Energy separation between two states?

[spaghettibretty]

Homework Statement

The wavelength of the radiation emitted when the outermost electron of Al (Aluminum) falls from the 4s state to the ground state is about 395 nm. Calculate the energy separation (in joules) between these two states in the Al atom. Draw an energy level diagram of the states and transitions discussed.

Homework Equations

The ground state electron configuration of Al is 1s²2s²2p⁶3s²3p¹, if that helps.
In my attempted solution I also use E = h * c / λ.
Rydberg equation: E = -(2.18e-18 J) * (Z)² * (1/n₂² - 1/n₁²)

The Attempt at a Solution

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I'm not one hundred percent sure on what the question is asking. Would the outermost electron falling to the ground state mean it goes from 4s to 3p? In this case do I have to use the rydberg equation with the 2 n's being 3 and 4?
Or does that not matter and all I have to do is plug it into E = h * c / λ, where E is the energy separation between the 4s state and the ground state? I'm also suppose to draw an energy level-diagram, I know how to set it up and all that, but would the arrow go from 4s to 3p or would it go from 4s to the very bottom (the ground state)?

 

[DrClaude]

Would the outermost electron falling to the ground state mean it goes from 4s to 3p?

Correct.

In this case do I have to use the rydberg equation with the 2 n's being 3 and 4?

The Rydberg formula is only valid for one-electron atoms. (In some special cases, it can be adapted to some other atoms using quantum defect theory, but this is not relevant here.)

Or does that not matter and all I have to do is plug it into E = h * c / λ, where E is the energy separation between the 4s state and the ground state?

This.

I'm also suppose to draw an energy level-diagram, I know how to set it up and all that, but would the arrow go from 4s to 3p or would it go from 4s to the very bottom (the ground state)?

What do you think?