# What are the quantum numbers of carbon?

Mar 30, 2018

$n = 2$, $l = 0 , 1$, ${m}_{l} = - 1 , 0 , 1$, ${m}_{s} = \setminus \pm \frac{1}{2}$

#### 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 $2$.

$l = 0 , 1 , 2 , \ldots , \left(n - 1\right)$ where $n$ the principal quantum number. [1]
Electrons fill both $\text{s}$ and $\text{p}$ orbitals in a ground-state carbon atom; which correspond to orbital angular momentum numbers (Azimuthal quantum number) $l = 0$ and $l = 1$.

${m}_{l} = - l , - l + 1 , - l + 2 , \ldots , - 1 , 0 , 1 , \ldots , l - 2 , l - 1 , l$ [1]
giving magnetic quantum numbers ${m}_{l}$ values of $- 1 , 0 , 1$ which corresponds to the three $2 \text{p}$ orbital in a carbon atom.

${m}_{s} \frac{=}{\pm} \frac{1}{2}$, 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