Origines de la physique quantique .Loi de Planck,Wien et Stefan

Introduction

This tutorial explores the origins of quantum physics, focusing on the laws established by Planck, Wien, and Stefan. Understanding these laws is crucial for grasping the foundations of quantum mechanics and their implications in modern science.

Step 1: Understanding Planck's Law

• Concept Overview: Max Planck introduced the idea that energy is quantized, meaning it can only exist in discrete amounts, or "quanta."

• Planck's Formula: The law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium.

  The formula is given by:

  B(ν, T) = (2hν^3 / c^2) * (1 / (e^(hν / kT) - 1))
  

  Where:

  • B(ν, T) is the spectral radiance.
  • h is Planck's constant (6.626 x 10^-34 Js).
  • ν is the frequency of the radiation.
  • c is the speed of light (3 x 10^8 m/s).
  • k is the Boltzmann constant (1.38 x 10^-23 J/K).
  • T is the absolute temperature in Kelvin.

• Practical Advice: To visualize this, consider using simulations or graphing software to plot Planck's law and see how the spectral density changes with temperature.

Step 2: Exploring Wien's Displacement Law

• Concept Overview: Wilhelm Wien formulated a law that describes how the wavelength of maximum emission of a black body shifts with temperature.

• Wien's Law Formula: The law is expressed as:

  λ_max = b / T
  

  Where:

  • λ_max is the wavelength at which the emission is maximized.
  • b is Wien's displacement constant (approximately 2898 μm·K).
  • T is the absolute temperature in Kelvin.

• Practical Application: This law helps in fields like astronomy to determine the temperature of stars based on their color.

Step 3: Understanding Stefan-Boltzmann Law

• Concept Overview: The Stefan-Boltzmann Law relates the total energy radiated per unit surface area of a black body to the fourth power of its temperature.

• Stefan-Boltzmann Formula: The law is given by:

  j* = σT^4
  

  Where:

  • j* is the total energy radiated per unit surface area.
  • σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m²·K⁴).
  • T is the absolute temperature in Kelvin.

• Practical Advice: This law is significant in climate science and astrophysics, helping to calculate the energy output of stars and the thermal radiation of Earth.

Conclusion

The laws of Planck, Wien, and Stefan-Boltzmann form the core principles of thermal radiation and quantum physics. Understanding these concepts is essential for further studies in physics and related fields. Consider exploring practical applications of these laws in technology and natural phenomena to deepen your understanding.