How Does Threshold Frequency Affect the Photoelectric Effect?
The photoelectric effect is a phenomenon in which light causes electrons to be released from a metal's surface. Photoelectrons are the electrons that are expelled. It's worth noting that the frequency of the light incident on the metal's surface affects the emission of photoelectrons and the kinetic energy of the expelled photoelectrons. Photoemission is the term used to describe the process by which photoelectrons are emitted from the metal's surface owing to the action of light.
The photoelectric effect happens when electrons at the metal's surface absorb energy from incoming light and utilise it to overcome the attractive forces that bind them to the nuclei of the metal. In this article, students will get to learn about photoelectric threshold frequency in detail. The material is revised and provided by Vedantu’s subject matter expert with an in-depth concept and easy explanation. Students preparing for JEE, NEET and other competitive exams can get an upper hand if they study the topic from Vedantu as Vedantu covers the topic very concisely.
Work Function and Threshold Frequency
The emission of electrons with help of electromagnetic radiation like light from the surface of a photoelectric material is called the photoelectric effect. The electrons emitted are known as photoelectrons. The photoelectric threshold frequency is the minimum frequency of the electromagnetic rays which when strikes a surface, causes a photoelectric effect. The photoelectric effect is a subject of study for quantum chemistry, condensed matter physics, for the behavioural study of various properties of solids, atoms, and molecules. The concept of emission of electrons from metal surfaces when electromagnetic waves, typically of short wavelength like the visible or ultraviolet rays strike the surface is known as photoconductive, photoelectrochemical effect since it is initiated by light energy.
Photons
A photon can be defined as a quantum of light that carries energy proportional to radiation frequency but has zero rest mass, and moves at the speed of light in the vacuum. Photons belong to the class of Boson and are elementary particles. The energy of light is considered to be quantized and hence, these small packets or quanta of energy are known as photons. Max Planck while studying Black Body Radiation discovered this fact.
Work Function and Threshold Frequency Formula
The first theory of the photoelectric effect was put forward by Einstein by using Max Planck’s theory of light energy. It was considered that each packet of light energy or photons carried energy hv where h was a proportionality constant known as the Planck constant and v was the frequency of the electromagnetic waves of light. Kmax is the maximum amount of kinetic energy delivered to the atoms before they leave their atomic bonding. To explain threshold frequency we can write the equation for photoelectric effect as:
Kmax = hv - W
Here W is the work function of the metal. It is the minimum energy that needs to be supplied to the metal body for the emission of photoelectrons. Now W can be written as:
W= hvo
Here vo is the photoelectric threshold frequency of the electromagnetic rays.
Steps for Photoemission from Metal Surfaces
The process of photoemission is a multistep process. These are:
The first step involves the striking of the electromagnetic radiation on the metal surface which causes the excitation of electrons.
The second step involves overcoming the energy barrier. The electrons impart the energy given to them by the photons. Or it can be said that the energy of photons is transmitted to electrons.
The valence electrons of the metal which are bound loosely to the nucleus start leaving the metal body with the help of the excess energy provided after utilising the work function of the metal.
Uses of Photoelectric Effect Threshold Frequency
The concepts threshold energy in photoelectric effect and threshold frequency find their application in many devices and processes. Some of which are:
Photomultipliers:
These are extremely light-sensitive vacuum tubes that have quoted photocathodes with caesium, rubidium and antimony for providing low work function as these metals have extremely low work function. This is so that when illuminated by very low levels of light the photocathodes start releasing electrons and photocurrent can be detected.
Photoelectron Spectroscopy:
Photoelectron spectroscopy measurements are done in a high vacuum environment to prevent electrons from being scattered by gas molecules present in the air. In this process monochromatic X-ray or UV rays of known frequency and kinetic energy are used to determine experimentally the composition of area samples.
Night Vision Devices:
Photons when strike alkali metal or semiconductor material like gallium arsenide in an image intensifier tube, causes the ejection of photoelectrons because of the photoelectric effect. This is accelerated by an electrostatic field where they strike a phosphor-coated screen thus converting electrons back into photons. Signals are generated and intensified due to the acceleration of electrons or increasing the number of electrons from the secondary emission. This concept is used in night vision devices.
Image Sensors:
Television in the early days had video camera tubes that used the photoelectric effect to transform an electronic signal into an optical image. However, currently, the mechanism of television working has changed.
As seen above, the concept of photoelectric emission, work function and photoelectric threshold frequency is indispensable for the study of quantum physical sciences. This is required for constructing various devices and various phenomena to occur.
