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The Z/A term for calculations of degeneracy pressure for white dwarfs is given as 0.5. But I can't find an explanation as to why. For my assignment, I am trying to find the degeneracy pressure for the core of the sun. I am given R = 0.1Rsun and M = 0.1Msun. I am also told that the core contains 50% hydrogen and 50% helium.
I need to find Z/A for this scenario in order to find the degeneracy pressure, but I don't know how to approach it.
Z is the atomic number, A is the atomic mass.
A white dwarf is typically made of carbon (A=12, Z=6) or Oxygen (A=16, Z=8). So Z/A = 0.5.
The reason you need Z/A is you need the ratio of the number of free electrons (Z) to the mass (A, in atomic mass units). You need that because the pressure depends on Z and that must support against the gravity that depends on A. So you are counting degenerate particles (Z) in relation to the particles that provide the mass (A). If you are told 50% H and 50% He, you have to know if they mean 50% by number or by mass. That is often left ambiguous! Let's assume they mean 50% by number, so you have a proton and an electron contributed by every H, and an equal number of He that contribute 4 nucleons and 2 electrons. So that's a total of 5 nucleons (A=5) and 3 electrons (Z=3). So Z/A = 0.6. But if they mean 50% by mass, then you have 4 protons and 4 electrons for every He, giving A=8 and Z=6, so Z/A = 0.75.
