[lateralus01]

I really need help understanding pretty much everything about quantum numbers.  We have a really bad chemistry teacher and I am trying to read the book to catch up but I still get really stuck.  I'm not stupid, i learned calculus by myself I just have a horrible chemistry teacher.
I can tell you what I know:

THE VOCAB IS WHAT STUMPS ME!!!!

I'll bold the vocab words and then tell my interpretation of the text.

*Statement from book
-My own interpretation
???question

*"An orbital is a three-dimensional region around the nucleus that indicates the probable location of an electron."
-So that's pretty easy to understand.  And here's a graphical representation of an orbital:

http://www.rmutphysics.com/charud/scibook/crystal-structure/porbital.gif

-I assume the origin is where the nucleus is and the colored space represents where an electron is most likely to be found in the space around it.

*"electrons of increasing energy occupy orbits farther and farther from nucleus."
???when they say "occupy orbits" by orbits do they mean orbitals or no?
???Does that mean an electron with a higher energy level would move to the next orbital; like an electron would go from the S to the P orbital if it gained more energy? 
???Does that mean the P orbital is farther from the nucleus? 

Here's the big one:  WHAT IS THE RELATIONSHIP BETWEEN ENERGY LEVELS AND ORBITALS?  WHAT ARE ENERGY LEVELS?

The best clue to this question I have is this sentence:

*"Electrons in atomic orbitals also have quantized energies"
-The definition for "quantized" is: 2.  apply quantum theory to; restrict the number of possible values of (a quantity) or states of (a physical entity or system) so that certain variables can assume only certain discrete magnitudes that are integral multiples of a common factor; "Quantize gravity"

???So that would mean that electrons in atomic orbitals have "restricted" or fixed energies for that orbital?
???So the leap here is that an energy level is an orbital?

*"the principal quantum number, symbolized by n, indicates the main energy level occupied by the electron"
-N is the main energy level.  Ok so they move from one energy level to another but they mostly stay in their "main" energy level.

"As n increases, the electron's energy and its average distance from the nucleus increase"
-This appears to support the fact that orbitals and energy levels are the same or at least vary directly

This one kills me:

"The total number of orbitals that exist in a given shell or main energy level is equal to n^2"

This just screws up everything i thought was true:

"electrons of increasing energy occupy orbits farther and farther from nucleus."
orbit varies directly as energy so orbit = energy
"Electrons in atomic orbitals also have quantized energies"
again orbitals depend on energy orbit = energy
"the principal quantum number, symbolized by n, indicates the main energy level occupied by the electron"
n = energy level

orbital = energy
energy = n
orbital = n
number of orbitals in energy level is orbital squared?

what?
please could someone answer these questions?

can you define for me:
orbital:
orbit:
energy:
energy level:
sublevel:

anything to clarify this it's a mess and i just need a foundation.

thanks, lateralus

[Alpha-Omega]

OH MY...one chunck at a time here..this is huge...Have to break this up into pieces...and you do seem to have a handle on this.

 assume the origin is where the nucleus is and the colored space represents where an electron is most likely to be found in the space around it.

YES

electrons of increasing energy occupy orbits farther and farther from nucleus."
???when they say "occupy orbits" by orbits do they mean orbitals or no?

I think they are using it synonomously-an orbital is a mathematically described region around a nucleus in an atom or molecule that may contain zero, one, or two electrons ?

??Does that mean an electron with a higher energy level would move to the next orbital; like an electron would go from the S to the P orbital if it gained more energy?

Let me be very careful here...you have to take n into consideration...there is 1S and 2S and 2P...2S and 2P are of the same energy but P has a higher degree of symmetry... the P shell has 3 orbitals each of which can hold a max of 2 electrons (2 max in each orbital) so holds total of 6.   

2S and 2P are of higher energy that 1S.  n is the quantum number that designates the energy level for an electron.

???Does that mean the P orbital is farther from the nucleus? 

mmm Technically YES....but there are other things more advanced options....for your purposes..YES..OK have: 1S 2S 2P 3S 3P....both 3S and 3P will be farther from the nucleus than 2S and 2P...

Energy levels are dsignated by n the principle quantum number.

OK take next chunck in next reply.

[Alpha-Omega]

You need to get a copy of Whitten, Davis and Peck general Chemistry Text...

Electrons in atomic orbitals also have quantized energies"

YES-T

he definition for "quantized" is: 2.  apply quantum theory to; restrict the number of possible values of (a quantity) or states of (a physical entity or system) so that certain variables can assume only certain discrete magnitudes that are integral multiples of a common factor; "Quantize gravity"

YES...there are allowed enrgy levels for transitions and forbidden energy levels for transitions...electrons can make some transitions in energy-so some are ALLOWED...others are FORBIDDEN...there are transitions that are FORBIDDEN

???So that would mean that electrons in atomic orbitals have "restricted" or fixed energies for that orbital?
???So the leap here is that an energy level is an orbital?

For any particular electron certain transitions to other levels are ALLOWED and certain transitions are FORBIDDEN....

*"the principal quantum number, symbolized by n, indicates the main energy level occupied by the electron"
-N is the main energy level.  Ok so they move from one energy level to another but they mostly stay in their "main" energy level.

n can change if an electron makes an ALLOWED transition...it does want to be in its lowest energy state...its HAPPY PLACE...to get to a higher energy level an electron has to experience an energetic event...like flourescense....

"As n increases, the electron's energy and its average distance from the nucleus increase"
-This appears to support the fact that orbitals and energy levels are the same or at least vary directly

This one kills me:

"The total number of orbitals that exist in a given shell or main energy level is equal to n^2"

That would be correct

The Shells are designated by s,p, d, and f and n the principle quantum number in fron t of the shell

Order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d,,,,

Notice the n in front of the s,p,d,f is changing right

A 1 shell has 1s and 1^2 = 1 and a 1s has 1 sherical orbital so 1^2 = 1 = 1 spherical orbital

A 2 shell has a 2s and a 2p...the  n^2 = 4  = 4 and that is correct: 1 orbital in the 2s and 3 orbitals in a 2 p so 1 + 3 = 4.

A 3 shell has a 3s, 3p, and 3d...the 3^2 = 9 and that is correct:  1 orbital in the 3s, and 3 orbitals in the 3p, and 5 orbitals in the 3d..so 1 + 3 + 5  =9

Do you understand so far?? 

[Sev]

"The total number of orbitals that exist in a given shell or main energy level is equal to n^2"

1st shell has 1 orbital: 1s², 2nd shell has 4: 2s²2p_x²2p_y²2p_z², 3rd shell has 9 orbitals - so n² rule is true.

edit: αώ was faster

[Alpha-Omega]

Now that you know all this CHOOSE QUANTUM....CHOOSE QUANTUM..

[Alpha-Omega]

OOPS MY BAD:  Quantum Numbers....Nice explanation here:

http://en.wikipedia.org/wiki/Quantum_number