Discovery Of Photoelectric Effect
Wilhelm Ludwig Franz Hallwachs initially proposed the photoelectric effect in 1887, while Heinrich Rudolf Hertz carried out the experimental proof. They discovered that when a surface is subjected to higher-frequency electromagnetic radiation, the energy is absorbed and electrons are released. The photoelectric effect is now understood to be a phenomenon in which a substance absorbs electromagnetic radiation and releases electrically charged particles.
To be more specific, the photoelectric effect causes electrons to be expelled when light is incident on a metal's surface. A photoelectron is an electron that is emitted as a result of the photoelectric effect and is symbolised by the letter e–. Photoelectric current is the current generated as a result of the expelled electrons.
Did You Know?
The lower the work function of a metal, the easier it is for us to achieve the process of photoelectric emission and lower the photo-energy required for it to emit electrons. Caesium, lithium, antimony are perfect metals to obtain photoelectric emission phenomena because of their low work function. Most of the photo devices are coated with these metals.
FAQs on Photoelectric Threshold Frequency Explained: Key Principles & Formulas
1. What is meant by the photoelectric threshold frequency?
The photoelectric threshold frequency (ν₀) is defined as the absolute minimum frequency of incident electromagnetic radiation (like light) that is required to eject an electron from a given metal surface. If the frequency of the incident light is below this value, no matter how intense the light is, photoelectric emission will not occur. It is a characteristic property unique to each metal.
2. What is the formula that connects threshold frequency to a metal's work function?
The threshold frequency is directly related to the work function of a metal. The formula is:
Φ = hν₀
Where:
- Φ (Phi) is the work function, which is the minimum energy required to liberate an electron from the metal surface.
- h is Planck's constant (approximately 6.626 x 10-34 J·s).
- ν₀ (nu-naught) is the threshold frequency in Hertz (Hz).
3. How is threshold frequency different from threshold wavelength?
Threshold frequency and threshold wavelength describe the same condition but have an inverse relationship.
- Threshold Frequency (ν₀) is the minimum frequency of light needed for photoemission.
- Threshold Wavelength (λ₀) is the maximum wavelength of light that can cause photoemission.
4. Why does every metal have a unique threshold frequency?
Every metal has a unique threshold frequency because each metal has a different atomic structure and electron binding energy. The energy required to free the most loosely bound electron from the surface is called the work function (Φ). This value depends on the metal's properties, such as the arrangement of atoms in its crystal lattice and the strength of the metallic bonds. Since threshold frequency is directly proportional to the work function (ν₀ = Φ/h), a different work function for each metal results in a unique and characteristic threshold frequency.
5. What happens if light with a frequency lower than the threshold frequency strikes a metal?
If the frequency of the incident light (ν) is less than the threshold frequency (ν₀), no photoelectric emission will occur. This is because each individual photon of the incident light has an energy (E = hν) that is less than the metal's work function (Φ). The energy from such a photon is insufficient to liberate an electron from the metal surface. Increasing the intensity of this low-frequency light only increases the number of photons hitting the surface per second, but each photon still lacks the required minimum energy, so no electrons are ejected.
6. How does the concept of threshold frequency support the particle nature of light?
The existence of a threshold frequency is strong evidence for the particle nature of light (photons) and a direct contradiction of the classical wave theory.
- According to wave theory, the energy of a light wave is spread out and depends on its intensity. It predicted that any frequency of light, if intense enough, could eventually supply enough energy to an electron to eject it.
- However, experiments show that emission is determined by frequency, not intensity. The particle model (proposed by Einstein) explains this perfectly: light consists of discrete packets of energy called photons. An electron is ejected only if it absorbs a single photon with enough energy (E = hν) to overcome the work function. If a photon's energy is too low (ν < ν₀), it cannot cause emission, supporting the one-photon, one-electron interaction model.
7. What are the key principles of the photoelectric effect related to threshold frequency?
The key principles or laws of the photoelectric effect are:
- Existence of Threshold Frequency: For a given metal, there is a minimum frequency of incident light below which no photoelectrons are emitted, regardless of the light's intensity.
- Instantaneous Process: Photoelectric emission is an immediate process. As soon as a photon with frequency ν ≥ ν₀ strikes the surface, an electron is ejected without any time delay.
- Kinetic Energy Dependence: The maximum kinetic energy of the emitted photoelectrons is directly proportional to the frequency of the incident light and is independent of its intensity, as per the equation K.E.max = hν - Φ.
- Photocurrent Dependence: For a frequency above the threshold, the number of photoelectrons emitted per second (the photoelectric current) is directly proportional to the intensity of the incident light.
