What do the notations 1s, 2s, and 2p mean in relation to atomic orbitals?

[joker_900]

Homework Statement

Hi, I've been given a problem set and there is suddenly new notation that I've never seen. Can anyone shed any light on what this means:

"Treating a0 as a parameter, write down the complete wavefunctions (including radial
and angular parts) for the states 1s, 2s, and 2p (giving all three ml possibilities in the last
case)."

Homework Equations

The Attempt at a Solution

I have no idea what the 1s, 2s and 2p mean. ml are the eigenvalues of the Lz operator, so I'm guessing 2p somehow corresponds to a state with l=1, as it says there are 3 m values, but other than that I don't know. Help!

 

[malawi_glenn]

the first figure is n, the principal quantum number. n starts from 1.

the letter is the L quantum number, from the eigenvalue of the L^2 operator: L(L+1). L starts from 0, and goes to n-1. It is convenient to have letters to these ones, since n is assigned by a number. The convention is:

L = 0, s
L = 1, p
L = 2, d
L= 3, f
L = 4, g

L is called the orbital quantum number, and now comes the part you understood, that m_L is eigenvalue of L_z with 2L + 1 distinct eigenvalues.

 

[tiny-tim]

For pretty pictures of the orbitals, see http://en.wikipedia.org/wiki/Atomic_orbital#Orbitals_table :tongue2: