# Ionization temperature of an atom

by Boltzmann2012
Tags: atom, ionization, temperature
 P: 31 Hi, How do we calculate the temperature required to ionize an atom, say, helium. Also how can we find the number of atoms ionized or unionized at a given temperature? Boltzmann
 P: 21 You should check out the Saha Ionization Equation(s) (or Saha-Langmuir Equation). I must say, wikipedia actually has a good page on the equation(s) and its use.
 P: 31 Thanks. I have read it and it is nice. But what should we do when the ionization fraction tends to 1, I.e the Saha ionization eqn is valid only for thermal equillibrium. Regards Boltzmann
P: 21

## Ionization temperature of an atom

- Firstly, sorry it took me so long to reply. I have to say I was stumped by your question and was looking for my notes when I learned about the equation, but unfortunately I couldn't find them.

- I'm just going to tell you what I know. When I learned it, my professor wrote the equation differently (in the equation below, I modified the variables so it has the same variable names as that for Wikipedia):
$\frac{g_{i}}{g_{i+1}}$$\frac{n_{i+1}}{n_{i}}$$\frac{n_{e}\Lambda^{3}}{2}$ = e$^{-\frac{\Delta\epsilon}{k_{B}T}}$

- As the entire term on the left tends to 1, then it will take an infinitely large temperature and thus an infinitely large amount of energy to further ionize atoms (in most cases we consider the first ionization state (so n0 and n1 for example). Therefore, this acts as a limiting scenario. I remember my professor ascribing a name to this scenario (as though someone had discovered it and had their ascribed to it). But to be honest I don't remember all that well so this is my educated guess.

- If I didn't answer your question I'm sorry, but that's all I've got (good question)!
 P: 31 Thank you for the reply. It was most useful. Regards L.Boltzmann
 Sci Advisor P: 2,406 The irony here is that the equation for fraction of atoms ionized at a given temperature is derived from Boltzmann distribution.
 P: 31 Ah, Thank you for reminding. Ludwig Boltzmann

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