Measuring Planck’s Constant with LEDs

An electron crossing a potential difference V transfers energy eV. In a simplified LED model, a characteristic emitted photon has energy hf, giving eV≈hf=hc/λ. Different colours have different characteristic wavelengths and therefore different onset voltages.

The approximation does not claim every joule of electrical input leaves as one identical photon. LEDs have finite spectral widths and non-radiative losses. No semiconductor-band theory is required here; focus on the measurement and the energy model.

Connect each LED with correct polarity, a protective series resistor and a variable low-voltage supply. Increase voltage slowly and measure the pd directly across the LED. Define a consistent onset criterion, such as a specified small current or an agreed low-light visibility method, rather than silently changing the criterion between colours.

Use manufacturer wavelength data or an appropriate spectral measurement and record its uncertainty. Repeat readings, control ambient light if judging visible onset, and keep current within the device rating. A resistor protects the LED but its voltage drop must not be included as part of the LED voltage.

Plot onset voltage vertically against frequency c/λ horizontally. The simple model predicts gradient h/e; a plot against 1/λ instead has gradient hc/e. A non-zero intercept and scatter can reveal that onset voltage is only an approximation to the characteristic photon energy.

Choose a wide range of frequencies and fit the dataset rather than relying on one colour. Repeated onset judgements assess random variation, but a consistently biased criterion or wavelength value remains systematic. Compare the estimated h and its uncertainty with the accepted value without forcing an intercept of zero to obtain agreement.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.