Rate of Lyman Alpha photons emitted....

[freetobe23]

First off, I'm not sure if this question should go here or in the homework section. It is an astronomy homework question BUT there are only physics subtopics and did not want to post it in the wrong section. Let me know if it should be moved to there!

Homework Statement

Consider a nebula consisting of an O star surrounded by an H II region surrounded by an H I region. (That is, assumed that the ionized H II region does extend as far as the edge of the nebula.) Let N be the rate at which ionizing photons are emitted by the O star. (e.g. in units s^-1). Assume that the nebula is dust free and made entirely of H (i.e. neglect He and the heavier elements).

A. In terms of N, what is the rate at which Ly-alpha photons are emitted by the nebula?
B. In terms of N, what is the rate at which Balmer photons (including all Balmer transitions and the Balmer continuum) are emitted be the nebula?
C. Describe in detail (and with the help of a diagram) the fate of a Paschen continuum photon emitted as the result of the capture of electron by a proton into the n=3 state. What can happen as a result of this capture?
D. Imagine viewing the nebula from a distance. From where is the Ly-alpha emission seen-the H II region, the H I region, or both? Why?

Homework Equations

(1). E = h*w/c
(2). F = L/4*pi*r²

The Attempt at a Solution

Start with A and B...This answer must use some probability to give a ratio of lyman alpha photons compared to total photons. Is this going to be the recombination coefficient? I'm getting rung up in my own thoughts and am now confused. Any tip would help get me started...don't do the problem, but maybe a hint!

Thanks in advance!

 

[mark726]

Hello,

Thank you for your question. I can understand your confusion as this problem does involve both astronomy and physics concepts. However, I believe this is the appropriate forum for this question.

To answer your first question, the rate at which Ly-alpha photons are emitted by the nebula can be calculated using the recombination coefficient, which is a measure of the probability of an electron recombining with a proton to form a neutral hydrogen atom. This coefficient depends on the temperature and density of the gas, as well as the energy of the photon. In this case, we can assume that the temperature and density of the nebula are constant, and the only variable is the energy of the photons. Therefore, the rate of Ly-alpha photon emission can be expressed as:

R(Ly-alpha) = α(Ly-alpha) * N

where α(Ly-alpha) is the recombination coefficient for Ly-alpha photons and N is the rate at which ionizing photons are emitted by the O star.

Similarly, the rate at which Balmer photons are emitted can be calculated using the recombination coefficient for Balmer photons, which includes all Balmer transitions and the Balmer continuum. This can be expressed as:

R(Balmer) = α(Balmer) * N

where α(Balmer) is the recombination coefficient for Balmer photons.

Moving on to part C, the fate of a Paschen continuum photon emitted as a result of the capture of an electron by a proton into the n=3 state can be described as follows:

1. The electron can make a transition to a lower energy state, emitting a photon with a specific energy corresponding to the difference in energy between the two states. This process is known as spontaneous emission.
2. The electron can be excited to a higher energy state by absorbing a photon with the correct energy. This is known as stimulated emission.
3. The electron can remain in the n=3 state and eventually make a transition to a lower energy state through collisions with other particles in the gas, emitting photons in the process. This is known as collisional excitation.

As for part D, the Ly-alpha emission is seen from both the H II region and the H I region. This is because Ly-alpha photons can be produced in both regions through the processes mentioned above. However, the Ly-alpha emission from the H II region is expected to be stronger due to the higher concentration of ionized hydrogen atoms in this region.

I hope this helps