Calculating Mean Free Path of Photons: Neutral Atomic Hydrogen Cloud Comparison

In summary, the conversation discusses the determination of mean free path of photons with energy of 20eV for various densities of neutral atomic hydrogen cloud (n_H = 1, 10, and 100 cm^{-3}). It also compares this to the mean free path for photons with ionization energy of hydrogen (13.6eV) at the same densities. The relevant equation given in the notes is \tau_{\nu}=\sigma_{0}*(\frac{\nu}{\nu_{0}})^{-3.5}*n_{H^{0}} and the question asks for clarification on where to input the energy in this equation.
  • #1
Ayame17
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Homework Statement


Neutral atomic hydrogen cloud, density [tex]n_H[/tex]. Absorption cross section [tex]\sigma_{0} = 6.3*10^{-18}cm^{2}[/tex]. Determine the mean free path of photons with energy of 20eV, for densities [tex]n_H[/tex] = 1, 10 and 100 [tex]cm^{-3}[/tex]. Compare this to mfp for photons with ionisation energy of hydrogen (13.6eV) at the same densities.


Homework Equations



The only possibly relevant equation given in our notes is [tex]\tau_{\nu}=\sigma_{0}*(\frac{\nu}{\nu_{0}})^{-3.5}*n_{H^{0}}[/tex]

The Attempt at a Solution



I'll be able to try the second bit once I figure out the first bit! I looked up some stuff on the mean free path, and figured that it could've just been [tex]l=\frac{1}{n_{i}*\sigma}[/tex], but then is [tex]n_i[/tex] the same as [tex]n_H[/tex]? And the equation given in the notes (above), all that is said about it is that the optical depth of photons above the Lyman limit [tex]\nu_0[/tex] can be derived from it. I simply can't see where to put in the amount of energy so that it will make a difference!
 
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  • #2
Anyone got any idea?
 

What is the mean free path of photons?

The mean free path of photons is the average distance a photon travels in a particular material before it is scattered or absorbed by the particles in that material. It is a measure of how far a photon can travel without interacting with other particles.

Why is the mean free path of photons important?

The mean free path of photons is important because it affects the behavior of light in different materials. It can determine how far light can travel through a material before being absorbed, and can also impact the diffusion and scattering of light.

How is the mean free path of photons calculated?

The mean free path of photons is calculated by dividing the total distance a photon travels by the number of interactions it has with particles in the material. This can be a complex calculation as it depends on factors such as the composition and density of the material, and the energy of the photon.

What factors can affect the mean free path of photons?

The mean free path of photons can be affected by several factors, including the composition and density of the material, the energy of the photons, and the temperature and pressure of the material. Other factors such as the presence of impurities or magnetic fields can also impact the mean free path.

How is the mean free path of photons used in scientific research?

The mean free path of photons is used in a variety of scientific research, such as in the study of light propagation in materials, the development of optical devices and sensors, and in the analysis of light-matter interactions. It is an important parameter in fields such as physics, chemistry, and material science.

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