Wait, What? The voltage where an LED first looks bright is not exactly the energy of one photon divided by the electron charge.
That approximation is good enough to reveal quantum physics in a classroom, but it hides the device physics. An LED is a semiconductor junction with a band gap, carrier transport, non-radiative losses, series resistance and a human or detector-defined threshold for “light begins.” The experiment can estimate Planck’s constant—but only if we understand why the estimate is approximate.
The practical’s RFE is therefore not “get 6.63 × 10⁻³⁴.” It is: can you build a defensible bridge from an electrical threshold and an optical wavelength to the quantum relation E = hf, while recognising what the LED adds to that bridge?
The idealised model
A photon of frequency f has energy:
E = hf
For light of wavelength λ in vacuum:
f = c/λ
In the simplest LED model, electrical energy eV associated with the junction threshold is linked to photon energy:
eV ≈ hf = hc/λ
Rearranging:
V ≈ (hc/e)(1/λ)
This predicts an approximately linear graph of threshold voltage V against 1/λ, with gradient hc/e. Hence:
h ≈ gradient × e/c
Why LEDs are useful
Different LED colours are produced by semiconductors with different band gaps. Blue LEDs emit higher-frequency photons than red LEDs and usually require a larger forward voltage before substantial light emission occurs.
The Institute of Physics notes that measuring the minimum or “striking” voltage for differently coloured LEDs can provide a classroom estimate of Planck’s constant. See the IOP Classroom Physics quantum-practical resource.
Threshold voltage is not a uniquely defined physical point
An LED current rises non-linearly with forward voltage. Light output can begin below the voltage where the human eye first notices it. Different observers, room lighting and LED brightness can therefore give different “turn-on” voltages.
A stronger method defines the threshold consistently—for example by a specified small current, a photodiode signal criterion, or extrapolation of a suitable portion of the I–V curve. The key is to use the same definition for every LED.
Why “just when visible” is a weak but educational method
Human vision is more sensitive to some wavelengths than others. A green LED may be seen at a lower optical power than a deep red one simply because the eye responds differently. Using visual onset can therefore create a colour-dependent systematic bias.
If the practical uses visual threshold, reduce ambient light, use the same observer, approach threshold in the same direction and repeat the estimate. Better still, use an optical detector where available.
Wavelength is not just “the colour written on the bag”
LEDs emit over a finite spectrum, not one infinitely sharp wavelength. A manufacturer’s nominal wavelength may differ from the actual peak or centroid wavelength of the device. Temperature and current can shift emission slightly.
For stronger work, measure the emitted wavelength with a diffraction grating or spectrometer and carry that uncertainty into the analysis. This connects naturally to the existing diffraction-grating practical without duplicating its measurement ownership.
Electrical protection matters
An LED should be used with an appropriate current-limiting resistor or controlled supply so current does not rise excessively once the junction conducts. The practical is about measuring threshold behaviour, not overheating the device.
Voltage should be measured across the LED itself, not across the LED-plus-resistor combination, because the idealised eV energy term belongs to the junction potential difference.
Semiconductor physics sets the evidence boundary
The photon energy is related to the semiconductor band structure, but the measured terminal voltage also reflects contacts, carrier distributions, recombination pathways and series resistance. Not every electron crossing the device produces exactly one photon with energy eV.
This is why the experiment typically gives an order-correct estimate of h rather than a metrology-grade determination. Since 2019, the SI defines Planck’s constant to the exact value 6.62607015 × 10⁻³⁴ J s; a classroom LED experiment is a test of the quantum relationship, not a new calibration of the SI. See the IOP Planck resource.
Quantitative window: one LED
Suppose a red LED has measured wavelength λ = 630 nm and threshold voltage V = 1.90 V.
Electrical energy scale:
eV = (1.602 × 10⁻¹⁹ C)(1.90 V) ≈ 3.04 × 10⁻¹⁹ J
Frequency:
f = c/λ ≈ 3.00 × 10⁸ /(630 × 10⁻⁹) ≈ 4.76 × 10¹⁴ Hz
A one-point estimate gives:
h ≈ eV/f ≈ 6.39 × 10⁻³⁴ J s
This is close to the defined h, but one data point cannot reveal whether the agreement is robust or accidental.
Graph method: stronger than one colour
Measure several LEDs across red, amber, green and blue where suitable. Calculate 1/λ for each and plot V against 1/λ.
