When a Student's Planck Constant Is 18% Low
A high school physics teacher is mentoring a student's independent project that estimates Planck's constant from the turn-on voltage of five LEDs. The student measured red, yellow, green, blue, and violet LEDs with a digital voltmeter, took the manufacturer's peak wavelength for each, and plotted V versus 1/λ. The slope gave h = 5.4 × 10−34 J·s, about 18% below the accepted value. The student wants to submit the work to a regional fair with the conclusion that 'the accepted value of Planck's constant may be wrong.' The teacher notices three problems: the violet LED was already glowing dimly when its turn-on voltage was recorded, the voltmeter has a 1 MΩ input impedance and was connected across the LED while the series resistor was in place, and the wavelengths came from the LED datasheet rather than the measured emission spectrum. The teacher must decide whether to discard the violet point, how to report uncertainty, and how to guide the student's conclusion.
1. Identify the most likely sources of systematic error in the student's estimate of Planck's constant and distinguish them from random error. For each source, state whether it would tend to make the fitted slope, and therefore h, too high or too low.
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The fit uses V = (h/e)f − φ/e, so with f = c/λ the slope of V versus 1/λ is hc/e and h = (slope)e/c. A systematic error shifts the slope in a consistent direction; random error scatters points about the line.
- Violet turn-on read while the LED was already glowing: the recorded V is lower than the true threshold. The violet point has the largest 1/λ, so pulling down the high-x end reduces the fitted slope and makes h too low. This is systematic and likely the dominant effect because the violet point has high leverage.
- Datasheet peak wavelength instead of measured spectrum: LED emission is broad and the peak shifts with current and temperature. If the true peak is at shorter wavelength (larger 1/λ) than the datasheet value, the point is plotted too far left; the effect on slope depends on the pattern across LEDs, but it is systematic, not random.
- Voltmeter loading: a 1 MΩ meter across an LED in a series circuit can draw a small current and read a voltage lower than the open-circuit threshold, especially near turn-on. That also biases V low and h low. The effect is systematic but probably smaller than the violet error.
- Random error: reading the meter to the nearest 0.01 V and judging the exact turn-on point by eye. These scatter points but do not consistently shift the slope. The fact that the final value is 18% low, rather than scattered around the accepted value, points to systematic error.
2. Propose a revised procedure and analysis that would allow a fair test of the accepted value. Include how to handle the violet LED and how to report the result.
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Revise the measurement, not just the fit. (1) Measure each LED spectrum with a grating spectrometer or a calibrated photodiode plus filter, and use the weighted mean photon energy rather than the datasheet peak. (2) Detect first light with a photodiode or by extrapolating the linear I–V region, rather than watching for a dim glow; this is especially important for violet, where the eye is insensitive. (3) Use a high-impedance electrometer or correct for meter loading, and measure the LED voltage directly across the LED with the series resistor in place. (4) Take several trials per LED and record the meter resolution.
For analysis, plot V versus f (not 1/λ), fit a straight line with uncertainty, and propagate uncertainties into h. Do not simply discard the violet point. Either replace it with a better measurement or keep it with a larger uncertainty and show a sensitivity analysis with and without it. Report h = (value ± uncertainty) J·s and compare the interval with 6.626 × 10−34 J·s. A result that is low by many standard uncertainties after corrections would still be a reason to look for remaining systematic error, not to revise the constant.
3. The student wants to conclude that the accepted value of Planck's constant may be wrong. How should the teacher respond, using the nature of scientific knowledge?
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The teacher should affirm that scientific knowledge is tentative and open to revision, but also explain that tentativeness does not make every discrepant classroom result evidence against a well-established constant. Planck's constant is supported by many independent phenomena-blackbody radiation, the photoelectric effect, atomic spectra, and quantum electrodynamics-and by measurements with uncertainties far below 18%. A single uncalibrated LED experiment with identified systematic errors is much more likely to be wrong than the accepted value.
The student should reframe the conclusion as an evidence-based statement: 'Our estimate is h = ... ± ..., which is lower than the accepted value; after correcting for identified systematic effects, the remaining discrepancy is ...' The teacher can require the student to list confounds, calibrate the apparatus, and have another group replicate the measurement. If the discrepancy survived those steps, then it would be appropriate to discuss possible explanations. This models peer review and uncertainty rather than treating one measurement as a decisive test.