Photoelectric Effect: Principle, Equation, Application, Experimental Setup

The photoelectric effect is a phenomenon where electrons can be ejected from the surface of a metal when it is exposed to light. The prefix “photo-” indicates that the electrons have been emitted from a metal surface due to the impact of light. This process is commonly known as photoemission, and the electrons that are emitted from the metal are referred to as photoelectrons. Photoelectrons are indistinguishable from other electrons in terms of their behavior and properties. The evidence provided by the photoelectric effect was significant in demonstrating that light is quantized, meaning it is transmitted in discrete packets.

What is Photoelectric Effect?

When a metal is exposed to light, the photoelectric effect occurs, causing the metal to emit electrons from its valence shell. The electron that is released as a result of the absorption of light is referred to as a photoelectron, and this process is widely recognized as photoemission.

The Photoelectric Effect provides evidence for the particle-like behavior of electromagnetic waves. Radiant energy can be classified into various types such as infrared, visible, or ultraviolet light, X-rays, or gamma rays. The material involved in the process can be a solid, liquid, or gas. Additionally, the particles released during the process can be ions (electrically charged atoms or molecules) or electrons.

The phenomenon had a crucial role in the advancement of modern physics due to the perplexing inquiries it posed regarding the characteristics of light, such as whether it behaves like a particle or a wave. These questions were ultimately resolved by Albert Einstein in 1905. The impact of this phenomenon is significant for research in various fields, ranging from materials science to astrophysics. Additionally, it serves as the foundation for numerous practical devices.

Principle of Photoelectric Effect

In the photoelectric effect, light is used to irradiate a metal surface. When light strikes the metal’s surface, photoemission takes place, and photoelectrons are ejected from the metal’s surface. The electrons in the metal atom get the wave’s photon’s energy, which causes them to become excited and release themselves with a specific velocity.

Equation for Photoelectric Effect

The energy of the photon is equal to the sum of the threshold energy of the metal and the kinetic energy of the photoelectron.

Thus, the equation of photoelectric wave is given by,

KE_max=hv–ϕ

where,

• KE_max = maximum kinetic energy of the photoelectron
• hv = energy of the photon.
• ϕ = work function of the metal

Work function is determined by the metal used, and it will change if the metal is changed. The work function is sometimes defined in terms of threshold frequency, which is the frequency of light for which the emitted Photoelectrons maximal kinetic energy is zero.

c=hv₀

where,

• v₀ = threshold frequency.
• h = Planck’s constant.

The maximum kinetic energy remains constant as the light intensity increases, but the value of photocurrent increases. 

Terminology Related to Photoelectric Effect

Photon

The smallest discrete unit of electromagnetic energy is a photon, also referred to as a quantum. It is the basic building block of all light.

All observers in a vacuum experience photons moving continuously at a constant speed of 2.998 x 108 m/s. The letter c represents the speed of light. Each photon possesses a unique amount of energy and momentum.

The energy held by a photon is related to the frequency of the light via Planck’s equation.

E = h𝜈 = hc/λ

Where,

• E denotes the energy of the photon
• h is Planck’s constant
• 𝜈 denotes the frequency of the light
• c is the speed of light (in a vacuum)
• λ is the wavelength of the light

Characteristics of a Photon

Photons possess fundamental characteristics that include:

• The photon flux density is directly proportional to the light intensity. It does not alter the energy of the radiation.
• A photon is not affected by electric and magnetic fields. It is electrically neutral.
• A photon is massless.
• It is a particle that has a strong and durable structure.
• The emission or absorption of radiation can result in the creation or annihilation of photons.
• In a photon-electron collision, the conservation of energy and momentum is maintained.
• A photon does not have the ability to undergo decay independently.
• The energy of a photon can be transferred through its interaction with other particles.
• In comparison to electrons that possess a spin of 1/2, photons exhibit a spin of one. The object’s rotational axis is perpendicular to its direction of motion. The property of photons that enables the polarization of light is their intrinsic angular momentum, also known as spin.

