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Viefleur [7K]
4 years ago
15

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

Chemistry
1 answer:
Alik [6]4 years ago
7 0
  • <em>n</em> = 3
  • <em>l</em> = 0
  • m_l = 0
  • m_s = 1/2 or -1/2
<h3>Explanation</h3>

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.
  • m_l, the magnetic quantum number.
  • m_s, the spin 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.

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 <em>l</em>. m_l 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 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 <em>n</em>, <em>l</em>, 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 <em>n</em>, <em>l</em>, 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.

<h3>Reference</h3>

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

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