Quantum Numbers for Hydrogen Atom Electron

[bon]

Homework Statement

Define the quantum numbers required to specify the state of an electron in hydrogen. The spatial part of the wave-function describing a particular hydrogen atom has no angular dependence. Give the values of all the angular momentum quantum numbers for the electron.

Homework Equations

The Attempt at a Solution

so am i right that the numbers are:

n - the total energy quantum number, n = L+1 where L is max value of l
l - total orbital angular mom quant number
m_l - z comp of orbital ang mom
s - total spin quantum number
m_s - z comp of spin

what about the next part?

if the spatial wavefunction has no angular dependence then i guess that l = 0, m_l = 0. We know that s = 1/2. What about m_s and n? Surely these can't be known?

 

[bon]

anyone?

 

[bon]

hellooo people - should this be in advanced?

 

[ehild]

n is the principal quantum number, it is assigned to the radial part of the wavefunction. The problem asks the quantum numbers of the angular momentum. Those are l and m.

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

ehild

 

[rwisz]

Yes, you are correct about the quantum numbers for the electron in hydrogen. The spatial part of the wave-function having no angular dependence means that the electron is in the s orbital, which has a value of l=0 and ml=0. The total energy quantum number (n) can take on any positive integer value, and the spin quantum number (s) can only have two values, either +1/2 or -1/2. The z component of the spin (ms) can take on either of these two values as well. Therefore, the values for all the quantum numbers for the electron in hydrogen are n, l=0, ml=0, s=1/2, and ms=+1/2 or -1/2.