Planck's Radiation Formula: Wavelength & How to Calculate

Thread starter CollectiveRocker
Start date Sep 17, 2004

In summary, Planck's radiation formula is a mathematical equation developed by Max Planck in 1900 that describes the spectral distribution of electromagnetic radiation emitted by a black body at a given temperature. It can be used to calculate the intensity of radiation at a specific wavelength and requires knowledge of the wavelength, temperature, and values of fundamental constants such as Planck's constant. This formula has various applications in physics and engineering, including the study of black bodies, astrophysics, and the design of thermal radiation-emitting devices.

Sep 17, 2004

CollectiveRocker

Express the Planck radiation formula in terms of wavelength. How is this to be accomplished?

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Sep 17, 2004

Dr Transport

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how about making the substution [tex] \hbar \omega = \frac{\hbar c}{\lambda} [/tex]?

Sep 20, 2004

CollectiveRocker

Into what?

Sep 21, 2004

Dr Transport

Science Advisor

Insights Author

Gold Member

WHat is the expression that you have so far, if it is in terms of energy, [tex] E = \hbar \omega = \frac{\hbar c}{\lambda} [/tex], make the substitution and go from there.

1. What is Planck's radiation formula?

Planck's radiation formula is a mathematical equation that describes the spectral distribution of electromagnetic radiation emitted by a black body at a given temperature. It was developed by the German physicist Max Planck in 1900, and is considered one of the foundational principles of quantum mechanics.

2. How is wavelength related to Planck's radiation formula?

Planck's radiation formula provides a way to calculate the intensity of electromagnetic radiation at a specific wavelength. This means that for a given temperature, the formula can be used to determine how much radiation is emitted at a particular wavelength.

3. How do you calculate Planck's radiation formula?

The formula is: I(λ,T) = (2πhc²/λ⁵) * 1/(e^(hc/λkT) - 1), where I is the intensity of radiation at a given wavelength (λ) and temperature (T), c is the speed of light, h is Planck's constant, and k is the Boltzmann constant. To calculate it, you will need to know the wavelength, temperature, and values of the constants.

4. What is the significance of Planck's constant in the formula?

Planck's constant (h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. In the context of Planck's radiation formula, it is used to calculate the energy of the radiation at a given wavelength and temperature.

5. What is the application of Planck's radiation formula?

Planck's radiation formula has many applications in physics and engineering. It is used to study the properties of black bodies, which are theoretical objects that absorb and emit all radiation. It is also used in fields such as astrophysics, where it helps to understand the temperature and composition of stars. Additionally, it is used in the design of incandescent light bulbs and other devices that emit thermal radiation.