Question

What is a possible quantum number set for an electron in the 3s orbital of a magnesium atom

Answer 1

• n = 3
• l = 0
• $m_l$ = 0

• $m_s$ = 1/2 or -1/2

Explanation

There are four quantum numbers in an electron that orbits the atom.

• n, the principal quantum number.
• l, the angular quantum number.
• $m_l$, the magnetic quantum number.
• $m_s$, the spin quantum number.

n is a positive integer. The value of n indicates the main shell of the electron. The electron in question is in the 3s orbital. As a result, n = 3.

l is a non-negative integer. The value of l indicates the type of subshell ("orbital") of the electron. The types of subshells possible depends on the main shell. For example, both s and p orbitals exist in the second main shell. However, only the s orbital exists in the first main shell. The value of l ranges from 0 to n - 1.

• l = 0 indicates an s orbital.
• l = 1 indicates a p orbital.
• l = 2 indicates a d orbital.
• l = 3 indicates an f orbital.

The electron in question is in an s orbital. As a result, l = 0.

$m_l$ is an integer. The value of $m_l$ indicates the position of the electron within the subshell. The range of $m_l$ depends on the value of l. $m_l$ ranges from -l to l (that's -l, ..., -1, 0, 1, ... l). Accordingly, there are 2 l  + 1 orbitals in a l subshell. l = 0 for this 3s electron. There's only one orbital in the 3s subshell. The only $m_l$ value possible for this electron is 0.

The value of $m_s$ is either - 1/2 or 1/2. It indicates the position of an electron within a single orbital. The value of $m_s$ does not depend on that of n, l, or $m_l$. However, by the Pauli Exclusion Principle, at least one of the four numbers must differ for two electrons in the same atom. In case all three of n, l, and $m_l$ are the same, the two electrons must differ in $m_s$. However, this question asks only for the number of one single electron. Thus, giving either - 1/2 or 1/2 shall work.

Reference

Vitz et. al, "5.8 Quantum Numbers (Electronic)",  ChemPRIME (Moore et al.), Chemistry Libretexts. 27 Oct 2017.