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four quantum numbers that could represent the last electron added (using the Aufbau principle) to the Argon atom. A n = 2, l =0, m_l = 1, m_s = +\frac12 B n = 3, l =0, m_l = 1, m_s = -\frac12 C n = 3, l =1, m_l = 1, m_s = +\frac12 D n = 3, l =2, m_l = 1, m_s = -\frac12

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Edufirst

Answer:

  • n = 3
  • [tex]l[/tex]  = 1
  • [tex]m_l[/tex] = 1
  • [tex]m_s=+1/2[/tex]

Explanation:

Argon atom has atomic number 18. Then, it has 18 protons and 18 electrons.

To determine the quantum numbers you must do the electron configuration.

Aufbau's principle is a mnemonic rule to remember the rank of the orbitals in increasing order of energy.

The rank of energy is:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7d

You must fill the orbitals in order until you have 18 electrons:

  • 1s² 2s² 2p⁶ 3s² 3p⁶   : 2 + 2 + 6 + 2 + 6 = 18 electrons.

The last electron is in the 3p orbital.

The quantum numbers associated with the 3p orbitals are:

  • n = 3

  • [tex]l[/tex] = 1 (orbitals s correspond to [tex]l[/tex] = 0, orbitals p correspond to [tex]l[/tex]  = 1, orbitals d, correspond to [tex]l[/tex]  = 2 , and orbitals f correspond to  [tex]l[/tex] = 3)

  • [tex]m_l[/tex] can be -1, 0, or 1 (from - [tex]l[/tex]  to + [tex]l[/tex] )

  • the fourth quantum number, the spin can be +1/2 or -1/2

Thus, the six possibilities for the last six electrons are:

  • (3, 1, -1 +1/2)
  • (3, 1, -1, -1/2)
  • (3, 1, 0, +1/2)
  • (3, 1, 0, -1/2)
  • (3, 1, 1, +1/2)
  • (3, 1, 1, -1/2)

Hence, the correct choice is:

  • n = 3
  • [tex]l[/tex]  = 1
  • [tex]m_l[/tex] = 1
  • [tex]m_s=+1/2[/tex]

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