If the idealised model were exact and there were no device offsets, the line would pass through the origin. Real data often show a non-zero intercept because threshold voltage includes device effects not captured by eV = hc/λ alone.
Use the gradient to estimate h rather than forcing the line through zero. The intercept is evidence about model incompleteness, not a reason to delete data.
Alternative graph: eV against frequency
Plot eV on the vertical axis against f on the horizontal axis. Then the gradient has units of J s and ideally approximates h directly:
eV ≈ hf + constant offset
This graph makes the quantum relation visually explicit and allows the intercept to represent systematic device threshold effects in a simple empirical model.
Uncertainty: wavelength and threshold both matter
If λ is quoted only to ±20 nm, frequency uncertainty may be several percent. If visual threshold is uncertain by ±0.05 V, that can also contribute several percent. A graph using multiple colours reduces dependence on any single LED but does not erase systematic threshold bias shared across all colours.
Repeat threshold estimates, report scatter, and avoid excessive significant figures. A result such as 6.4 × 10⁻³⁴ J s may be more defensible than 6.417382 × 10⁻³⁴ J s from school apparatus.
Observation versus inference
Observation: “The blue LED produced the chosen detector signal at 2.75 V; its measured peak wavelength was 465 nm.”
Transformation: calculate f and eV.
Inference: “Across several LEDs, electrical threshold energy increases approximately linearly with photon frequency.”
Stronger inference: “The graph gradient provides an approximate experimental estimate of Planck’s constant under the LED threshold model.”
Failure modes that cap standards
- Threshold defined by eye: human spectral sensitivity biases colours differently.
- Nominal wavelength used blindly: actual emission spectrum may differ.
- Voltage measured across resistor + LED: junction voltage is overestimated.
- Excess current: device heats and emission/voltage characteristics drift.
- Only two LEDs: gradient is fragile and outliers are hard to diagnose.
- Best-fit line forced through origin: systematic offset is hidden.
- Claiming eV equals photon energy exactly: semiconductor and junction effects are ignored.
Unfamiliar transfer: photoelectric effect
The photoelectric effect also links photon energy to an electron energy scale, but its equation includes a work function:
hf = Φ + Kmax
The LED experiment runs the logic in the opposite technological direction: electrical carriers recombine and emit photons. Both reveal that photon energy scales with frequency through h, but their intercept terms arise from different physics.
Secondary → JC → deeper Physics
Secondary: recognise that different LED colours have different wavelengths and electrical turn-on behaviour.
JC: use E = hf and f = c/λ, estimate h from a multi-LED graph, discuss threshold ambiguity and evaluate systematic uncertainty.
Deeper Physics: LED spectroscopy connects to semiconductor band structure, Fermi levels, electroluminescence, external quantum efficiency, temperature dependence and precision optical/electrical metrology.
Checkpoint 1: the bright-room problem
Student A finds red LED onset at 1.75 V in a dark room. Student B finds 1.92 V under bright classroom lighting. What changed?
Checkpoint 2: the intercept
The V-versus-1/λ graph is straight but does not pass through the origin. Should the student force it through zero because theory says V = hc/(eλ)?
Answer key and WHY reasoning
Checkpoint 1: the visual threshold criterion changed because ambient light altered detectability. This is an observer/method effect, not necessarily a change in LED band gap.
Checkpoint 2: no. Use an unconstrained best-fit line and interpret the intercept as evidence that the simple threshold model omits device offsets. Forcing zero can bias the gradient and therefore h.
How to study this practical
For each LED, write four quantities in a chain: wavelength → frequency → threshold voltage → electrical energy eV. Then ask which two are directly measured and which are calculated. Finally, list one optical and one electrical systematic error. This makes the experiment a model test rather than a constants exercise.
Evidence boundaries
An LED threshold experiment provides a classroom-scale estimate of Planck’s constant and evidence for energy-frequency proportionality. It does not determine h more accurately than the SI definition, and the simple eV ≈ hf model is an approximation to real semiconductor electroluminescence.
Authoritative next steps
- Institute of Physics: Classroom Physics quantum activities, including LEDs and Planck’s constant
- Institute of Physics: photon energy and frequency
- Institute of Physics: Planck and the exact SI value of h
- SEAB A-Level syllabus directory
Teaching Guide
For teachers and parents: ask students why an experiment can be scientifically valuable even though the accepted constant is already known exactly. Then compare visual-threshold and detector-threshold data. The lesson is not rediscovering h; it is learning how a simple device model exposes quantum proportionality—and how measurement assumptions shape the number obtained.