the slope of a straight trendline fitting the data. The slope equals h measured in eV, and the intercept gives an estimate of the contribution from thermal energy.
- Analysis
a. Make a table with a row for every LED, containing (given), f (=c/, c=3 108 m/s, Vt (measured), h (calculated using h (in eV) = Vt /f) b. Determine mean value of h and standard deviation c. Graph Vt (on y-axis = ordinate) vs frequency (on x-axis = abscissa) and determine the slope of the straight line – this is h in units of eV (“electron Volts”) d. The value of h obtained from the slope of the straight line may be different from that obtained in part b (from averaging the values of h obtained from different LEDs) – any explanation? What is the meaning of the intercept? Which of the two determinations is more reliable? e.
- References
http://hyperphysics.phy‐astr.gsu.edu/hbase/electronic/led.html#c http://micro.magnet.fsu.edu/primer/java/leds/basicoperation/ http://www.youtube.com/watch?v=oVtbWFphcCk http://www.youtube.com/watch?v=J10QmuB9WCY
spreadsheet and type =slope(y‐value range, x‐value range). This will put the slope of the line into the cell. You can also get h directly, typing =slope(y‐value range, x‐value range) Similarly you could also get the intercept by typing “= intercept(y‐value range, x‐value range)”
Explanation about average, standard deviation, uncertainties: (1) if you repeat measurements of the same quantity several times, in general you will see that the results vary from one attempt to the other; this is due to measurement errors. Repetition of measurements can be used to get a more precise estimate of the “true value” and also give information about the measurement precision.
(2) if you have N measurements Xi (i=1,2,…N) of some quantity X, the average value is
given by 1
1 N
i i
X X
N
(this means: sum all the values Xi, i.e. take X 1 + X 2 +….+XN, and then divide by the total number of measurements, N).
(3) the “standard deviation” is a quantity which provides an estimate for the precision with which you determined your best estimate of X. The square of the standard deviation (also called the “sample variance”) is given by 2 2 1
N X i i
X X
N
i.e. to calculate it, you take the sum of the squares of the deviations between the individual measurements Xi and the average, and then divide by (N‐1). The standard deviation (sometimes also called the “root‐mean‐squared deviation”) is then given by
the square root of this: 2 1
N X i i
X X
N
In Excel, you can get the standard deviation by using the function STDEV(data range).
(4) You can also try to estimate your measurement precision by making an educated guess (“guesstimate”) of how precisely you know the voltage and the frequency. Let
V V be the uncertainty (“error”, “imprecision”) of your measurement of the turn-on
voltage Vt , and f f the uncertainty of the frequency, then the “relative uncertainty”
h h h h
of h determined from this is: h^ h^ V^ ( V ) 2 ( f )^2 h h V V f
^
