Overview
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The photoelectric effect was first noticed in the late nineteenth century by Heinrich Hertz, who noticed that when ultraviolet light shines on a metal surface, electrons are ejected from the metal and create an electric current. It is possible to set up a circuit to see how many electrons come out of the metal and how fast. The following results can be observed:
- The number of electrons per second increases as the intensity of the light increases; the current turns out to be directly proportional to the intensity of the light.
- The electrons emerge with varying kinetic energies (speeds). However, the maximum energy of the electrons does not depend on the intensity of the light.
- If the frequency of the light falls below a minimum value, called the threshold frequency, there are no electrons ejected no matter how intense the light is.
- The threshold frequency is different for different metals.
- No matter how low the intensity of the light, electrons are ejected instantaneously, assuming the frequency of the light is higher than the threshold frequency.
Not all of these results can be explained with the classical wave model of light. If light is acting like a wave, energy should be proportional to intensity. More intense light would eject electrons more quickly and give photo-electrons more energy. In the leading model at the time, there would be no reason for any dependency on the frequency of the light.
The explanation of the photoelectric effect is credited to Albert Einstein. He suggested that light does not act as waves when it interacts with matter; instead the light has its’ energy concentrated in photons. Each photon has energy E = hf, where h is the Planck’s constant (6.63 x 10-34 Js) and f is the frequency of the light.
Electrons are bound in a metal; ordinarily they do not spontaneously jump from metal surfaces and create currents. Work must be done to free an electron from a metal. The deeper the electron is in the metal, the more work must be done to free the electron. The minimum energy required to remove an electron from a piece of metal applies to an electron at the surface of the metal. This minimum energy is called the work function and is given the symbol Eo. The work function energy differs for different metals. Einstein assumed that when light strikes a metal, a single photon interacts with a single electron, meaning the full energy of the photon is transferred to the electron. If the energy of the photon is greater than the work function energy of the metal, the electron will be ejected from the metal and any excess energy will be present in the form of the kinetic energy after the electron is removed.
The following equation describes the conversion of energy in the photoelectric effect:
Where hf is the energy of the photon (f is the frequency, h is planck's constant, given above), E0 is the work function of the metal, m is the mass of the electron, and v is the speed of the electron (1/2mv2 is the kinetic energy of the electron).
It is very difficult to measure the speed of an electron in the lab (they tend to move very fast), so instead we can measure the amount of voltage required to stop the electron: the stopping voltage. Voltage is what usually pushes electrons through circuits, so instead of speeding up the electrons through the circuit, we can slow them down until they stop. The work (or energy) required to stop an electron can be written as:
Where W is the work, e is the charge of an electron (1.6x10-19 C), and V is the voltage. We can now express the energy of the electrons in terms of the voltage required to stop them:
So we can use the the frequency of the light and the stopping voltage to find the work function of a metal (with a little rearranging):
In this lab, you will be given the wavelength of several different light emitting diodes, which will be able to eject electrons from the metal inside the apparatus. You will not be able to see electrons directly, but you will be able to measure the voltage needed to stop them. From that, you can calculate the work function of the metal, and Planck’s constant. It is helpful to know that the wavelength and frequency of a light wave are related by the speed of light:
Where c is the speed of light (3x10^8 m/s), frequency is in hertz, and wavelength is in meters.
Procedure:
Follow the instructions from your TA to setup the Pasco CAPSTONE data collection software.
You will be using five different LEDs. Each can be plugged into the connector at the end of the black wire at the end of the box. Please be careful when removing the lights from the connector: Pull the connector, not the cord. If the LED looks like it's a white bluish color, it's probably the UV LED: Do not look directly into the ultraviolet light; it can harm your eyes.
Once attached to the cord and producing light, place the LED into the hole on top of the apparatus, light side down. The CAPSTONE software should display a graph of voltage versus time. The voltage will also be recorded in the box marked “Digits.” Rotate the LED slowly in the hole until the voltage is maximized. (This may be more noticeable in some colors than others, due to the differences in the internal design of the LEDs.) The highest voltage you can get is the stopping voltage, you should record that value. Be sure to press the red reset button on the box after each different diode.