Measuring Plancks constant using LEDGroup 5

Introduction:

When we think of the evaluation of fundamental physical constants, such as the speed of light or the force of gravity, we probably think of famous, large-scale experiments but classroom equipment can also be used to calculate these unvarying values. The Planck constant may seem a rather rarefied concept unlike, say, the speed of light, but it plays an absolutely central role in understanding the behavior of matter at the subatomic level. It is a cornerstone of the theory of quantum mechanics, which describes the strange behavior of particles at this level. Here energy, as well as matter, is made up of particles. Light and other electromagnetic radiation, for example, consists of particles called photons. Named after German physicist Max Karl Planck (18581947), the Planck constant tells us how the energy of individual photons relates to the wavelength of their radiation, as this key equation shows: (1)

An LED is a two terminal semiconductor light source. In the unbiased condition a potential barrier is developed across the p-n junction of the LED. When we connect the LED to an external voltage in the forward biased direction, the height of potential barrier across the p-n junction is reduced. At a particular voltage the height of potential barrier becomes very low and the LED starts glowing, i.e., in the forward biased condition electrons crossing the junction are excited, and when they return to their normal state, energy is emitted. This particular voltage is called the knee voltage or the threshold voltage. Once the knee voltage is reached, the current may increase but the voltage does not change.If V is the forward voltage applied across the LED when it begins to emit light (the knee voltage), the energy given to electrons crossing the junction is,(2)Equating (1) and (2), we get (3)

The knee voltage V can be measured for LEDs with different values of (wavelength of light). (4)Now from equation (4), we see that the slope s of a graph of V on the vertical axis vs. 1/ on the horizontal axis is (5)To determine Plancks constant h, we take the slope s from our graph and calculateusing the known value Alternatively, we can write equation (3) ascalculate h for each LED, and take the average of our results.

Objectives: To determine Plancks constant experimentally

Materials:1) Four LEDs emitting coloured light one each of red, orange, green and blue. Choose LEDs with a clear, colourless casing surrounding the LED, so that the colour of the light comes from the device itself, not from the coloured casing.2) 9 V battery or AC source 3) Two multimeters (one to be used as a voltmeter and the other as an ammeter).4) 1 k potentiometer or rheostat.

Procedure:

1) Set up the circuit as shown in the diagram above. Connect the ammeter in series with the LED to measure the current through it, and connect the voltmeter in parallel to the LED to measure the voltage across it. The applied voltage can be changed by using the potentiometer or rheostat.2) Change the voltage in steps of 0.05 V from 0 V to 3 V, and measure the resulting electrical current. Note that when the current flowing through the LED is small, the LED might not light up, but the ammeter can still measure the current. To protect the LED, take care to keep the current below 5 mA.3) For each LED, plot a graph of current against voltage, similar to the graphs shown to the left. On each graph, find the straight line of best fit to join up the points that slope up from the x-axis. If the points lie close to the line, this shows that a linear relationship holds between the applied voltage and the current in this region of the graph4) Finally, determine the activation voltage (Va) from the collected data. This is the point at which the current begins to increase linearly with voltage. It can be read off the graph by extrapolating the straight line representing the linear response region backwards until it intercepts the x-axis. Students can do this visually using a ruler, or mathematically by applying linear regression to the experimental data points in the linear region.LED colourTypical wavelength, (cm)Activation voltage, Va (V)

Red6231.78

Orange5861.90

Green5672.00

Blue4672.45

Fig 1. Shows the typical values for activation voltages