Energy Levels

[madisondesilva1c]

Can someone please explain why as one increases energy level, the distance between the levels decreases? E.g Energy level 3 and 4 are closer together than Energy level 2 and 3. Also, is there a way to calculate the energy of the photon emitted per transition of energy level?

[Jovian Cheung 1K]

I've always been taught that the energy levels get closer and closer and eventually converge - just as a rule of thumb - but I'd like to know why too.

As for the second question, calculate the E_FINAL and E_INITIAL for whichever two energy levels that you are transitioning between (respectively) by using E_n = -hR/n² and find the difference between them! h & R are constants while n is the energy level. Note that this equation is only valid for hydrogen.
^ At least this is my current understanding, please let me know if something's wrong!

:o)

[Andrewwiner4D]

It has to do with the effective nuclear charge. Shielding also plays a factor. The shielding effect describes the balance between the pull of the protons on valence electrons and the repulsion forces from inner electrons. The effective nuclear charge is the net positive charge experienced by valence electrons. It can be approximated by the equation: Zeff = Z – S, where Z is the atomic number and S is the number of shielding electrons. Essentially, the more electron valence shells, the further they will get from the nucleus because there is less of a pull from the protons.

[Andrewwiner4D]

That reply is by Andrew Winer^^

[Jovian Cheung 1K]

It has to do with the effective nuclear charge. Shielding also plays a factor. The shielding effect describes the balance between the pull of the protons on valence electrons and the repulsion forces from inner electrons. The effective nuclear charge is the net positive charge experienced by valence electrons. It can be approximated by the equation: Zeff = Z – S, where Z is the atomic number and S is the number of shielding electrons. Essentially, the more electron valence shells, the further they will get from the nucleus because there is less of a pull from the protons.

Oh yes! Thank you Andrew for mentioning the shielding effect.
So I'm guessing that technically, as the higher energy levels are further away from the nucleus, the weaker nuclear charge means that less energy is needed for an electron to move up an extra level?
For example, it takes a lot of energy for an electron to be excited from n=2 to n=3, but takes much less energy for it to move from n=6 to n=7. Does that make sense?