Degrees of freedom in HII regions

[sarahrose]

I have to calculate the number of degrees of freedom within an HII region. I am asked to find the number of degrees of freedom before and after the hydrogen gas gets ionized by the star and forms an HII region. Does each particle have 3 degrees of freedom? I am given the number of ionizing photons per second, the temperature of the HII region, and the density of molecular hydrogen. I have calculated the stromgren radius.

To find the number of degrees of freedom in the resulting HII region, do I just multiply the volume of the region times the molecular hydrogen density and then multiply by 6 to take into account the fact that the hydrogen atom gets decomposed into protons and electrons??

I have no idea how to find the number of degrees of freedom in the molecular hydrogen gas before it gets ionized. What volume would I use?

 

[lippyka]

The number of degrees of freedom in the molecular hydrogen gas before it gets ionized depends on the size of the region. This can usually be calculated from the density and temperature of the gas, or from the number of ionizing photons per second. You would need to calculate the total mass of the gas, and then multiply that by the number of degrees of freedom per particle (3). This will give you an estimate of the total number of degrees of freedom in the molecular hydrogen before it gets ionized. For the HII region, you can simply multiply the volume of the region by the molecular hydrogen density and then multiply by 6 (to account for the fact that the hydrogen atom gets decomposed into protons and electrons). This will give you an estimate of the total number of degrees of freedom in the resulting HII region.