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Planck's constant can be measured in a variety of ways. One method uses the activation voltage of an array of LEDs. The other is a more traditional method using an applied stopping voltage to reduce the photoelectric current in a photoelectric cell to zero.
LED array
LEDs are produced by the junction of two ‘doped’ semiconductor materials, one of which has an excess of electrons (n-type) and the other a lack of electrons – also designated as holes (p-type). When an electrical current is passed through this ‘p-n’ junction, the recombination of electrons and holes releases energy in the form of photons.
The colour of the light emitted from an LED is determined by the energy of the photons, which can be controlled by changing the chemical composition of the semiconductor materials. Each colour of LED has a different activation voltage Va at which photons start being produced. Measuring this voltage, along with the wavelength λ of the light allows Planck’s constant to be determined.
This experiment uses and LED array like the one shown below.
For each LED in the array you will plot a graph of current against voltage, similar to the graphs shown below.
On each graph, the straight line of ‘best fit’ is found for the points that slope up from the x-axis.
The activation voltage (Va) 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.
The energy (qV) released by each electron as it travels through the LED is transferred to a photon. To measure the energy released by each electron multiply the activation voltage Va by the charge on the electron q (1.6 x 10–19 C). The frequency f of the photons can be determined from the wavelength λ of the maximum intensity of photon emitted by the LED (stated on the LED array).
Comparing this with the linear equation,
y=mx+b
if Va (y-axis) is plotted against 1/λ (x-axis) then the gradient of the line can be used to determine Planck’s constant.
gradient = hc / q
Set up the circuit as shown in the diagram below.
Connect the current sensor in series with the LED to measure the current through it, and connect the voltage sensor in parallel to the LED to measure the voltage across it. The applied voltage can be changed by using the variable power supply.
Connect the current sensor and voltage sensor to the LabQuest2 and zero both sensors by clicking on the red and blue fields and selecting Zero. The screen should look similar to the one below.
Click on the Mode:/Rate:/Duration: window and choose Selected Events.
Click on the OK button.
Click on the Collect button . The data point for current and voltage will be displayed as shown below.
Click on the Keep button .
Switch on the power supply and record the current and corresponding voltage at small regular intervals by adjusting the slider on the potentiometer. In the example below, 14 different data points were collected.
When the voltage reading on the voltmeter has reached 6 Volts click on the Stop Collection button .
Set the Graph Options as shown in the gif below so that a single graph of current (y-axis) against voltage (x-axis) is shown.
The graph should now look like the one below.
Use your graph to determine the activation voltage of the LED by extrapolating the straight part of the graph to find where it intercepts the x-axis. Select the desired portion of the graph by clicking and dragging on the graph as shown below.
Click on the Analyze tab and choose Curve Fit and check the Current box. From the Choose Fit drop down box select Linear and click OK, as shown in the gif below.
Click on the Analyze tab again and choose Interpolate and click on the x-axis intercept of the line with the stylus.
The value of the intercept is shown in the bottom corner as shown above. In this case the activation voltage is 2.41 V (to 3 sig.digs.)
Repeat this process for the other five LEDs. Note that the final LED emits infra-red radiation and therefore it is not visible with your own eyes.However it can be observed using the camera from your phone or laptop which can detect some of the infra-red range of the spectrum.
Plot a graph of Va against 1/λ and determine Planck's constant from the gradient.
PhET Simulation
PhET Simulation
If you do not have access to the Planck's constant apparatus you can conduct the experiment virtually using the photoelectric effect simulation from PhET.
Click on the image below to launch the PhET simulation Photoelectric Effect.
Set the metal to sodium – the most reactive of the metals given.
Set the intensity of the radiation to a set value e.g. 100%.
Adjust the wavelength of the radiation until a current begins to flow in the circuit. This will happen somewhere in the blue part of the visible spectrum. The ejected electrons now have kinetic energy.
Then apply a voltage to counteract the current. When the current reading is zero then the voltage is known as the stopping voltage. In the example shown the stopping voltage is 0.40 V.
Continue to change the wavelength of the radiation from visible into ultra violet and record the stopping voltage for each wavelength.
At the stopping voltage the electric potential energy eV is equal to the maximum kinetic energy Emax of the photoelectrons, eV = Emax.
Calculate the maximum kinetic energy of the electrons from the product of the stopping voltage and the charge of an electron.
Calculate the frequency of the radiation using the speed of light in a vacuum divided by the wavelength in metres.
Plot a graph of maximum kinetic energy against frequency.
The gradient of the straight line graph is Planck’s constant and the x-intercept is the work function of sodium.
Planck's Constant Resources / Problem Set
Planck's Constant Resources / Problem Set
Topic_12_-_Activity_2_-_Notes.pdfTopic_12_-_Activity_2_-_Problems.pdfPage updated
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