# Threshold frequency and wavelength relationship

### Photoelectric work function, Threshold frequency and Threshold Wavelength

Most elements have threshold frequencies that are ultraviolet and only a few dip down an energy-amplitude relationship and not the energy-frequency relationship except for tiny ripples on the surface (low intensity, short wavelength light). Find the threshold frequency of the metal and the wavelength of emitted electrons . Wavelength of incident light λ = nm. Work function of the. This gives rise to the equation E=hf. E In short, the smaller the work function the lower the threshold frequency. Now calculate the wavelength of this photon .

Later studies by J. Thomson showed that this increased sensitivity was the result of light pushing on electrons — a particle that he discovered in While this is interesting, it is hardly amazing. All forms of electromagnetic radiation transport energy and it is quite easy to imagine this energy being used to push tiny particles of negative charge free from the surface of a metal where they are not all that strongly confined in the first place.

The era of modern physics is one of completely unexpected and inexplicable discoveries, however. Subsequent investigations into the photoelectric effect yielded results that did not fit with the classical theory of electromagnetic radiation. When it interacted with electrons, light just didn't behave like it was supposed to.

Repairing this tear in theory required more than just a patch.

### Photoelectric effect (article) | Photons | Khan Academy

It meant rebuilding a large portion of physics from the ground up. It was Philipp Lenardan assistant of Hertz, who performed the earliest, definitive studies of the photoelectric effect.

Lenard used metal surfaces that were first cleaned and then held under a vacuum so that the effect might be studied on the metal alone and not be affected by any surface contaminants or oxidation.

The metal sample was housed in an evacuated glass tube with a second metal plate mounted at the opposite end.

## Homework Help: Threshold frequency and wavelength of electrons in the photoelectric effect

The tube was then positioned or constrained in some manner so that light would only shine on the first metal plate — the one made out of photoemissive material under investigation. Lenard connected his photocell to a circuit with a variable power supply, voltmeter, and microammeter as shown in the schematic diagram below.

He then illuminated the photoemissive surface with light of differing frequencies and intensities. Knocking electrons free from the photoemissive plate would give it a slight positive charge. Since the second plate was connected to the first by the wiring of the circuit, it too would become positive, which would then attract the photoelectrons floating freely through the vacuum where they would land and return back to the plate from which they started.

Keep in mind that this experiment doesn't create electrons out of light, it just uses the energy in light to push electrons that are already there around the circuit. The photoelectric current generated by this means was quite small, but could be measured with the microammeter a sensitive galvanometer with a maximum deflection of only a few microamps. It also serves as a measure of the rate at which photoelectrons are leaving the surface of the photoemissive material.

Note how the power supply is wired into the circuit — with its negative end connected to the plate that isn't illuminated. This sets up a potential difference that tries to push the photoelectrons back into the photoemissive surface.

When the power supply is set to a low voltage it traps the least energetic electrons, reducing the current through the microammeter. Increasing the voltage drives increasingly more energetic electrons back until finally none of them are able to leave the metal surface and the microammeter reads zero. It is a measure of the maximum kinetic energy of the electrons emitted as a result of the photoelectric effect. What Lenard found was that the intensity of the incident light had no effect on the maximum kinetic energy of the photoelectrons.

Those ejected from exposure to a very bright light had the same energy as those ejected from exposure to a very dim light of the same frequency. In keeping with the law of conservation of energy, however, more electrons were ejected by a bright source than a dim source. Later experiments by others, most notably the American physicist Robert Millikan infound that light with frequencies below a certain cutoff value, called the threshold frequency, would not eject photoelectrons from the metal surface no matter how bright the source was.

These result were completely unexpected. Given that it is possible to move electrons with light and given that the energy in a beam of light is related to its intensity, classical physics would predict that a more intense beam of light would eject electrons with greater energy than a less intense beam no matter what the frequency.

This was not the case, however. Actually, maybe these results aren't all that typical. Most elements have threshold frequencies that are ultraviolet and only a few dip down low enough to be green or yellow like the example shown above.

The materials with the lowest threshold frequencies are all semiconductors.

• Wave particle duality
• Photoelectric Effect
• Problems on Energy of Photon and Work Function

Some have threshold frequencies in the infrared region of the spectrum. The classical model of light describes it as a transverse, electromagnetic wave. See this article for more information about the basic properties of light. Scientists also believed that the energy of the light wave was proportional to its brightness, which is related to the wave's amplitude.

In order to test their hypotheses, they performed experiments to look at the effect of light amplitude and frequency on the rate of electron ejection, as well as the kinetic energy of the photoelectrons. Based on the classical description of light as a wave, they made the following predictions: The kinetic energy of emitted photoelectrons should increase with the light amplitude. The rate of electron emission, which is proportional to the measured electric current, should increase as the light frequency is increased.

To help us understand why they made these predictions, we can compare a light wave to a water wave. Imagine some beach balls sitting on a dock that extends out into the ocean.

The dock represents a metal surface, the beach balls represent electrons, and the ocean waves represent light waves. If a single large wave were to shake the dock, we would expect the energy from the big wave would send the beach balls flying off the dock with much more kinetic energy compared to a single, small wave.

This is also what physicists believed would happen if the light intensity was increased. Light amplitude was expected to be proportional to the light energy, so higher amplitude light was predicted to result in photoelectrons with more kinetic energy.

## Photoelectric effect

Classical physicists also predicted that increasing the frequency of light waves at a constant amplitude would increase the rate of electrons being ejected, and thus increase the measured electric current. Using our beach ball analogy, we would expect waves hitting the dock more frequently would result in more beach balls being knocked off the dock compared to the same sized waves hitting the dock less often. Now that we know what physicists thought would happen, let's look at what they actually observed experimentally!