Derivation for black body radiation. What is the 2 bout?

In summary, the equation ${\rho}({\lambda}) d{\lambda}=E({\lambda})*f({E(\lambda}))*D({\lambda})d{\lambda}$ describes the density of radiative energy, with $E({\lambda})= k_BT$ representing the energy of an atom vibrating in 3D and $f({E(\lambda}))=1$ being the probability distribution based on the equipartition theorem. The term $D({\lambda})d{\lambda}=2 *{\frac{4V\pi}{\lambda^4}}d{\lambda}$ represents the number of states, and the factor of 2 is due to the two polarisation modes through which atoms can shed their
  • #1
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$${\rho}({\lambda}) d{\lambda}=E({\lambda})*f({E(\lambda}))*D({\lambda})d{\lambda}$$
$${\rho}({\lambda}) d{\lambda}$$ is density of radiative energy,
$$E({\lambda})= k_BT$$ is the energy of an atom vibrate in 3D,
$$f({E(\lambda}))=1$$ is the probability distribution. Equals to 1 because we follow equipartition theorem,
$$D({\lambda})d{\lambda}=2 *{\frac{4V\pi}{\lambda^4}}d{\lambda}$$ ,$$D({\lambda})d{\lambda}$$ is the number of state. And 2 there is because "Another technical problem is that you can have waves polarized in two perpendicular planes, so we must multiply by two to account for that. " from hyperphysics.

My question is : do I define every terms above correctly?
And I don't understand why wave polarize then we have to time two in the number of state? There will be double states because I the polarize wave are boson. But boson is not in classical.how do they so sure have to times two there?
Thanks.
 
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  • #2
It sounds like you answered your own question: The factor of two comes about because there a two polarisation modes through which atoms can shed their energy. Like having two taps to empty a water tank.

Claude.
 
  • #3
Claude Bile said:
The factor of two comes about because there a two polarisation modes through which atoms can shed their energy. Like having two taps to empty a water tank.

Claude.

Can you please explain more? How two taps to empty a water tank? Water go from taps to tank then?
How should I prove the two polarization modes? Please tell me. Thanks.
 

1. What is black body radiation?

Black body radiation refers to the electromagnetic radiation emitted by an object due to its temperature. This radiation is continuous and follows a specific distribution based on the object's temperature, known as the black body curve.

2. How is the black body curve derived?

The black body curve is derived using the principles of thermodynamics and statistical mechanics. It involves calculating the energy distribution of photons emitted by a black body at different wavelengths and temperatures.

3. What is the significance of black body radiation?

Black body radiation is important because it allows us to understand the behavior of thermal radiation and its relationship to temperature. This concept is crucial in fields such as astrophysics, where it helps us study the properties of stars and other celestial bodies.

4. What is the Planck's law of black body radiation?

Planck's law is a mathematical formula that describes the spectral energy density of black body radiation at a given temperature. It is derived from the principles of quantum mechanics and accurately predicts the behavior of black body radiation at all wavelengths.

5. How does the black body curve change with temperature?

As the temperature of a black body increases, the peak of the black body curve shifts to shorter wavelengths and the curve becomes broader. This is known as Wien's displacement law and is a fundamental principle in understanding the behavior of black body radiation.

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