Photon

Photon is a fundamental particle of electromagnetic radiation. It is a quantum of light and other electromagnetic waves. It is the force carrier of the electromagnetic force. Photons can display wave-like behaviors such as interference and diffraction. They can also exhibit particle-like behaviors such as the photoelectric effect. This is known as wave-particle duality.

Photons carry momentum and travel at the speed of light. Photons are produced through processes such as electron transitions in atoms, particle interactions, and particle-antiparticle annihilation. In the photoelectric effect, photons transfer their energy to electrons in a material, leading to the emission of photoelectrons.

Photons are fundamental particle of electromagnetic radiation, traveling at the speed of light. It is a quantum or discrete energy packet of electromagnetic energy. Photons are massless particles that are the carriers for electromagnetic energy.

Photons can be produced through various processes depending on the source of electromagnetic radiation. Production of photon is explained using the analogy,

“Think of atoms like tiny solar systems: electrons orbiting around a nucleus. When we give these electrons a boost of energy, they jump to higher orbits. But they can’t stay there forever – eventually, they come back down to their normal orbits. When they do, they release energy in the form of photons, which are like tiny packets of energy. Frequency of a photon is determined by the distance the electron falls, giving rise to distinctive characteristics for each photon.”

Why does Photon have Momentum?

Despite lacking mass, a photon has momentum proportionate to its energy. Based on the photon’s energy and frequency, the momentum can be calculated using the Planck-Einstein relation

E = hv

However, a photon cannot have any mass because it is always travelling at the speed of light, according to Einstein’s calculations. However, it is evident that the photon still needs energy in order to cause the photoelectric effect. Consequently, it stands to reason that all photon energy is in the form of motion. Thus, a photon needs momentum in order to move and have energy.

Difference between Photon and Electron are as follows:

Properties of a photon include:

• Photons are quantized particles, meaning they can only exist as discrete energy packets. This plays a fundamental role in the photoelectric effect and the emission and absorption of light by atoms and molecules.
• Photons are massless particles.
• Photons are neutral particles.
• Energy of a photon is directly proportional to its frequency, as described by Planck’s Equation

E = ℎν

where,

• ℎ is Planck’s Constant
• ν is Frequency

Photons carry momentum (p = h/λ) and can transfer it to other objects.

• Photons travel at the speed of light(c), approximately 3×10⁸ meters per second in a vacuum. This constant speed is a fundamental aspect of Einstein’s theory of relativity.
• Photons show characteristics of both particles and waves. This is known as the wave-particle duality.
• Photons exhibit polarization. Polarization is the orientation of oscillations of electric and magnetic fields. Polarization can be linear, circular, or elliptical, depending on the orientations and phases of the fields.

Wave-Particle Duality of photons refers to the concept that photons can exhibit both wave-like and particle-like behaviours. It is the experimental setup and the type of measurement that decide whether the photon will behave as a wave or a particle.

Wave-Particle Duality challenges the classical notions of particles and waves. This pushed for a quantum theory of the behaviour of light and electromagnetic radiation. This concept has profound implications for quantum mechanics, optics, and particle physics.

Wave-Like Properties

• Photons exhibit wave-like properties in phenomena such as interference and diffraction. When multiple photons are in superposition, they can interfere with each other and form interference patterns.

For example, in the double-slit experiment, where photons are sent through two slits, they produce an interference pattern on the screen behind the slits, similar to the interference pattern produced by waves.

Particle-Like Properties

• Photons also display particle-like properties in phenomena such as the photoelectric effect. In this effect, photons interact with electrons in a material, causing them to be emitted from the material. The energy of the ejected electrons depends on the frequency (or energy) of the incident photons, not their intensity.

Additionally, photons can be detected as discrete packets of energy when they are absorbed or emitted by atoms or molecules.

Quantum Superposition

Like other quantum particles, photons can exist in a state of superposition, where they simultaneously show both wave-like and particle-like characteristics. This superposition is described by the wave function in quantum mechanics.

Electron Transitions in Atoms

When an electron in an atom transitions from a higher energy state to a lower energy state, it emits a photon with energy equal to the energy difference between the two states.

E₂ – E₁ = hν

This process is responsible for the emission of photons in various spectral lines observed in atomic spectra. For example, in a fluorescent light bulb, photons are produced when electrons in gas atoms transition from higher to lower energy levels.

Particle Interactions

Photons can be generated through particle interactions, such as when high-energy charged particles, like electrons or protons, collide with matter. These interactions can produce bremsstrahlung radiation (emission of photons due to the deceleration of charged particles) or synchrotron radiation (emission of photons by charged particles moving in curved paths).

Particle-Antiparticle Annihilation

Particle-antiparticle annihilation is a process in particle physics where a particle and its corresponding antiparticle collide and annihilate, resulting in the conversion of their mass into energy. This energy is often emitted in the form of photons.

2m₀c² = hν

Photoelectric effect is a phenomenon where electrons are ejected from a material when it is exposed to electromagnetic radiation. This occurs when photons, the particles of light, transfer their energy to electrons in the material. This minimum energy required by an electron to leave the surface of the metal is called the work function of the metal(denoted by ϕ₀). The minimum frequency of light that can emit an electron from the metal surface is known as threshold frequency and is denoted by v₀.

Photoelectric effect was studied experimentally in a vacuum tube, with photoelectrons emitting from the cathode and moving towards the anode. The minimum retarding potential V0 of the anode for which the photocurrent becomes zero is called the cut-off or stopping potential. The energy lost due to this stopping potential is the maximum kinetic energy of the electron.

