Quantum Numbers and Total number of Orbitals

[kirsten_2009]

Homework Statement

How many orbitals have the values n = 4, l = 3, and m_l = -2?

Homework Equations

First of all, is this question asking me how many orbitals there are with the given quantum numbers? Second, how do I go about finding that out

The Attempt at a Solution

I thought that I could figure out the number of orbitals by using 2*l +1 but the answer I get is wrong? Help please :)

 

[JJMB]

I think your answer would be correct if only n and l were given. The reason that 2*l + 1 does not apply is because the magnetic quantum number (m_l) is specified. The magnetic quantum number has to do with energy level within a subshell, and if I remember correctly, each orbital is associated with a single m_l.

So what does that tell you about the number of orbitals that meet the criteria above?

 

[kirsten_2009]

Hi! Thanks for your reply...I'm not quite sure at what you're trying to get at here...sorry :S I wish I did.

 

[JJMB]

The four quantum numbers are used to describe an electron.

1st QN tells you what shell it is in. n = 1,2,3,...
2nd QN tells you what subshell it is in. l = 0,1,2,...
3rd QN specifies an orbital. m_l can be anywhere from -l to positive l, including 0. This is the reasoning behind the 2l + 1 equation. That equation tells you how many possible m_l values there are for a specific subshell, and thus how many orbitals are in a subshell.
4th QN tells you the spin of the electron. m_s = +1/2 or -1/2

In your problem, they told you what the m_l value was. The possible m_l values for the given subshell were -3,-2, -1, 0, 1, 2, 3, but they narrowed it down and told you that it was -2.

How many orbital choices does that leave you with?

 

[kirsten_2009]

Just one! That makes perfect sense! Thanks so much!