Planck’s constant with LEDs

The aim of this experiment is to explore the photoelectric effect and hence determine Planck’s constant (h). For this we use different colour LEDs to determine the threshold voltage. The equipment used is a photon energy array (see below), though all you would need to replicate this kit is a potentiometer with some different coloured LEDs.

Background Physics

Electrons emitted as a result of the photoelectric effect have a certain kinetic energy and is independent of the intensity of the light. Einstein’s explanation for these observations was that light itself is quantized. The size of these “packets” of energy, photons, was determined in units of as Planck’s energy element. At low voltage no light is emitted form an LED. As V increases electrons in the semi-conductor gain sufficient energy from the electric field to make a transition from the conduction to the valence band. During the transition an electron loses energy equal to the gap between these bands. Energy is converted to a photo of light. For small energy (E) values, the photon frequency (f) will be low: E = hf

In the experiment the measured voltage is the threshold voltage (V). Since we know the wavelength we can calculate Planck’s constant for each LED remembering that the energy (E) is given by: E = eV where e is the charge of the electron (1.6×10^-19C). Thus we are left with:

E = eV = hf = hc / λ

where c is 3×10⁸ m/s

Method

To use the photon energy array a 5V dc power supply is used. The photo energy array operated between 430 -> 950nm.

• Using a multimeter measure the voltage and current.
• Visually observe when the light appears (to avoid background light the black tube should be used – this is the threshold voltage
• Alternatively measure when the current is just flowing.
• For each reading you can use the above equation to determine h
• This can also be determined by drawing a graph of wavelength and voltage
• A graph of the inverse wavelength against V should give a straight line and the gradient will be Planck’s constant.

Comments

The above is an adequate description of the experiment however there are further complications. Electron transitions across the gap usually result in the production of lattice vibrations (phonons), so this will mean that each photon are of slightly lower energy than measured from the equations.