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The Photoelectric Effect

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The photoelectric effect is the name given to the emission of electrons in electromagnetic radiation.

The photoelectric effect and photoelectrons

An example is for electrons to be ejected from a metallic material after being set free from an atom by light with high energy impacting that material. The electrons ejected from the material are called photoelectrons. A simple explanation of the effect and important developments of the theory are listed below.

• The light energy depends on its wavelength and frequency. Higher frequency and shorter wavelength lead to more electrons being ejected.
• The photoelectric effect was first observed by Heinrich Hertz, who could not understand why it happened. Subsequent experiments made by other scientists helped to explain the phenomenon now known as the ‘photoelectric effect’.
• Theoretical developments by Albert Einstein and Max Planck explained the phenomenon by assuming that light as radiation was composed of discrete particles with fixed amounts of energy.
• A photon only needs a minimum amount of energy, called the work function, to release an electron from the material.
• Once the minimum amount of energy is surpassed, the rest of the energy is used to push the electron out of the metal plate at a certain velocity.
• Solar cells are an application of the photoelectric effect.

Frequency energy dependence

Experiments carried out to measure how light affects the emission of electrons from the plates delivered two main results.

1. The intensity of the light had no effect on the energy of the electrons emitted.
2. The frequency of the light affects the energy of the emitted electrons. The higher the frequency, the faster the electrons were emitted.

The work function

The amount of energy needed to release an electron is called the ‘work function’ (φ), which is different for each material. The energy is specified as the product of the Planck constant ‘h and the light frequency ‘f’:

The Planck constant has a value of:

The work function is measured in electron volts or eV.

Albert Einstein and the photoelectric effect

The first experiments describing the photoelectric effect failed to explain why the brightness of the light did not affect the emitted electrons. The electron velocity did not change when the lights were brighter; the electrons only moved faster when higher light frequencies were used.

Albert Einstein discovered that the increase of the kinetic energy affecting the photoelectrons was proportional to an increase in the frequency of the light. If conservation must occur, then the lights energy was proportional to its frequency, and the light was acting as a particle where its energy is equal to the product of the Planck constant h and the light frequency f.

And if the lights energy is carried by the photons (lights particles), we get:

How are the photon theory of light and the photoelectric effect related?

If we connect Einstein’s explanation concerning the light and the photoelectric effect discovered by earlier experiments, we arrive at the expression that explains the photoelectric effect.

A certain amount of energy is needed to remove an electron from the metal plate. A photon must provide this minimum amount of energy known as the work function:

If the energy exceeds this minimum value, we get the work function plus an excess.

The energy excess that is transferred to the electron is the photons energy in the form of kinetic energy.

Figure 1. The photoelectric effect can be described using energy conservation between the photon energy impacting the electron at the metallic plate and the energy used to remove the electron from the metal plate or φ and the energy excess that is transformed into kinetic energy. Source: Manuel R. Camacho, StudySmarter.

An example of the photoelectric effect

You have a particle emitted from a copper plate that has a kinetic energy of 2.0 [eV]. You wish to determine the energy and the frequency of the photon that released the electron.

The work function of copper (Cu) is 5 [eV]. This is the energy needed to release the first electron.

If the kinetic energy of the electron after the photon impact is 2.0 [eV], then the photon energy must be the sum of both.

One electron volt (eV) is equal to 1.6 * 10^-19 Joules, which we multiply by seven.

If the photon energy is equal to the Planck constant and the photons frequency, we can replace Ephoton with hf .

The Planck constant is 6.62 * 10 ^ -34 [J / Hz]. Using this, we can solve for f and divide 11.22⋅10^-19 [J] by 6.62 * 10 ^ -34 [J / Hz].

This gives us the frequency of the photon.

The Photoelectric Effect - Key takeaways

• The photoelectric effect is a phenomenon describing the emission of electrons from a metallic plate caused by the impact of electromagnetic radiation, also known as photons.
• In order to release a photoelectron, a certain amount of energy, known as the work function, must be applied to the plate.
• The relationship between the kinetic energy and the frequency means that the energy of the photons is directly proportional to their frequency.
• Early experiments used brighter light, thinking the intensity was related to the electron energy. However, this turned out to be wrong.

It is the minimum frequency needed for an electron to be released from the material.

Some well-known applications are solar panels, light metres for cameras, phototransistors, photodiodes, and copy machines.

Einstein explained light as a particle with a certain amount of energy, which was directly proportional to the light frequency and the Planck constant. The conservation of energy then says that the energy of the light impacting the electron had to be transferred as kinetic energy plus the energy needed to release the electron from the material.

The short answer is yes. The photoelectric effect is the ionisation of a material due to the emission of a photoelectron by a photon.

However, this phenomenon can also happen in gases, liquids, and solids. Solids and liquids are somewhat special, as the structure of the atom’s molecules causes them have something called an ‘electronic band structure’.

Final The Photoelectric Effect Quiz

Question

What is the photoelectric effect?

It is the emission of electrons after high-frequency light impacts a metallic plate.

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Question

Who first observed the photoelectric effect?

Heinrich Hertz.

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Question

Name two scientists who contributed to explaining the theory behind the photoelectric effect?

Albert Einstein and Max Planck.

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Question

What is the work function?

It is the minimum energy needed to release an electron by a high-frequency photon.

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Question

Which light did Hertz use in his experiments?

UV light.

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Question

Does the energy of the light depend on the brightness?

No, it doesn’t.

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Question

What property of the light was found to eject the electrons more easily?

The frequency.

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Question

Does the energy of the light depend on its frequency?

Yes, it does.

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Question

The energy of a photon is equal to the product of a constant and a variable. Can you name them?

The Planck constant and the photon frequency.

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Question

The energy of the photon releasing the electron is split in two. One part, the work function, removes the electron from the metal? What happens to the rest of the energy?

It becomes the kinetic energy of the emitted electron.

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Question

If the frequency of the photon increases, what happens to the photoelectrons emitted by the material?

They move faster.

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Question

What happens if the energy of the photon is smaller than the work function?

No photoelectrons will be released.

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Question

What happens if you shine a light with lower energy than the work function on the copper plate and then increase the brightness?

Nothing, as the energy does not depend on the intensity of the light.

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Question

What happens if you shine a light with lower energy than the work function on the copper plate and then increase the frequency considerably.

Some electrons might start to be ejected.

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Question

If the work function of silver can be taken as 4.5[eV] and a photon of 4.0[eV] impacts it, will it emit an electron?

No, it won’t, as the energy is lower than the work function.

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Question

If the work function of gold is 5.1[eV] and a photon of 7.0[eV] impacts it, will it emit a photoelectron?

Yes, it will, and its kinetic energy will be equal to 1.9[eV].

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