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Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
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Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
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Energy Conduction in a 2D Numerically Modeled Solid Lattice Unbalanced Gas Dynamics:Energy Flow in a Gas
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Photoelectric Effect

Introduction

The photoelectric (PE) effect was the second big pillar that supported the quantum theory that had been initiated by Max Planck in 1901 to explain black body radiation. The PE effect data that had been obtained experimentally was explained by a surprisingly simple theory for which Albert Einstein received the Nobel prize. It showed that electrons were emitted from a photocathode individually and with kinetic energy that depended on the wavelength of the light incident on the cathode.

Basic Workings

To avoid a lot of other difficulties, I elected to use the oscilloscope on the right as a readout for the PE effect. The equation for the electron kinetic energy, `E_e`, at the collecting electrode (CE) is:

`E_e=hc/lambda-eV`

where h is Planck's constant, c is the speed of light, `lambda` is the wavelength of the incident light, `e` is the charge on the electron and V is the retarding voltage. As a reference, for lambda=400 nm, `hc/lambda=5*10^(-19)` Joules while, for V=1 volt,

To avoid a lot of other difficulties, I elected to use the oscilloscope on the right as a readout for the PE effect. The equation for the electron's kinetic energy at the CE is: where h is Planck's constant, c is the speed of light, `lambda` is the wavelength of the incident light, e is the charge on the electron and V is the retarding voltage. As a reference, for `lambda=400 nm`, `hc/lambda=5*10^(-19)` Joules while, for V=1 volt, `eV=1.6*10^(-19) "Joules"`. Thus it will require about 3 volts to completely cut off the photocurrent when `lambda`=400 nm.

Electron Work Function

To remove an electron from the photocathode, the photon has to supply enough energy to overcome the cathode surface potential barrier which is called the work function. For simplicity, in this animation we will set the work function energy to zero.
Work Function
Electron Affinity

Effect of Voltage Applied to Collector

We want to know how much energy the photoelectrons have at the collector. Since these electrons have negative charge we can apply just the right negative voltage, `V`, to the collector to cancel their speed and energy. In the cylindrical geometry that we use here the radial potential, `V_r`, versus distance from the collector center is

`V_r=V/(r_c)'`

where `r_c` is the collector radius. Since the electrons start at the photocathode radius `r_(pc)` and colud be collected at `r_c` their energy loss, `deltaE', is

`deltaE=-eV(1/r_(pc)-1/(r_c))`

where `e` is the electron charge which is negative.

I order to compute changes in electron radial speed inward, we need the radial electric field, `E_r`, due to the potential which is just the negative of the radial gradient of `V_r`.

`E_r=-(dV_r)/(dr)=V/(r^2)'`

Since V is negative and e is negative, the radial force, `(eV)/r^2`, on an electron is positive outward which slows the electron's inward moving speed as expected.

How the Animation is Arranged

To keep it simple I use short monochromatic light pulses that start at the exit of the monochromator (MC). The photon directions are such that they will fill the entire photocathode. The photocathode is a semicircle which is centered on the collection electrode. Also to keep it simple, the photoelectrons are emitted toward the center of the circle. When the electrons hit the collection electrode, that results in a negative current flow through a current meter. The above assumes that the negative bias on the collection electrode (CE) is not large enough to repel the photoelectrons. The photoelectrons will have energies that are a function of the frequency of the light photon that ejected them. After all the photoelectrons have been ejected, a new light pulse of different optical frequency is started at the MC.

Measuring the Energy of the Photon

Since we know the maximum energy that the collector electrode (CE) can exert to stop the photo-electron (PE) and we know the initial kinetic of that photon for each wavelength, for some MC wavelength the PE will just make its way to the CE. For that wavelength the energy is just the maximum energy that the CE can exert. As the MC wavelength is stepped, the photon energy is listed above the animation. Also the electron turnaround radius is listed. Comparison of either pair these figures shows how close the photon energy is to the maximum CE repulsion energy.

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