Finding the Quantum States for a Nitrogen Atom

[TChill]

Homework Statement

how many possible quantum states for a nitrogen atom with electronic configuration of 1s²2s²2p³

Homework Equations

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The Attempt at a Solution

So, the answer for this question is 20, but I can't for the life of me find out how. The book we're given is Physical Chemistry by Atkins. Quantum state isn't even listed in the index. My professor uses a statistical thermodynamics book by engel & reid, I believe is where he takes these questions from. I don't believe that he is using the phrase quantum states to mean quantum numbers. Please help!

 

[jncarter]

To find the number of possible configurations you need to do some counting. There are formulas out there to do this for a given electron configuration (see Introduction to Quantum Mechanics by Griffiths).

Let's start with an example. For atomic hydrogen you have one electron in configuration 1s<sup>2. An s orbital has one orbit available, which can be occupied by electrons of opposite spin; therefore, the s orbital can hold 2 electrons. The single electron in atomic hydrogen has two possible states available to it, spin up or spin down in the 1s orbital.

For atomic helium, you have two electrons in configuration 1s2. So there are two electrons in the 1s orbital. One is spin up and the other is spin down. There is only one way for this to occur because we cannot tell the difference between the two electrons. There is only one available quantum state.

Only the unfilled orbitals have multiple states available. So you need to count the number of ways you can fit 3 electrons into a p-orbital. Remember that all three slots must have at least one electron. So it will come down to the spin states.</sup>