Planck’s Law Calculator

\( B(\lambda, T) = \frac{2hc^2}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda kT}} – 1} \)

Results:

– W/m²/sr


What is Planck’s Law

Planck’s Law is a fundamental principle in quantum physics that describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium. Named after Max Planck, the German physicist who formulated it in 1900, this law marked a pivotal moment in the development of quantum theory. Planck’s Law explains how the energy emitted by a black body varies with frequency and temperature, challenging classical physics’ explanations. It is crucial in understanding the mechanisms of thermal radiation and has applications in fields ranging from astrophysics to engineering.

Planck’s Law Equation

\( B(\lambda, T) = \frac{2hc^2}{\lambda^5} \left( \frac{1}{e^{\frac{hc}{\lambda kT}} – 1} \right) \)

Where:

  • B(λ, T) – Spectral radiance of the black body,
  • λ – Wavelength of the radiation,
  • T – Absolute temperature of the black body,
  • h – Planck’s constant,
  • c – Speed of light in a vacuum,
  • k – Boltzmann’s constant.

Planck’s Law in Terms of Wavelength

\( \lambda_{max} = \frac{b}{T} \)

Where:

  • λmax – Wavelength at which the spectral radiance is maximum,
  • b – Wien’s displacement constant (approximately 2.897771955 × 10-3 m·K),
  • T – Absolute temperature of the black body.

Understanding the Planck Constant in Planck’s Law

The Planck constant (h) is a pivotal element in quantum physics, particularly in Planck’s Law. Defined as ℎ = 6.62607015 × 10^−34 joule seconds (J s), this constant is central to the quantum mechanics realm. It plays a fundamental role in the quantization of energy, action, and other physical quantities, representing the scale at which quantum effects become significant.

In the context of Planck’s Law, the Planck constant directly influences the calculation of the spectral radiance of a black body. It establishes a critical relationship between the energy (E) of a photon and the frequency (ν) of its corresponding electromagnetic wave, encapsulated in the equation E=hν. This relationship unveils the quantized nature of light and electromagnetic radiation, a concept that was revolutionary at the dawn of the 20th century.

Conclusion

Planck’s Law has been a cornerstone in the field of physics, offering profound insights into the behavior of matter and energy at a quantum level. For engineering enthusiasts, the law provides a foundational understanding of thermal radiation principles, essential in various technological and industrial applications. From enhancing astrophysical studies to advancing thermal imaging technology, Planck’s Law continues to be a testament to the pioneering spirit of scientific inquiry and technological advancement. Understanding this law not only enriches our knowledge of the physical world but also drives innovation in engineering and science.