Objective: Determination of Planck’s constant using light emitting diodes (LED’s) by observing the ‘reverse photo-electric effect’.
Theory: If a bias voltage is passed across the LED, which is equal or greater than the difference in the energy of the bands, i.e. the barrier potential, then the bands will ‘line up’ and a current will flow. When current flows, electrons flow from the conduction band of the N type conductor and are forced up into the conduction band of the P type. Since the P type conductor’s valance band is lacking in electrons and we are overpopulating its conduction band with the bias voltage the electrons readily fall into the ‘holes’ in the valance band of the P type conductor. When they fall, this energy is released in the form of a photon. The energy of the photon emitted can be written as:
Where h is Planck’s constant and v is its frequency. The energy of one electron is the charge of an electron (i.e. the current flow of one electron per second in amps) times the voltage. Using this knowledge we then form the equation:
where e = 1.6 x 10-19 C (electron charge)
We then solve equation (1) for h and replace the E term with the equivalent of E in equation (2), as well as replace with:
Where c = 3 x 108 m/sec (speed of light)
We then get:
Or this equation can be rewritten as
It is this equation that we will use to determine Planck’s constant.
The Setup facilitates determination of Planck’s Constant (h) by measuring the voltage drop across light-emitting diodes (LEDs) of different colors at a constant current. Current is chosen such that bulk resistance of the LED is neglected. A graph of V vs. λ-1 is plotted and its gradient gives the value of Planck’s Constant as per equation (5).
Planck’s Constant Kit consists of the following parts: