Which of the following is the correct set of 4 quantum numbers of the 19\(^{\text{th}}\) electron in Chromium (Atomic number = 24) in accordance with the Aufbau principle?
Detailed Step-by-Step Solution
This question evaluates your understanding of the Aufbau Principle, which dictates the order in which electrons fill atomic orbitals based on increasing energy levels.
Step 1: Write the Filling Order
According to the \((n+l)\) rule of the Aufbau principle, orbitals are filled in the following order:
Step 2: Track the 19\(^{\text{th}}\) Electron
Let's count the maximum number of electrons each subshell can hold until we reach the 19\(^{\text{th}}\) electron:
- \( 1s^2 \) (2 electrons)
- \( 2s^2 \) (4 electrons total)
- \( 2p^6 \) (10 electrons total)
- \( 3s^2 \) (12 electrons total)
- \( 3p^6 \) (18 electrons total)
The first 18 electrons perfectly fill up to the \( 3p \) orbital (forming the Argon core, \([\text{Ar}]\)).
Therefore, the very next electron (the 19\(^{\text{th}}\) electron) must enter the \( 4s \) orbital.
Note: While Chromium (Z=24) has an anomalous ground state configuration of \([\text{Ar}] 4s^1 3d^5\), the 19\(^{\text{th}}\) electron entering the system based on the Aufbau sequence is strictly the \(4s\) electron.
Step 3: Assign Quantum Numbers to the 4s orbital
For an electron residing in a \( 4s \) orbital, the four quantum numbers are:
- Principal (\(n\)): Indicates the shell. For \(4s\), \( \mathbf{n = 4} \).
- Azimuthal (\(l\)): Indicates the subshell. For an \(s\)-orbital, \( \mathbf{l = 0} \).
- Magnetic (\(m\)): Ranges from \(-l\) to \(+l\). Since \(l=0\), \( \mathbf{m = 0} \).
- Spin (\(s\)): The first electron entering an orbital is conventionally assigned a positive spin, so \( \mathbf{s = +\frac{1}{2}} \).
Conclusion: The 4 quantum numbers are \( n = 4, l = 0, m = 0, s = +\frac{1}{2} \). Therefore, the correct option is (D).
Mastering Quantum Number Trick Questions
This question is designed as a clever trap. When students see "Chromium," they immediately think of its anomalous \(3d^5 4s^1\) configuration and often look for quantum numbers associated with the \(3d\) orbital. However, the question specifically asks about the 19\(^{\text{th}}\) electron according to the Aufbau principle, which is always the \(4s\) electron!
To master these subtle concepts involving the \((n+l)\) rule, half-filled stability anomalies, and quantum numbers, we strongly encourage reviewing our comprehensive guide on the Structure of Atom Class 11 Chemistry.
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