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- <em>n</em> = 3
- <em>l</em> = 0
= 0
= 1/2 or -1/2
There are four quantum numbers in an electron that orbits the atom.
- <em>n</em>, the principal quantum number.
- <em>l</em>, the angular quantum number.
<em>n</em> 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, <em>n</em> = 3.
<em>l</em> is a non-negative integer. The value of <em>l</em> 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 <em>l</em> ranges from 0 to <em>n</em> - 1.
- <em>l</em> = 0 indicates an <em>s</em> orbital.
- <em>l</em> = 1 indicates a <em>p</em> orbital.
- <em>l</em> = 2 indicates a <em>d</em> orbital.
- <em>l</em> = 3 indicates an <em>f</em> orbital.
The electron in question is in an <em>s</em> orbital. As a result, <em>l </em>= 0.
is an integer. The value of
indicates the position of the electron within the subshell. The range of
depends on the value of <em>l</em>.
ranges from -<em>l</em> to <em>l </em>(that's <em>-l</em>, ..., -1, 0, 1, ... <em>l</em>). Accordingly, there are 2 <em>l</em> + 1 orbitals in a <em>l</em> subshell. <em>l </em>= 0 for this 3s<em> </em>electron. There's only one orbital in the 3s subshell. The only
value possible for this electron is 0.
The value of is either - 1/2 or 1/2. It indicates the position of an electron within a single orbital. The value of
does not depend on that of <em>n</em>, <em>l</em>, or
. 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 <em>n</em>, <em>l</em>, and
are the same, the two electrons must differ in
. However, this question asks only for the number of one single electron. Thus, giving either - 1/2 or 1/2 shall work.
Vitz et. al, "5.8 Quantum Numbers (Electronic)", <em>ChemPRIME (Moore et al.)</em>, Chemistry Libretexts. 27 Oct 2017.