What is the Photoelectric Effect?

Though originally observed in 1839, the photoelectric effect was documented by Heinrich Hertz in 1887. It was originally called the Hertz effect in fact, though this name fell out of use. When a light source (or, more generally, electromagnetic radiation) is incident upon a metallic surface, the surface can emit electrons. Electrons emitted in this fashion are called photoelectrons (although they are still just electrons).

By administering a negative voltage potential to the collector, it takes more energy for the electrons to complete the journey and initiate the current. The point at which no electrons make it to the collector is called the stopping potential or voltage cutoff V_co, and can be used to determine the maximum kinetic energy KE_max of the electrons. It is significant to note that not all of the electrons will have this energy, but will be emitted with a range of energies based upon the properties of the metal being used. The above equation allows us to calculate the maximum kinetic energy or, in other words, the energy of the particles knocked free of the metal surface with the greatest speed, which will be the trait that is most useful in the rest of this analysis.

The Classical Wave Explanation

In classical wave theory, the energy of electromagnetic radiation is carried within the wave itself. As the electromagnetic wave (of intensity I) collides with the surface, the electron absorbs the energy from the wave until it exceeds the binding energy, releasing the electron from the metal. The minimum energy needed to remove the electron is called the work function of the material.

Three main predictions come from wave theory:

1. The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy.

2. The photoelectric effect should occur for any light, regardless of frequency or wavelength.

3. There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.

There was also no significant delay (less than 10^-9 s) between the light source activation and the emission of the first photoelectrons. As you can tell, these three laws are the exact opposite of the wave theory predictions. Therefore, Max Planck speculated that just like matter is composed of small particles called atoms, energy is composed of small "chunks" called quanta. Einstein said that light also consisted of particles or quanta called photons. The energy of each photon of light is given by the following equation where h is called Planck's constant (6.63 x 10^-34 Js)

E=hf

In the early 1900’s Einstein won the Nobel Prize for the following simple Photoelectric Equation:

KE = hf - w

This simply says that if the work function (w) of a certain metal is less than the energy of an incoming photon (hf) then photoelectrons will be ejected with a certain amount of kinetic energy (KE). The larger the photon energy (hf) is compared to the work function of the metal, the more kinetic energy and thus the more velocity the ejected photoelectrons will have.

If the photon energy is equal to or less than the work function of the metal then the photoelectric effect will not be observed because no photoelectrons will be ejected. If you set the kinetic energy of the photoelectrons to zero, then the cutoff frequency can be calculated by simply dividing the work function of the metal by Planck’s constant. In the graphic at the top of this page, the frequency is given by the Greek letter (nu) which looks like a v. Don't get confused! To perform calculations in this excel program you will need to know at least three other conversions:

c = fλ (where c is the speed of light and is equal to 3x10⁸ m/s)

1 meter = 1x10⁹ nm

1 electronVolt (eV) = 1.6x10^-19 J

Before we start on this excel program we better test ourselves to see if we understand the math behind the photoelectric effect. Let's do this by validating the information about the blue photon in the picture at the top of this page. Clearly we can see that a photoelectron is ejected because the incoming blue photon energy of 3.1 eV is greater than the work function of Potassium metal which is 2.0 eV. This means that the ejected electron will have kinetic energy of 1.1 eV.

The blue photon has a wavelength of 400 nm. Convert this to meters:

λ = 400/1x10⁹ = 4x10^-7 meters

Determine the frequency of this blue photon:

frequency = c/λ = 3x10⁸/4x10^-7 = 7.5x10¹⁴ Hz

Determine the energy of this blue photon in Joules:

Energy = hf = (6.63 x 10^-34)(7.5x10¹⁴) = 4.97x10^-19 Joules

Convert the energy of this blue photon into eV:

Energy = 4.97x10^-19/1.6x10^-19 = 3.1 eV

(This confirms the above graphic)

Convert the work function into Joules:

Energy = (2.0)(1.6x10^-19) = 3.2x10^-19

Determine the kinetic energy of the ejected electron in Joules:

KE = hf-w = 4.97x10^-19 - 3.2x10^-19 = 1.77x10^-19 Joules

Knowing that KE = 0.5mv² and the mass of an electron is 9.1x10^-31 kilograms, determine the velocity of the ejected electron:

Solving for v=SQRT(2KE/m)

velocity = SQRT((2)*(1.77x10^-19)/(9.1x10^-31)) = 6.2x10⁵ m/s

(This confirms the above graphic)

Program Criteria:

INPUTS:

• A user can choose from a dropdown of these 10 elements: Cadmium, Calcium, Carbon, Cesium, Lithium, Neodymium, Potassium, Silver, Sodium and Zinc.

• A user can choose from a dropdown of incident photon wavelengths from 100-700 nm with increments of 25.

• A user will click a button to see the results.

OUTPUTS:

• A graphical output of KE vs. frequency will be displayed.

• The background color of the chosen wavelength will change to whatever the user chooses.

• The critical wavelength (nm) for the chosen element will be displayed.

• The background color of the critical wavelength will change to whatever is in the cell.

• The kinetic energy (eV) of the emitted electron will be displayed.

CRITERIA & CONSTRAINTS:

• You will have to research the work functions of the given elements.

• Your program should have an impressive interface. (colors and graphics)