Plank's Constant experiment

Purpose:


To determine experimentally the value of Plank's constant.

Method:

Use a diffraction grating, 2 meter sticks, and a voltmeter to record the wavelength and potential drop across a collection of differently colored LEDs.

The data from our experiment can be found here.
Four LEDs were chosen;
blue
red
yellow
and green
their differences in wavelength should allow for the construction of a graph of photon energy vs. wavelength.


Quantum physics predicts that photons which are emitted from an atom are created when an electron travels from an excited state to a relaxed state. The energy levels of each of those states are of definite energy, and thus every photon emitted should have an identical wavelength. If the atom which emits the electron is bound in a crystal lattice, the energy levels of each state cannot overlap with nearby atoms because of the Pauli Principle. Thus the energy levels of each atom exist in a band approximately centered around the original energy level. This allows for photons of various wavelengths to be emitted from a sample of uniform atomic nature.

The observation associated with this effect is a smearing of the observed emission line when viewed through a diffraction grating.

A light emitting diode, or LED, is an electronic device which takes advantage of this property to generate photons in the visible spectrum. It is usually fabricated using p-type and n-type silicon in such a way that the energy an electron gains by traveling across the LED is equal to the energy of the desired photon.

Upon analysis of of data, a graph of photon energy vs. frequency was obtained from Microsoft Excel.

Unfortunately, the units on the vertical axis are too small to be properly displayed, but they can be viewed in the associated spreadsheet. The slope of this graph is found to be 8.8269 E-34 J/m, which is in error of 33% when compared to the accepted value of plank's constant, 6.626 E-34.

This value of error is unsatisfactory, so a separate method was used to estimate Plank's constant.

If the data points for energy are divided by their corresponding frequency, a set of ratios is obtained.

                   E/f
Red:           6.38E-34 J/m
Yellow:      5.97E-34 J/m
Green:       7.08E-34 J/m
Blue:          6.81E-34 J/m

These numbers are much closer to the accepted value of Plank's constant, and when averaged, yields a ratio of 6.56E-34 J/m, which is in error by only a single percent.