# The Photoelectric Effect

The photoelectric effect is when electrons are emitted from electromagnetic radiation. This process is named after the way light (electromagnetic radiation) can knock electrons loose from metal. It's an important concept in physics and helps us understand how light and matter interact. If you want to learn more about the photoelectric effect, keep reading!

## The photoelectric effect and photoelectrons

The photoelectric effect happens when light with high energy knocks electrons loose from a metal material. These electrons are called photoelectrons. The amount of electrons ejected depends on the light's wavelength and frequency. Heinrich Hertz was the first person to observe the photoelectric effect, but he didn't understand why it happened. Other scientists later explained it by saying that light was made up of particles with fixed amounts of energy. These particles are called photons. A photon only needs a minimum amount of energy, called the work function, to release an electron from the material. Once the energy surpasses the minimum amount, the electron is pushed out of the metal plate at a certain speed. Solar cells use the photoelectric effect to work.

### Frequency energy dependence

Scientists conducted experiments to see how light affects the emission of electrons from plates. They found two main results. First the light didn't affect the energy of the emitted electrons. Second, the frequency of the light affected the energy of the emitted electrons. If the frequency was higher, the electrons were emitted faster.

### The work function

The Planck constant has a value of 6.626 x 10^-34 Js . The work function is the amount of energy needed to release an electron from a material and is measured in electron volts (eV). The energy is specified as the product of the Planck constant 'h' and the light frequency 'f': hf = φ [^2]. This can be seen in the Khan Academy article on the photoelectric effect [^3], which states: "The energy of the incident photon must be equal to the sum of the metal's work function and the photoelectron kinetic energy: h*v = φ + KE". The LibreTexts article on the photoelectric effect also states: "These direct measurements allow us to determine experimentally the value of Planck’s constant, as well as work functions of materials."

## 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 light’s 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’.

The photon theory of light and the photoelectric effect are related in that the photon theory 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, the work function plus an excess is transferred to the electron in the form of kinetic energy.

### An example of the photoelectric effect

To determine the energy and frequency of the photon that released the electron, we can use the given information. The kinetic energy of the electron is 2.0 [eV], and the work function of copper is 5 [eV]. Therefore, the energy of the photon is equal to the sum of the kinetic energy and the work function:

E_photon = E_kinetic + work function
E_photon = 2.0 [eV] + 5 [eV]
E_photon = 7.0 [eV]

To convert this energy to joules, we can multiply by the conversion factor 1.6 * 10^-19 [J/eV]:

E_photon = 7.0 [eV] * 1.6 * 10^-19 [J/eV]
E_photon = 1.12 * 10^-18 [J]

The energy of a photon is equal to the product of the Planck constant 'h' and the frequency 'f':

E_photon = h * f

Rearranging this equation, we can solve for the frequency 'f':

f = E_photon / h

Substituting the values we have calculated, we get:

f = 1.12 * 10^-18 [J] / 6.62 * 10^-34 [J/Hz]
f = 1.69 * 10^15 [Hz]

Therefore, the energy of the photon that released the electron is 7.0 [eV] and the frequency is 1.69 * 10^15 [Hz].

Key takeaways from the photoelectric effect include:

• The emission of electrons from a metallic plate is caused by the impact of electromagnetic radiation, or photons.
• A certain amount of energy, known as the work function, must be applied to the plate to release a photoelectron.
• The energy of the photons is directly proportional to their frequency.
• Early experiments incorrectly assumed that the intensity of the light was related to the electron energy.

## The Photoelectric Effect

What is the threshold frequency for the photoelectric effect?

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

What are the applications of the photoelectric effect?

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

How did Einstein explain the photoelectric effect?

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.

Does the photoelectric effect only work on metals?

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’.

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