What are the quantum numbers of carbon?

1 Answer
Mar 30, 2018

Answer:

#n=2#, #l=0, 1#, #m_l=-1, 0, 1#, #m_s=\pm 1/2#

Explanation:

Carbon (atomic number #6#) can be found in the second row of the periodic table; at the ground state, the six electrons occupy two of its principle energy levels, giving the electron with the highest energy a principal quantum number #n# of #2#.

#l=0, 1, 2, ..., (n-1)# where #n# the principal quantum number. [1]
Electrons fill both #"s"# and #"p"# orbitals in a ground-state carbon atom; which correspond to orbital angular momentum numbers (Azimuthal quantum number) #l=0# and #l=1#.
Table from the Wikipedia page for Azimuthal quantum number[2]

#m_l=-l, -l+1, -l+2, ..., -1, 0, 1, ..., l-2, l-1, l# [1]
giving magnetic quantum numbers #m_l# values of #-1, 0, 1# which corresponds to the three #2"p"# orbital in a carbon atom.

#m_s=/pm 1/2#, a property of electrons independent of the atom in question.

References
[1] Quantum Numbers, Libretext, https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/10%3A_Multi-electron_Atoms/Quantum_Numbers

[2]Azimuthal quantum number, the English Wikipedia, https://en.wikipedia.org/wiki/Azimuthal_quantum_number