Work function (ϕ)

In a metallic substance, the electrons are held in place by the attractive force of the nucleus. A specific amount of energy, known as the work function, is necessary to extract an electron from a metal surface. The term used to describe this phenomenon is the Work Function of the metal. The work function is an intrinsic property of a metal.
The work function is measured in electron volts (eV).
o1 eV = 1.6*10-19

Work function is determined by the metal used, and it will change if the metal is changed. Here is the work function of some elements.

The work function or threshold energy is the smallest quantity of thermodynamic work needed to extract an electron from a conductor and transfer it to a spot in the vacuum that is immediately outside the surface of the conductor.

Φ = hγ_th = hc/λ_th

Threshold frequency (γ_th)

It refers to the minimum frequency of light or radiation that can cause the photoelectric effect, which is the release of electrons from a metal surface. The property is consistent within a single metal, but different metals may exhibit different values.

If γ = Frequency of the incident photon and γ_th= Threshold frequency, then,

Condition I: γ < γ_Th, there will be no ejection of photoelectron and, therefore, no photoelectric effect.

Condition II: γ = γ_Th, photoelectrons are just ejected from the metal surface; in this case, the kinetic energy of the electron is zero.

Condition III: If γ > γ_Th, then photoelectrons will come out of the surface, along with kinetic energy.

Threshold Wavelength (λ_th)

The threshold wavelength (λth) refers to the wavelength of incident light that corresponds to the metal surface with the highest electron emission during photoelectric effect.

λ_th = c/γ_th

Experimental Setup for the Photoelectric Effect

The device is comprised of a glass tube that has been emptied of air, with a photosensitive material serving as the cathode (C) and a collector plate functioning as the anode (A). The quartz window allows the incident light to pass through. To facilitate the evacuation of photoelectrons, a battery is connected to the cathode. When the emitted photoelectrons hit the anode, it generates photocurrent. The photocurrent is measured by connecting a microammeter in series with the battery.

• An evacuated tube consists of two electrodes that are connected to an external circuit. The metal plate, which is to be irradiated, serves as the anode.
• Some photoelectrons that are emitted from the radiated surface have enough energy to reach the cathode, even though it has a negative polarity. These photoelectrons make up the current. This is a description of the apparatus.
• As the retarding potential increases, a decreasing number of electrons can reach the cathode, resulting in a drop in current. When the value of V exceeds a certain threshold, denoted as V₀, no additional electrons are able to strike the cathode, resulting in a complete drop of current to zero.

Read Also: Beer-Lambert Law

History and Timeline of Photoelectric Effect Discovery

• Heinrich Rudolf Hertz, a German physicist, discovered the photoelectric effect in 1887. Hertz made an observation regarding radio waves that when ultraviolet light is directed on two metal electrodes with a voltage applied across them, the voltage at which sparking occurs changes.
• In 1902, Philipp Lenard, a German physicist, clarified the relationship between light and electricity, which is why it is called photoelectric. He showed that when a metal surface is illuminated, electrically charged particles are released from it.
• These particles were found to be identical to electrons, which were first discovered by the British physicist Joseph John Thomson in 1897.
• Upon conducting additional research, it was discovered that the photoelectric effect is an occurrence where light and matter interact in a manner that cannot be accounted for by classical physics. This is due to the fact that classical physics solely characterizes light as an electromagnetic wave.
• An inexplicable observation was made that the maximum kinetic energy of the released electrons remained constant regardless of the intensity of the light. This contradicts the wave theory and instead shows that the kinetic energy is directly proportional to the frequency of the light. The light intensity determined the number of electrons released from the metal, which was measured as an electric current.
• Another intriguing observation was the lack of time delay between the radiation’s arrival and the electrons’ emission.
• In 1905, Albert Einstein developed a new corpuscular theory of light after observing unexpected behaviors. According to this theory, each particle of light, known as a photon, contains a specific amount of energy or quantum, which is determined by the frequency of the light. A photon carries energy denoted by E, which is equivalent to hf, where f represents the frequency of the light. The universal constant h was derived by the German physicist Max Planck in 1900 to explain the wavelength distribution of blackbody radiation, which refers to the electromagnetic radiation emitted from a hot body. The relationship between energy and wavelength can also be expressed as: E = hc/λ, where c represents the speed of light and λ represents its wavelength. This demonstrates that the energy of a photon is inversely proportional to its wavelength.
• Einstein believed that a photon would pass through the substance and give an electron its energy. The electron’s kinetic energy would decrease by a quantity known as the work function (comparable to the electronic work function), which indicates the energy needed for the electron to escape the metal, as it swiftly travelled through the metal until it ultimately exited from the substance. The photoelectric equation Ek = hf − ϕ , where Ek is the maximal kinetic energy of the expelled electron, was developed by Einstein using the principle of energy conservation.
• Despite the fact that Einstein’s model predicted the emission of electrons from a lit plate, his photon idea was so radical that it was not widely accepted until it was given more experimental support.
• Additional confirmation came in 1916 when Robert Millikan, an American physicist, used exceedingly precise measurements to confirm Einstein’s equation and demonstrate with high precision that the value of Einstein’s constant h was equal to Planck’s constant.
• In 1921, Einstein received the Nobel Prize in Physics for describing the photoelectric effect.

