Astronomy: Local Thermodynamic Equilibrium, Gaunt Factor

This is due to the higher frequency of photons at the Balmer limit, resulting in a larger absorption cross-section. In summary, the problem involves showing that a hydrogen gas cloud at 10000K is twice as optically thick at the Balmer limit compared with the Paschen limit, using the equations an(f)=[64/(3*3^0.5) A] (pi a0^2)n(fn/f)^3 gbf(n) and hf1/k=1.578*10^5K. This is due to the higher frequency of photons at the Balmer limit, resulting in a larger absorption cross-section.
  • #1
Rokon117
1
0
1. The problem statement, all variables and given/known


Homework Equations


show that a hydrogen gas cloud at 10000K is about twice as optically thick at the Balmer limit compared with the Paschen limit. Assume that the H atoms are in Local Thermodynamic Equilibrium, the Gaunt factor is unity at all energy levels, and include absorption by H to levels up to n=10. Note that hf1/k=1.578*10^5K for lyman limit photon of frequency f1.

The Attempt at a Solution


an(f)=[64/(3*3^0.5) A] (pi a0^2)n(fn/f)^3 gbf(n)
gbf(n)=1
sorry just don't know how to type those symbols
 
Physics news on Phys.org
  • #2
.a0=0.0529nmfn=1.5809*10^15 Hz at Balmer limitfp=7.9579*10^14 Hz at Paschen limitn=1 to 102. Relevant equationsan(f)=[64/(3*3^0.5) A] (pi a0^2)n(fn/f)^3 gbf(n)3. The attempt at a solutionan(f) at Balmer limit = [64/(3*3^0.5) A] (pi a0^2)n(fn/f)^3 gbf(n)= [64/(3*3^0.5) A] (pi 0.0529nm^2)n(1.5809*10^15 Hz/1.578*10^5K)^3 1= 8.106*10^-19 m^2an(f) at Paschen limit = [64/(3*3^0.5) A] (pi a0^2)n(fn/f)^3 gbf(n)= [64/(3*3^0.5) A] (pi 0.0529nm^2)n(7.9579*10^14 Hz/1.578*10^5K)^3 1= 4.049*10^-19 m^2Therefore, the hydrogen gas cloud at 10000K is about twice as optically thick at the Balmer limit compared with the Paschen limit.
 

Related to Astronomy: Local Thermodynamic Equilibrium, Gaunt Factor

1. What is Local Thermodynamic Equilibrium (LTE) in astronomy?

Local Thermodynamic Equilibrium (LTE) in astronomy refers to a state in which the temperature and density of a gas are uniform throughout a volume, and the gas is in thermal equilibrium with its surroundings. This is an important concept in understanding the physical processes that occur in stars and other astronomical objects.

2. How does LTE affect the formation of spectral lines?

In LTE, the gas particles are in constant collisions with each other, causing them to reach a balance between the rates of emission and absorption of radiation. This results in the formation of spectral lines with specific intensities and wavelengths, which can be used to study the composition and physical properties of celestial objects.

3. What is the Gaunt factor in astrophysics?

The Gaunt factor is a dimensionless factor that accounts for the deviation of spectral line intensities from their expected values in LTE. It takes into account the effects of quantum mechanics and relativity on the emission and absorption of radiation, and is often used in calculations of spectral line intensities in astrophysics.

4. How is the Gaunt factor calculated?

The Gaunt factor is calculated using a formula that takes into account the temperature, density, and electron number density of the gas, as well as the energy levels and transition probabilities of the spectral line being studied. It is also affected by the ionization state and magnetic field of the gas.

5. What role does the Gaunt factor play in astrophysical research?

The Gaunt factor is an important factor in understanding the physical processes that occur in stars and other astronomical objects. It is used in calculations of spectral line intensities, which can provide valuable information about the composition, temperature, density, and other properties of celestial objects. It also helps scientists to better understand the behavior of matter in extreme environments, such as the cores of stars and the interstellar medium.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Special and General Relativity
Replies
23
Views
2K
Replies
152
Views
5K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Special and General Relativity
3
Replies
75
Views
4K
  • Math Proof Training and Practice
2
Replies
39
Views
10K
  • Math Proof Training and Practice
3
Replies
71
Views
9K
  • Math Proof Training and Practice
Replies
20
Views
5K
  • Special and General Relativity
Replies
1
Views
1K
Replies
13
Views
2K
Back
Top