# What Is the Planck Radiation Formula for Wavelength?

• elessar_telkontar
In summary, the conversation was about finding the Planck radiation formula for wavelength in a course on astrophysics. The formula for frequency was already found, but the one for wavelength was needed. The solution was provided to substitute for wavelength and use the given formula for frequency to get the desired formula for wavelength. The request for a quick response was also mentioned.
elessar_telkontar
I'm taking a course on astrophysics, and at this time I get the astrophysics of stars. In this section, I have to use the Planck radiation formula, but I have got it for the frecuency of radiation. What's the one for wavelenght? I have found one but I tried to reconstruct the one for frecuencies but I can't do it:

The one for wavelength I have found is:

Bf(T)=((2hc2)/(l5))(1/ehc/klT-1)

elessar_telkontar said:
The one for wavelength I have found is:

Bf(T)=((2hc2)/(l5))(1/ehc/klT-1)

Just substitute:

$$\lambda=\frac{c}{\nu}$$

and

$$d\lambda=-\frac{c}{\nu^2}d\nu$$

That'll give you the frequency formula.

Last edited:

The Planck radiation formula is a fundamental equation in astrophysics that describes the distribution of energy emitted by a blackbody at a given temperature. It was first derived by German physicist Max Planck in 1900 and is essential in understanding the properties and behavior of stars.

The formula you have provided is indeed the Planck radiation formula for wavelength, also known as the spectral radiance. It describes the amount of energy emitted per unit time, per unit area, per unit solid angle, and per unit wavelength interval by a blackbody at a given temperature. This formula is often used to calculate the intensity of radiation emitted by stars at different wavelengths.

To understand the formula, let's break it down into its components. "B" represents the spectral radiance, which is the dependent variable we are trying to calculate. "f" is the frequency of the radiation, "T" is the temperature of the blackbody, "h" is Planck's constant, "c" is the speed of light, "k" is the Boltzmann constant, and "l" is the wavelength.

The first part of the formula, (2hc^2/l^5), represents the spectral radiance of a blackbody at a given temperature and is a constant value. The second part, (1/ehc/kT - 1), is the Planck distribution function, which is used to calculate the probability of a photon having a specific energy at a given temperature. This function takes into account the energy of the photon, the temperature of the blackbody, and the Boltzmann constant.

To reconstruct the formula for frequency, simply replace "l" with "f" and "c" with "l" in the formula you provided. This will give you the Planck radiation formula for frequency:

Bf(T)=((2hf2)/(c5))(1/ehf/kT-1)

I hope this helps you understand the Planck radiation formula better. It is a complex equation, but with practice and understanding, you will be able to use it confidently in your astrophysics studies. Remember to always double-check your calculations and units to ensure accurate results. Best of luck in your course!

## What is the Planck radiation formula?

The Planck radiation formula is a mathematical equation that describes the spectral energy density of electromagnetic radiation emitted by a black body at a given temperature. It was developed by German physicist Max Planck in 1900 and is considered one of the foundational equations of quantum physics.

## What is a black body?

A black body is an idealized object that absorbs all incoming electromagnetic radiation and emits it in the form of thermal radiation. It is often used as a theoretical model for understanding the behavior of real objects that emit and absorb radiation, such as stars and planets.

## How is the Planck radiation formula used in science?

The Planck radiation formula has numerous applications in different fields of science. It is used in astrophysics to study the properties of stars and other celestial bodies, in thermodynamics to understand the behavior of matter at different temperatures, and in engineering to design and optimize devices that use thermal radiation, such as solar panels and infrared cameras.

## What are the variables in the Planck radiation formula?

The Planck radiation formula contains several variables, including the temperature of the emitting body, the speed of light, and the Planck constant. It also includes the wavelength of the radiation, which is related to its frequency and determines the type of electromagnetic radiation being emitted (e.g. infrared, visible light, or ultraviolet).

## Is the Planck radiation formula accurate?

The Planck radiation formula has been extensively tested and has been found to accurately predict the spectral energy distribution of black bodies at different temperatures. However, it is important to note that it is a simplified model and does not account for all factors that can affect the emission of radiation, such as the composition and structure of the emitting body.

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