# Homework Help: Question regarding the d Orbitals

1. Apr 17, 2005

### mathzeroh

hey everyone! good morning!

can anyone please clarify this statement for me?

True of False (correct statement if false)

There are five d orbitals at both the fourth and sixth principal energy levels.

i said it was false because there's only one d orbital per principal energy level. now i know that that is completely wrong (what i said was wrong) but i guess i'm just having a hard time understanding what the principal energy levels are and what that mean...that statement was actually true, but can anyone help me understand why its true?

thanks alot!!

2. Apr 17, 2005

### whozum

I believe that there are five orbitals in any d shell, but I think this may be a problem of vocabulary. If orbital means the item that holds two electrons, then yes there are 5 of them.

At the 4th and 6th principle energy levels:

$$1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6$$

The fourth principle energy level has a coefficient of 4 in the above electron configuration. You can write it out to the 6th level but I'm not sure how it goes after that. as you can see the d shell on the fourth energy level has 5 orbitals, since it holds 10 electrons.

3. Apr 17, 2005

### dextercioby

In spectroscopic notation "d" stands for $l=2$ to which 5 possible values for $m_{l}$ correspond.Therefore,it doesn't matter what the value of [itex] n\geq3 [/tex] is.

Daniel.

4. Apr 17, 2005

### whozum

Good call dex. Quantum numbers never lie.

5. Apr 17, 2005

### mathzeroh

Thank you for the help but i appologize because i'm a little slow...i still don't get it. so the 4th principle energy level is the $$4s^2$$? That one? but i only see two, because of the superscript 2, unless i'm missing something here...how does the d shell hold five? please help me!

thanks to both of you btw!

6. Apr 17, 2005

### dextercioby

What is principle energy level?Never heard of this notion.Care to explain?

Daniel.

7. Apr 17, 2005

### christinono

Each principle energy level has different types of orbitals (except for the first, of course). The fourth energy level has:
4s, 4p, 4d, 4f.

The d shell consists of FIVE orbitals, each containing a maximum of 2 electrons (max of 10 electrons).

8. Apr 17, 2005

### mathzeroh

^^^ OHHHH so that's what's meant by it??? ok!! thanks!!

dextercioby, here's what it says in the glossary:

principal energy level(s): the main energy levels within the relectron arrangement in an atom. They are quantized by a set of integers beginning at n=1 for the lowest level, n=2 for the next, and so forth; also called the principal quantum number.

so does that mean that the "principal quantum number/principal energy level" is the periods in the periodic table of elements??

9. Apr 17, 2005

### christinono

Yes, the period an element is in represents the valence energy level.

10. Apr 17, 2005

### OlderDan

The adjective "principal" is used with energy levels because there is a small dependence of energy level on orbital angular momentum. That is why the sequence written earlier as
$$1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6$$
is not strictly in the order 1, 2, 3, 4, 5. These small differences give rise to fine structure in atomic spectra.

11. Apr 17, 2005

### dextercioby

There's no such thing as "main/principal" energy levels.There's only ENERGY LEVELS.

Daniel.

12. Apr 18, 2005

### maverick280857

I don't know about you folks, but this is what I was taught as vocabulary:

Shell-->Subshell-->Orbital

For n = 6 (the 6th shell if you want to call it that way), l can range from 0 to 5, so for n = 6, the subshells are s,p,d,f,g,h. There are 5 d orbitals whenever the d-subshell is present for some n as whozum has correctly pointed out.

The orbital orientations (dx, dy, dz, d(x^2-y^2),d(z^2)) are described by m (allowed to range from -l to +l including zero). If you know how the quantum numbers work you know which orbital "exists" for any energy level (whether or not it contains electrons is something different).