# Ionization Energies

1. Oct 15, 2013

### physicsnobrain

1. The problem statement, all variables and given/known data
The energy of particles in a flame at a temperature T might be described by a
Boltzmann distribution. Temperature can be converted to energy (and thereby velocity)
using the gas constant R = 8.3145 J mol-1 K-1. Let us approximate thermal energy in the
flame by RT (squiggly lines mean approximately) where T is in degree Kelvin:
thermal energy ≈ RT
The first ionization energy for Li is 5.20 x 10 2 kJ/mol and the second ionization energy
is 7.29 x 103 kJ/mol. Assume that your Bunsen burner reached 869 ºC, and that nearly all
of Li atoms heated in your Bunsen burner had energies less than 4 x RT. Would you or
would you not expect significant ionization in the flame? Explain.

3. The attempt at a solution
The ionization energy for Li is the opposite of the ionization energy of the flame. The second Li ionization is fairly high, and as a result, I would expect that the ionization energy of the flame is not very significant because the Li ionization is high. Lithium is high on the list of reactive elements, they increase in reactivity going down, example, francium is much more reactive than lithium, I would expect a much larger ionization of flame from franciums ionization compared to lithium.

Am I correct?

2. Oct 16, 2013

### Staff: Mentor

What does "ionization energy of the flame" mean?

I don't understand what this has to do with the problem. You only have to consider lithium in the flame. Is it significantly ionized or not?

3. Oct 16, 2013

### physicsnobrain

no it is not significantly ionized. I said that.

4. Oct 16, 2013

### Staff: Mentor

But based on what? I would like to see some calculations...

5. Oct 16, 2013

### physicsnobrain

well obviously R x T is wayyyyyyyyy less than 4(R)(T)

That is why

6. Oct 16, 2013

### Staff: Mentor

You're comparing $RT$ with $4RT$? I think you misunderstood the statement of the problem. First, it says that $E_\mathrm{thermal} \approx RT$, then that $E_\mathrm{thermal}$ is at most $4RT$ (the energy follows a distribution, it is not a fixed value). So how does that compare to the ionization energy?