How many electrons can have #n = 3#, #l = 2#, #m_l = 2#, #m_s = -1/2#?

1 Answer
Mar 18, 2016

Answer:

Only one electron in a given atom can have the set of quantum numbers given in the question.

Explanation:

No two electrons in an atom can have the same set of quantum numbers.

The first quantum number is the principle quantum number , which is #n=3#. This means the electron is in the third energy level (shell).

The second quantum number, the angular momentum , is #l=2#, and means the electron is in the #"d"# sublevel (subshell).

The third quantum number, the magnetic quantum number , #m_l=2#, represents one of the five #"3d"# orbitals.

Lastly, we have the spin quantum number , #m_s=-1/2#. It indicates the direction of the spin of the electron.

Each electron in an atom has a unique set of quantum numbers.

The given quantum numbers for the electron in the question tell us that there is a high probability that the electron is in one of the #"3d"# orbitals of the atom.

http://www.meta-synthesis.com/webbook/34_qn/qn_to_pt.html

Resources:
http://www.meta-synthesis.com/webbook/34_qn/qn_to_pt.html
http://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Quantum_Mechanics/10%3A_Multi-electron_Atoms/Quantify_Numbers