Properties of Photoelectric Effect

• Absence of lag time: Electrons are emitted from the target material in the electrode almost instantaneously when radiation strikes it, even at low intensities of incident radiation.
• The threshold frequency is material-dependent, meaning that different materials exhibit different threshold frequencies.
• The current resulting from the photoelectric effect exhibits a linear relationship with the magnitude of the incident light.
• The energy of photoelectrons is directly proportional to the frequency of the incident light.
• The relationship between frequency and stopping potential is linear, and the process is instantaneous.

Factors Affecting the Photoelectric Effect

• The intensity of incident radiation: The photoelectric current is observed to vary with the intensity of incident radiation, while holding the frequency and potential between the metal plate and collector constant. The relationship between photoelectric current and the intensity of incident radiation is proportional. The photoelectric current measures the rate at which photoelectrons are ejected per second.
• A potential difference between metal plate and collector: The positive potential of C is gradually increased while maintaining a constant intensity and frequency of light. The photoelectric current experiences a positive increase when the potential between the metal plate and the collector increases up to a certain characteristic value. When the accelerating voltage is increased beyond the characteristic value, there is no corresponding increase in the photoelectric current. The maximum value of current is referred to as the saturation current.
• Frequency of incident radiation: When the intensity of incident light is fixed, changing the frequency of the incident light results in a linear change in the cut-off potential or stopping potential of the metal. Research has demonstrated that the cut-off potential (Vc) exhibits a linear relationship with the frequency of the incident light. The kinetic energy of photoelectrons is directly proportional to the frequency of incident light required to completely halt their motion. To prevent the emitted photoelectron from reaching the collector, we need to reverse the potential between the metal plate and collector to a negative value and increase it.

Applications of Photoelectric Effect

The effect has a wide range of applications, including measuring light intensity and converting light into electrical energy. There are several applications available, including:

• The construction of solar cells, a non-conventional energy source highly sought after in today’s world, is of great importance.
• Photo-telegraphy is a process that involves the use of photo-tubes to convert the light and shades of pictures into electrical waves. These waves are then transmitted to distant stations.
• The opacity of solids and liquids can be determined by measuring the intensity of transmitted light through them.
• This term is also utilized in the field of astronomy. Although the light emitted by stars may be too weak to be easily detected and analyzed, it is still sufficient to reach the cathode of a photoelectric cell and generate electrons. These electrons can then be interpreted as measures of the intensities and temperatures of the stars.
• The photoelectric effect has proven to be a valuable tool in the study of nuclear reactions. The distinctive energy carried by released electrons from an atomic source is utilized in the chemical study of materials.
• In the early days of television, the photoelectric effect found its application in imaging technology, particularly in video camera tubes. These tubes were a type of cathode ray tube that captured the television image.
• In addition, it is utilized for chemical analysis of materials by studying the emitted electrons, which enables the examination of electronic transitions between energy states and specific nuclear processes.

Frequently Asked Questions (FAQ)

Video on Photoelectric Effect

References

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