Determination of Planck's constant using LEDs

Determination of Planck’s constant using LEDsThe purpose of this lab activity is to determine Planck’s constant by measuring the turn-onvoltage of several LEDs1. IntroductionLight-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 voltagebetween the p side and the n-side is above the “turn-on” voltage). This is caused byelectrons 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' voltageV ttimes e (electron charge) is about the same as the energy lost by an electron as it fallsfrom the n to the p region, and this is also approximately equal to the energy of the emittedphoton.If we measure the minimum voltage V trequired to cause current to flow and photons to beemitted, and we know (or measure) the wavelength of the emitted photons and use it tocalculate the photon energy hf, wealways find that eV t< hf. Some of thephoton energy is supplied by thermalenergy..

spreadsheet and type =slope(y‐value range, x‐value range). This will put theslope 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 interceptby 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 seethat 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 “truevalue” 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 isgiven byX1 N XiN i 1 (this means: sum all the values Xi, i.e. take X 1 + X 2 +….+X N , and then divide by the totalnumber of measurements, N).(3) the “standard deviation” is a quantity which provides an estimate for the precision withwhich you determined your best estimate of X. The square of the standard deviation(also called the “sample variance”) is given byN2 12X ( Xi X ) ,N 1i1i.e. to calculate it, you take the sum of the squares of the deviations between theindividual measurements Xi and the average, and then divide by (N‐1). The standarddeviation (sometimes also called the “root‐mean‐squared deviation”) is then given byN12the square root of this: X ( XiX) .N 1i1In 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 educatedguess (“guesstimate”) of how precisely you know the voltage and the frequency . LetV Vbe the uncertainty (“error”, “imprecision”) of your measurement of the turn-onvoltage V t , and f the uncertainty of the frequency, then the “relative uncertainty” hhhh of h determined from this is:fh h V V ( ) ( )h h V V f2 f 2