Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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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) \( n = 3, \ell = 1, m\ell = 1, ms = +\frac{1}{2} \)](https://content.bartleby.com/qna-images/question/42021111-4ced-4c6f-84e9-5b1969157ec2/fdd8cc8b-5798-4c70-be57-b543a26624f1/8hwvtpb_processed.jpeg)
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 \( m_\ell = 2 \).](https://content.bartleby.com/qna-images/question/42021111-4ced-4c6f-84e9-5b1969157ec2/fdd8cc8b-5798-4c70-be57-b543a26624f1/609nwto_processed.jpeg)
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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