Photoelectric effect was first successfully explained by Einstein that led him to winning the Nobel Prize in 1921 (not theory of relativity, mind you). The governing equation for all of photoelectric effect is the following

1/2 mν_max² = eV₀ = hν – ϕ₀ = h(ν – ν₀)

Numerous technical uses exist for photons, a few of which are covered here:

• An significant use of photons is in lasers. Photon beams in a laser beam travel at the same wavelength and in the same direction. By passing the energised electrons via an optical gain medium, like glass or a gas, is accomplished.
• In design, engineers utilise Planck’s energy formula, E (= hv), to calculate the energy change resulting from photon absorption and to ascertain the frequency of light emitted from a specific photon emission.
• Single photon detection is used in a variety of hardware random number generators.

Photons, the fundamental particles of electromagnetic radiation are the basic packets of energy and travells at the speed of light. In this article we have describe the characteristics of photons, including their wave-particle duality, quantized nature, mass lessness, and role as carriers of electromagnetic force.

1. Monochromatic light of frequency 6 × 10¹⁴ Hz is produced by a laser. What is the energy of a photon in the light beam?

Solution:

To calculate energy of a photon in the light beam, we use Planck’s Equation:

E = hν

Given,

Frequency(v) = 6 × 10¹⁴ Hz

E = 6.63 × 10^-34 × 6 × 10¹⁴

E = 3.98 × 10^-19 J

2. Power emitted by a laser of frequency 6 × 10¹⁴ Hz is 2 × 10^-3 W. How many photons per second, on an average, are emitted by the source?

Solution:

To calculate number of photons emitted per second by laser, we use relationship between power (P) and energy (E):

P = N⋅E

where,

• P is Power emitted by the laser (in watts)
• N is Number of photons emitted per second
• E is Energy of a single photon (in joules)

E = hν

Given,

Frequency(v) = 6 × 10¹⁴ Hz

E = 6.63 × 10^-34 × 6 × 10¹⁴

E = 3.98 × 10^-19 J

For N:

N = P/E

N ​= (2×10^-3 W)/(3.98×10^-19J)

N ≈ 5.025×10¹⁵ photons/second

So, on average, approximately 5.025×10¹⁵ photons are emitted per second by source.

3. Work function of Cesium is 2.14 eV. Find threshold frequency for Cesium.

Solution:

For Cesium with a work function of 2.14 eV

Φ₀ = 2.14 eV × (1.602176634 × 10^-19 J/eV)

Φ₀ ≈ 3.427 × 10^-19 J

Now, we equate work function to energy of a photon: Φ₀ = hν₀

Solving for v₀:

v₀ = Φ₀ /h

Substituting the values:

ν₀ = (3.427 × 10^-19 J)/(6.62607015 × 10^-34 J·s)

ν₀ ≈ 5.174 × 10¹⁴ Hz

So, threshold frequency for Cesium is approximately 5.174 × 10¹⁴ Hz.

4. For the above problem, find the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of 0.6 V.

Solution:

Photoelectric effect equation: eV₀ = hν₀ – Φ₀

ν₀ = (eV₀ + Φ₀) / h ≌ 6.62 × 10¹⁴ Hz

Once we have the frequency, we can use the speed of light formula to find the wavelength:

ƛ = c/ν₀ = 3 × 10⁸ /6.62 × 10¹⁴

ƛ = 4.53 × 10^-7 m

ƛ = 453 nm

5. Find the frequency of two photons emitted when an electron and a positron collide?

Solution:

Given,

Rest mass of an electron (or positron) is m₀= 9.1 × 10^-31 kg

E_total = 2m₀c²

Total energy is converted into the energy of the photons produced in the annihilation process. Since two photons are produced, we divide this total energy by two to find the energy of a single photon.

E_photon = E_total/2 = m₀c²

Now, we can use the equation E = hv to find the frequency of photon:

v = E_photon/h

v = m₀c²/h

v = ( 9.1 × 10^-31 × 9 × 10¹⁶ )/6.626 x 10^-34

v = 1.24 × 10²⁰ Hz

So, frequency of two photons emitted when an electron and a positron annihilate is 1.24 × 10²⁰ Hz.

Q1: A hydrogen nucleus (H⁺) and an antiproton collide and annihilate each other. If the mass of a hydrogen atom (¹H) is 1.67×10^-27 kg, find the frequency of the two emitted photons.

Q2: If the energy for an electron in the n^th orbit around the atom is given by E_n =-13.6/n² eV, find the frequency of the photon released when an electron jumps from the 3rd to the 1st orbit.

Q3: Threshold frequency for a certain metal is 3.3 × 10¹⁴ Hz. If light of frequency 8.2 × 10¹⁴ Hz is incident on the metal, predict the cut-off voltage for the photoelectric emission.

Q4: Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made.

Q5: Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. Find the energy and momentum of each photon in the light beam.

What is a Photon?

A photon is a fundamental particle of electromagnetic radiation, travelling at the speed of light. It is a quantum or discrete energy packet of the electromagnetic field.

What determines energy of a Photon?

Energy of a photon is directly proportional to its frequency, as described by Planck’s equation (E = ℎν).

Can Photons Transfer Momentum?

Photons carry momentum (p = h/λ) and can transfer it to other objects through interactions.

Are photons electrons?

No, photons are not electrons. Photon are elementary particle that acts as a carrier of energy, while an electron is a subatomic particle that are responsible for electric property of any material.

Are photons massless?

Rest mass of Photon is zero but as photon is a matter its mass can not be absolute zero. Mass of photon is wave length dependent.

How does a photon travel?

Photons in vacuum, travel at the speed of light.