Advice needed for science project.

[MonsieurWise]

I need some ideas for my project. I'm really new to quantum physics.
I did a project about the Bohr's theory for the school's science fair (just ended this week). It was about proving the Bohr's theory, the Rydberg constant, and test the Bohr's theory availability to explain the spectrum of bigger atoms other than Hydrogen (I used Helium and Lithium).
I assumed that the spectrum of Helium should be a combination of Z=2 spectrum (ionized He) and Hydrogen spectrum (neutral He). And Lithium should be a combination of Z=3 spectrum (doubly ionized Li), He spectrum and Hydrogen spectrum.
My result for Lithium was almost just what I expected, but for helium, there are 3 mysterious lines come from nowhere (I recall one very bright yellow line and two not-so-bright blue lines). I asked around and they say it was transition of the l (orbital quantum number), but not of the n (principal quantum number).
My conclusion was Bohr theory was correct, but for bigger atoms, we need to also consider other quantum numbers.
That was my project. Now I'm considering building more on it or make a totally new project (for the county, and I have about only 4 weeks left). And if I choose to build more, what can I build more on my project to meet the level of a county project? Can I do some more experiment or something to build on it...?
Please help me. Thank you a million in advance!

 

[alxm]

I assumed that the spectrum of Helium should be a combination of Z=2 spectrum (ionized He) and Hydrogen spectrum (neutral He).

Not a correct assumption. The Bohr model only works for a single electron, and the way multiple electrons interact isn't a simple thing to describe. If you were to have an atom with two non-interacting electrons, then the solution would roughly correspond to the Z=2 case - for both electrons, since they occupy a single shell.

I asked around and they say it was transition of the l (orbital quantum number), but not of the n (principal quantum number).
My conclusion was Bohr theory was correct, but for bigger atoms, we need to also consider other quantum numbers.

The number 'n' in the Bohr model is not the n that is the principle quantum number (which wasn't 'invented' until 15 years later). The Bohr model does take into account transitions between all n,l,m states. But not changes in spin-states, since with a single electron it only has a single spin state. Nor does it take into account various coupling effects that split the levels.

There is no simple formula like the Bohr one for any other atom; the Schrödinger equation is only analytically solvable for Hydrogen. Almost immediately (1927) people started working on Helium, and they were still going at it well into the 1960's!* An accurate calculation of Helium energy levels was one of the more noteworthy results produced by WEIZAC, Israel's first computer.

That was my project. Now I'm considering building more on it or make a totally new project (for the county, and I have about only 4 weeks left). And if I choose to build more, what can I build more on my project to meet the level of a county project? Can I do some more experiment or something to build on it...?
Please help me. Thank you a million in advance!

Well, the photoelectric effect is a fairly simple and visible experiment that was important for the development of quantum theory. I'd suggest that.

* Actually some people are still calculating it for the fun of it.
Current best value for the ground state of Helium is E = -2.903724377034119598311159245194404446696925310 Hartrees.
Which is actually extremely silly since it's the non-relativistic value, and therefore wrong after the fifth decimal or so.

 

[MonsieurWise]

Thank you ^^