Wavefunction and Electron Configuration

[Sapper6]

The wave function for a particular electron is given by:

Psi= 4/(9√(4π)) * (6/a)^(3/2) * (r/a)^2 * e^(2i(phi) - (2r)/a) * sin^2 (θ)

a) This is an electron in which subshell?
b) This is an electron in an atom of which element?
c) What is the ionozation energy for this electron, assuming H-like behavior?
d) In a neutral atom (not H-Like) can this electron be in the ground state?
e) What is the probability of finding this electron within Bohr's radius of the nucleus?


I am not sure where to start here, I am assuming I would normalize the wave function by squaring it, but then how do I pull out quantum number data? I am very confused here.. Could someone please walk me through this or point me in the right direction.

 

[Borek]

Have you tried to compare function given with known orbital functions? I have them listed in my quantum chemistry book, but it is in Polish, so even giving you title will probably not help. But I guess you should be able to locate the solution in your book or even googling it - then comparing constants you should be easily able to find out Z and quantum numbers.

 

[Sapper6]

I think you are referring to the radical substitution tables that are also in my quantum book, but the equation here does correlate to the tables here, I am not sure if i need to normalize it or separate terms or what.

 

[Borek]

Quantum function for a hydrogen atom is a product of two functions, one of them describes angular part of the solution, the other one - radial part. From what I have checked, presence of sin²(θ) (belonging to angular part) nicely tels you something about quantum numbers l and m. Finding quantum numbers and Z is what will allow you answer at least first two questions.

 

[Sapper6]

are you saying that since the theta funtion part has sin^2 theta in it, and the only one in my table that does is theta 22, then both l and m are 2

since the function overall is a product of R(nl) and Theta(lm) Phi(m)

 

[Borek]

Yes, that's what I was referring to. Now, radial part depends on Z, that should give you some more information. Then you are on your own, I have already used all my quantum chemistry knowledge.

 

[Borek]

Topic locked, discussion continues here:

https://www.physicsforums.com/showthread.php?t=442241