Saha equation to determine fraction of hydrogen atoms ionised

[can't.do.phys]

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?

 

[gtoguy97]

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.