The Planck constant

Written by Johannes Schlaf

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tags: Quantum Physics, Measuring h, LEDs, Threshold voltage
categories: Quantum mechanics

- Setup and Execution -


phyphox:h box	Blackout box	Support element
Various LED insets	Connector cable	Smartphone

Download the phyphox experiment PLA (Planck constant) using the QR code below.

Open the phyphox experiment PLA.
Select your phyphox:h box (numbering on the side of the box). \[\Rightarrow\] Now the box connects to the app an begins to send the absolute value of the voltage applied.
Place your smartphone on the blackout box so that the smartphone camera is situated directly above the reflective material (white). Use the support element if necessary.

Insert the LED inset into the blackout box.
Set the voltage control dial of the phyphox:h box to the maximum. Set the selection rectangle of the camera so that no selected area is overexposed (i.e. the selection rectangle must not contain any areas marked red).
Turn back the voltage control dial and switch to the tab “Identifying the threshold voltage”.
Start the measurement
Record a characteristic curve of the LED by slowly turning the voltage control dial. Alternatively, you can also try the sawwave mode, in which the characteristic curve is automatically traced from left to right.
Pause the measurement when you have recorded a usable characteristic curve.
Place the green line of best fit by adjusting the minimum and the maximum light intensity taken into account. The line of best fit should run through the linear part of the characteristic curve.
Write down the treshold voltage \[U_\mathsf{threshold}\] calculated by the experiment on the analysis worksheet. Also write down the associated measurement uncertainty. Next, enter the wavelength into the phyphox experiment and save the wavelength - threshold voltage value pair. The value pair is now available in the “Measuring h” tab.
Delete the recorded measurement data by selecting the corresponding button and start again at step 4 with a different LED.

Calculate the photon energies (including uncertainties) from the treshold voltages. Reminder: \[e=1.602\cdot 10^{-19}\,\mathrm{C}\]
Plot the obtained frequency-energy value pairs in the corresponding diagram on the analysis worksheet (including uncertainties).
Plot an approximate line of best fit in the diagram and determine its slope. What is the physical significance of the slope?
Plot a line with minimum slope an a line with maximum slope (within the uncertainties).
Calculate the uncertainty on the value obtained for the Planck constant.

The Bluetooth connection is interrupted Close the phyphox app and restart the phyphox experiment.
The characteristic curve shows a hysteresis This is often the case if the voltage is varied to quickly. Delete the measurement curve by selecting the corresponding button and restart the measurement.