Question

Which of the following is correct set of 4 quantum numbers of 19th electron in Chromium (Atomic number = 24) in accordance with Aufbau principle?

• A. \(n=3, l=2, m=+2, s=+\frac{1}{2}\)
• B. \(n=3, l=2, m=-2, s=+\frac{1}{2}\)
• C. \(n=4, l=1, m=0, s=+\frac{1}{2}\)
• D. \(n=4, l=0, m=0, s=+\frac{1}{2}\)

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Aufbau principle states that electrons fill lower-energy atomic orbitals before filling higher-energy ones. We need to write the electron configuration step-by-step up to the 19th electron to determine its quantum numbers.
Step 2: Key Formula or Approach:
The order of orbital filling is governed by the \((n+l)\) rule: \(1s, 2s, 2p, 3s, 3p, 4s, 3d, \dots\).
For the 19th electron, we must track the total electron count across these subshells.
Step 3: Detailed Explanation:
Let's build the configuration for Chromium (\(Z=24\)) strictly following the standard Aufbau filling order (ignoring half-filled stability exceptions, as we are looking sequentially for the 19th electron's designated entry orbital):
\(1s^2\) (2 electrons, total 2)
\(2s^2\) (2 electrons, total 4)
\(2p^6\) (6 electrons, total 10)
\(3s^2\) (2 electrons, total 12)
\(3p^6\) (6 electrons, total 18)
The first 18 electrons completely fill the subshells up to \(3p\), corresponding to the Argon core [Ar].
According to the \((n+l)\) rule, the next lowest energy orbital is the \(4s\) orbital (\(n+l = 4+0 = 4\)), which is lower than the \(3d\) orbital (\(n+l = 3+2 = 5\)).
Therefore, the 19th electron will enter the \(4s\) orbital.
Determine the quantum numbers for an electron in the \(4s\) orbital:
Principal quantum number (\(n\)) = 4.
Azimuthal quantum number (\(l\)) = 0 (for an s-orbital).
Magnetic quantum number (\(m\)) = 0 (since \(m\) ranges from \(-l\) to \(+l\), and \(l=0\)).
Spin quantum number (\(s\)) = \(+\frac{1}{2}\) (or \(-\frac{1}{2}\), typically the first electron is designated spin up).
Step 4: Final Answer:
The correct set of quantum numbers is \(n = 4, l = 0, m = 0, s = +\frac{1}{2}\).