# Quantum numbers - Total Energy and Orbital Momentum

• I
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 Lz (the z-component of the orbital angular momentum.

stevendaryl
Staff Emeritus
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 Lz (the z-component of the orbital angular momentum.

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.

secur
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
Staff Emeritus
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,

$E = \frac{- m q^4}{\hbar^2 n^2}$

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

$L = \sqrt{l(l+1)} \hbar$
$L_z = m \hbar$

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

jtbell
Mentor
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