You're basically on the right track, but some points:

Why is λ = 6.23e-3? (I can see why, but it's good to make it explicit, in case mistakes creep in.)

If λ = 6.23e-3, 1/λ is not 6.23e3. What is it?

Dividing by Avogadro's number gives you moles, not atoms, and you need to multiply by the molar mass ("atomic weight"). Your procedure is correct but the wording is wrong.

What is the molar mass of F-18? Is it 18.998?