Quantum Physics: Exploring the Wave-Particle Duality of Light

Introduction to Quantum Physics

Quantum physics is a fundamental branch of physics that describes the behavior of matter and energy on the atomic and subatomic scale. It challenges our classical understanding of the nature of light and matter, introducing the concept of wave-particle duality.

The Photon Model of Electromagnetic Radiation

Electromagnetic radiation, including visible light, was traditionally described as a wave phenomenon. However, experiments such as the photoelectric effect and the Compton effect revealed that light also exhibits particle-like properties. This led to the development of the photon model, where light is described as a stream of discrete packets or particles called photons.

Planck's Constant and Energy of Photons

The energy of a photon is directly proportional to the frequency of the electromagnetic radiation, as described by the equation:

E = hf

where E is the energy of the photon, h is Planck's constant (6.63 × 10^-34 J⋅s), and f is the frequency of the radiation.

The Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are ejected from the surface of a metal when it is exposed to electromagnetic radiation of sufficient energy (frequency). The key observations of the photoelectric effect are:

• Electrons are ejected instantaneously, regardless of the intensity of the incident light.
• There is a specific minimum frequency (threshold frequency) below which no electrons are ejected, regardless of the intensity.
• The maximum kinetic energy of the ejected electrons increases with increasing frequency of the incident light.

Work Function and Stopping Potential

The work function of a metal is the minimum energy required to remove an electron from the metal's surface. The stopping potential is the minimum voltage required to prevent the most energetic electrons from reaching the anode in a photoelectric experiment.

Worked Example

Problem: Calculate the stopping potential for a photoelectric experiment where the incident light has a wavelength of 300 nm and the work function of the metal is 4.2 eV.

Solution:

1. Convert the wavelength to frequency: f = c/λ = (3 × 10^8 m/s) / (300 × 10^-9 m) = 1 × 10^15 Hz
2. Calculate the energy of the photon: E = hf = (6.63 × 10^-34 J⋅s)(1 × 10^15 s^-1) = 6.63 × 10^-19 J = 4.14 eV
3. The maximum kinetic energy of the ejected electrons is E - ϕ, where ϕ is the work function.
4. The stopping potential V is related to the maximum kinetic energy by eV = (E - ϕ), where e is the charge of an electron.
5. Rearranging, we get V = (E - ϕ)/e = (4.14 eV - 4.2 eV)/(1.6 × 10^-19 C) = -0.38 V

Wave-Particle Duality and Applications

The wave-particle duality of light is a fundamental concept in quantum physics, which states that electromagnetic radiation exhibits both wave-like and particle-like properties. This duality has led to numerous applications in modern technology, such as lasers, semiconductors, and quantum computing.