13 Jul 2026
Determination of Planck's Constant Using LEDs
Aim
To determine Planck’s constant using the threshold voltages of LEDs of different colours.
Apparatus
LED panel, regulated DC supply, series resistor, voltmeter, milliammeter, and connecting leads.
Experimental arrangement
Theory
An LED is a forward-biased p-n junction. The forward bias lowers the junction barrier and injects electrons and holes into the active region, where they recombine. The electrical energy supplied per carrier is approximately $eV$, while the emitted photon carries energy $h\nu$. At threshold,
\[eV\approx h\nu=\frac{hc}{\lambda}.\]The measured voltage also contains a nearly constant junction and contact contribution. It therefore affects the intercept but not the slope of a graph of threshold voltage $V$ against frequency $\nu$. The slope is $h/e$:
\[h=e\frac{\Delta V}{\Delta\nu}.\]Observations
| LED colour | Wavelength (nm) | Frequency ($10^{14}$ Hz) | Threshold voltage (V) |
|---|---|---|---|
| red | 650 | 4.61 | 1.82 |
| yellow | 590 | 5.08 | 2.00 |
| green | 565 | 5.31 | 2.11 |
| blue | 470 | 6.38 | 2.55 |
Graph
Calculation
Using the red and blue readings,
\[\frac{\Delta V}{\Delta\nu}=\frac{2.55-1.82}{(6.38-4.61)\times10^{14}}=4.12\times10^{-15}\,\text{V s}.\]Therefore,
\[h=e\frac{\Delta V}{\Delta\nu}=(1.602\times10^{-19})(4.12\times10^{-15})=6.60\times10^{-34}\,\text{J s}.\]The straight-line fit using all four observations reduces the effect of individual LED threshold uncertainty and gives the final value close to this endpoint estimate.
Result
The value of Planck’s constant obtained from the LED graph is approximately
\[\boxed{h\approx6.6\times10^{-34}\,\text{J s}}.\]Viva Questions
- Why are LEDs of different colours used? Their emission frequencies are different.
- Why is a series resistor used? It limits current and protects the LED.
- What does the slope represent? $h/e$.
Discussion