Saha equation to determine fraction of hydrogen atoms ionised

In summary, the question is asking for the fraction of hydrogen atoms that are ionized at the center of the sun, given the temperature and number density. The Saha equation is used to solve for this fraction, but it needs to be applied iteratively and the correct units and ionization potential must be used. After making these corrections, the correct answer can be obtained.
  • #1
can't.do.phys
3
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So i have a homework question which i can't figure out.
Use the saha equation to determine the fraction of hydrogen atoms that are ionised at the centre of the sun (N_II/N_tot)
T=15.7x10^6K
number density n=6.1x10^31 m^-3
m = mass of electron

the saha equation is
N_(i+1)/Ni = 2*Z_(i+1)/n*Z_i * (2π*m*kT/h^2)^(3/2) * exp(-χ_i/kT)

i get that Z_I=2 and Z_II=1 because we are assuming most of the hydrogen is in the ground state(or is that what I am doing wrong)? I've also tried changing units from J to eV but that doesn't seem to be doing anything.

i think at the end of this I am meant to get a fraction or percentage, but i keep getting stupid numbers like to the power of -34. can someone tell me what I am doing wrong?
 
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  • #2
You are correct in assuming that the majority of hydrogen atoms would be in the ground state. You have to use the Saha equation iteratively, starting with the ionized fraction at the start and finding the fraction of neutral atoms by reversing the equation. You then use the fraction of neutral atoms as your starting point for the next iteration. The equation you gave is incomplete; you need to include the ionization potential (χ_i) for the ground state hydrogen atom, which is 13.6 eV. The units for mass need to be in kilograms (m = 9.1x10^-31 kg). Finally, you will need to convert the temperature from Kelvin to electron volts (1 eV = 11,600 K). After making these corrections, you should be able to get the correct answer.
 

FAQ: Saha equation to determine fraction of hydrogen atoms ionised

1. What is the Saha equation used for?

The Saha equation is used to determine the fraction of hydrogen atoms that are ionised in a given environment. It is commonly used in astrophysics to understand the ionisation state of the gas in stars and other celestial bodies.

2. How does the Saha equation work?

The Saha equation takes into account the temperature and density of the gas, as well as the ionisation energy of the element, to calculate the ratio of ionised to neutral atoms. It is based on the principles of thermodynamics and statistical mechanics.

3. What is the significance of the Saha equation?

The Saha equation is important because it allows us to understand the ionisation state of hydrogen in different environments, which in turn helps us to understand the physical processes happening in stars and other celestial bodies. It also has applications in fields such as plasma physics and nuclear fusion.

4. Can the Saha equation be applied to other elements besides hydrogen?

Yes, the Saha equation can be applied to other elements as well. However, it is most commonly used for hydrogen due to its abundance in the universe and its crucial role in astrophysical processes.

5. Are there any limitations to the Saha equation?

Yes, there are some limitations to the Saha equation. It assumes that the gas is in thermal equilibrium and that the ionisation process is the dominant process in determining the ionisation state. It also does not take into account other factors such as magnetic fields and radiation, which can affect the ionisation state of the gas.

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