Quantum numbers - Total Energy and Orbital Momentum

[klw289]

With the quantum numbers l=1, n=2 and m=-1 how do I calculate the total energy E, L² (the square of the orbital momentum) and L_z (the z-component of the orbital angular momentum.

I've been trying for two hours and am getting no were. Please help

 

[stevendaryl]

With the quantum numbers l=1, n=2 and m=-1 how do I calculate the total energy E, L² (the square of the orbital momentum) and L_z (the z-component of the orbital angular momentum.

I've been trying for two hours and am getting no were. Please help

Is this a homework problem? If so, it should be moved to the homework section, and should be put in the proper homework problem format.

 

[klw289]

This was not "homework" I am just reading a physics book for my own enjoyment and I was reading a section and I have no clue how to get started. I could post it in homework if its more suitable?

 

[stevendaryl]

This was not "homework" I am just reading a physics book for my own enjoyment and I was reading a section and I have no clue how to get started. I could post it in homework if its more suitable?

Well, the actual way that these things are figured out is to start with Schrodinger's equation. That's a pretty complicated undertaking, which can't really be described in a post. If you just want to skip to the answers: For a hydrogen atom,

[itex]E = \frac{- m q^4}{\hbar^2 n^2}[/itex]

where [itex]m[/itex] is the mass of an electron, [itex]q[/itex] is the charge of an electron (in CSU units), [itex]n[/itex] is the principal quantum number, and [itex]\hbar[/itex] is Planck's constant.

[itex]L = \sqrt{l(l+1)} \hbar[/itex]
[itex]L_z = m \hbar[/itex]

For an atom other than a hydrogen atom, replace [itex]q^4[/itex] by [itex]N^2q^4[/itex], where [itex]N[/itex] is the number of protons in the atom.

 

[jtbell]

We consider this to be a "homework-like" problem. If your trouble is that you can't find the appropriate formulas, try here:

http://hyperphysics.phy-astr.gsu.edu/hbase/qunoh.html

Follow the links for "Principal quantum number", etc.

If you have the formulas but you can't get the numbers to come out right, go to the Introductory Physics Homework forum:

https://www.physicsforums.com/forums/introductory-physics-homework.153/

Post what you've done (show your work), and someone can probably find your mistake.

(stevendaryl slipped in ahead of me)

 

[klw289]

Thank you, that can get me started. I'll also go back to schrodingers equation.