[Ar] A single electron occupies has the quantum numbers n = 3, { = 2, ml = 2, ms = +12. Based on this and the orbital diagram, which of the following is an acceptable set of quantum numbers for the next electron added? 11 Smy 3d MacBook Air A) n = 3, l = 2, ml = 2, ms = +12 B) n = 3, l = 2, ml = 2, ms = -12 C) n = 4, l = 0, ml = 0, ms = -12 D) n = 3, l = 2, ml = 0, ms = +12 E) n = 3, l = 1, ml = 1, ms = +½

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A single electron occupies the quantum numbers \( n = 3, \ell = 2, m\ell = 2, ms = +\frac{1}{2} \). Based on this and the orbital diagram, which of the following is an acceptable set of quantum numbers for the next electron added?

**Orbital Diagram Explanation:**

The diagram showcases:

- [Ar] 3d: This represents the electronic configuration starting with the argon core ([Ar]) followed by the 3d subshell.
- The 3d subshell has five boxes, each containing an upward arrow, indicating that each orbital is singly occupied with electrons having parallel spins.

**Options for Next Electron:**

A) \( n = 3, \ell = 2, m\ell = 2, ms = +\frac{1}{2} \)

B) \( n = 3, \ell = 2, m\ell = 2, ms = -\frac{1}{2} \)

C) \( n = 4, \ell = 0, m\ell = 0, ms = -\frac{1}{2} \)

D) \( n = 3, \ell = 2, m\ell = 0, ms = +\frac{1}{2} \)

E) \( n = 3, \ell = 1, m\ell = 1, ms = +\frac{1}{2} \)
Transcribed Image Text:A single electron occupies the quantum numbers \( n = 3, \ell = 2, m\ell = 2, ms = +\frac{1}{2} \). Based on this and the orbital diagram, which of the following is an acceptable set of quantum numbers for the next electron added? **Orbital Diagram Explanation:** The diagram showcases: - [Ar] 3d: This represents the electronic configuration starting with the argon core ([Ar]) followed by the 3d subshell. - The 3d subshell has five boxes, each containing an upward arrow, indicating that each orbital is singly occupied with electrons having parallel spins. **Options for Next Electron:** A) \( n = 3, \ell = 2, m\ell = 2, ms = +\frac{1}{2} \) B) \( n = 3, \ell = 2, m\ell = 2, ms = -\frac{1}{2} \) C) \( n = 4, \ell = 0, m\ell = 0, ms = -\frac{1}{2} \) D) \( n = 3, \ell = 2, m\ell = 0, ms = +\frac{1}{2} \) E) \( n = 3, \ell = 1, m\ell = 1, ms = +\frac{1}{2} \)
**Quantum Numbers and Electron Configuration**

A single electron occupies a subshell and has the quantum numbers \( n = 3, \, \ell = 2, \, m_\ell = 2, \, m_s = +\frac{1}{2} \). Which of the following is an acceptable set of quantum numbers for the next electron added to this subshell?

**Diagram Explanation:**

The diagram illustrates electron configurations, showing the arrangement of electrons in the orbitals. It includes:

- The \( [Ar] \) symbol denotes the electron configuration of Argon, which is used as a reference.
- The \( 4s \) orbital box contains two electrons represented by arrows indicating opposite spins.
- The \( 3d \) orbital is shown with five sub-boxes, each containing a single upward arrow, which signifies unpaired electrons with parallel spins in accordance to Hund's rule.

**Options:**

A) \( n = 3, \, \ell = 2, \, m_\ell = 2, \, m_s = +\frac{1}{2} \)

B) \( n = 3, \, \ell = 2, \, m_\ell = 2, \, m_s = -\frac{1}{2} \)

C) \( n = 4, \, \ell = 0, \, m_\ell = 0, \, m_s = -\frac{1}{2} \)

D) \( n = 3, \, \ell = 2, \, m_\ell = 0, \, m_s = +\frac{1}{2} \)

E) \( n = 3, \, \ell = 1, \, m_\ell = 1, \, m_s = +\frac{1}{2} \)

**Conclusion:**

In considering the addition of the next electron, option B is suitable. This choice complements the existing quantum numbers by providing the opposing spin (\( m_s = -\frac{1}{2} \)) for stability within the magnetic quantum number \( m_\ell = 2 \).
Transcribed Image Text:**Quantum Numbers and Electron Configuration** A single electron occupies a subshell and has the quantum numbers \( n = 3, \, \ell = 2, \, m_\ell = 2, \, m_s = +\frac{1}{2} \). Which of the following is an acceptable set of quantum numbers for the next electron added to this subshell? **Diagram Explanation:** The diagram illustrates electron configurations, showing the arrangement of electrons in the orbitals. It includes: - The \( [Ar] \) symbol denotes the electron configuration of Argon, which is used as a reference. - The \( 4s \) orbital box contains two electrons represented by arrows indicating opposite spins. - The \( 3d \) orbital is shown with five sub-boxes, each containing a single upward arrow, which signifies unpaired electrons with parallel spins in accordance to Hund's rule. **Options:** A) \( n = 3, \, \ell = 2, \, m_\ell = 2, \, m_s = +\frac{1}{2} \) B) \( n = 3, \, \ell = 2, \, m_\ell = 2, \, m_s = -\frac{1}{2} \) C) \( n = 4, \, \ell = 0, \, m_\ell = 0, \, m_s = -\frac{1}{2} \) D) \( n = 3, \, \ell = 2, \, m_\ell = 0, \, m_s = +\frac{1}{2} \) E) \( n = 3, \, \ell = 1, \, m_\ell = 1, \, m_s = +\frac{1}{2} \) **Conclusion:** In considering the addition of the next electron, option B is suitable. This choice complements the existing quantum numbers by providing the opposing spin (\( m_s = -\frac{1}{2} \)) for stability within the magnetic quantum number \( m_\ell = 2 \).
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