Measuring Planck's Constant with LED Thresholds for H2 Physics Practicals

TL;DR
Use a string of different coloured LEDs, a variable power supply, and spreadsheet regression to plot photon energy against frequency.
The intercept of the best-fit line gives h/e; when multiplied by the electronic charge it delivers Planck's constant within 5 %.
Bake in calibration checks, dark-room controls, and full uncertainty paragraphs to turn a simple demo into a top-tier Paper 4 investigation.

Why This Experiment Hits the 9478 Syllabus

H2 Physics candidates must demonstrate mastery of quantum photoelectric ideas and linear data analysis. The LED threshold experiment ticks both boxes:

• Threshold voltage maps directly onto photon energy E = hf, making the link between circuit measurements and quantum theory explicit.
• The procedure mirrors SEAB Paper 4 expectations — control temperature, justify graphical methods, and estimate uncertainties on slope and intercept.
• Students rehearse digital acquisition workflows that Cambridge and SEAB examiners highlight in recent examiner reports.

Apparatus Checklist

Setup and Calibration

1. Fuse safety first. Keep the current below the LED's rated limit — 10 mA is plenty for threshold determinations.
2. Calibrate meters. Zero the multimeter using its REL function and record the least count for later uncertainty paragraphs.
3. Stabilise temperature. LEDs warm up quickly; wait 60 s between readings or mount each diode on an aluminium heat sink to maintain a constant junction temperature.
4. Log wavelength references. If you cannot find the manufacturer's datasheet, capture each LED's dominant wavelength using a shared diffraction grating workflow that your lab already uses.

Data Collection Workflow

1. Increase the supply voltage in 0.02 V steps until the LED barely begins to glow in the darkened enclosure.
2. Record the “turn-on” voltage V_0 and capture a short video; frame-by-frame playback lets multiple students agree on the exact threshold.
3. Repeat the trial three times per colour, noting ambient temperature and any drift.
4. Convert wavelength \lambda to frequency f = c/\lambda and photon energy E = eV_0.
5. Plot E against f in Google Sheets or Logger Pro. Use LINEST to extract gradient h and y-intercept (work function).
6. Document absolute and percentage uncertainties for both the slope and intercept. Compare your experimental h to 6.626\times10^{-34}\text{ J s}.

Error Analysis That Impresses Examiners

• Subjective threshold detection: Mitigate by using a light sensor (photodiode) or by averaging multiple observers' readings.
• Series resistance drop: Measure the actual LED voltage with a differential probe rather than trusting supply readouts.
• Temperature drift: Quantify LED forward-voltage shift (~2 mV K⁻¹) with a thermocouple so you can state a systematic correction.
• Frequency accuracy: Note the ±1 nm uncertainty if you use diffraction-grating calibration and propagate it through to f.

Extension Pathways

• Swap discrete LEDs for a white LED and narrow-band interference filters to test whether broadband sources still obey the linear model.
• Deploy an Arduino-based constant-current driver so students can script the voltage sweep and collect hundreds of data points in minutes.
• Pair the practical with the H2 Physics Definition and Formulae guide to reinforce quantum terminology before Paper 4.
• Bundle the apparatus into an Eclat “Quantum Starter Kit” and offer a weekend bootcamp on linear regression and uncertainty budgets.

References

• de Sousa, M. A., Measuring Planck's constant using LEDs, arXiv:physics/0412009
• PhET Interactive Simulations, Photoelectric Effect
• Cambridge International, AS & A Level Physics 9702 overview