Chemistry - Atomic Structure Question with Solution | TestHub

The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers ($n$, $l$, $m_l$, $m_s$). This implies that an atomic orbital can hold a maximum of two electrons, and these two electrons must have opposite spins.

Let's analyze each option:

1. $1s^2,2s^2,2p^4$:

The $1s$ orbital has 2 electrons (spin-paired).

The $2s$ orbital has 2 electrons (spin-paired).

The $2p$ subshell has 3 orbitals, which can accommodate up to 6 electrons. Here, it has 4 electrons, which is permissible (e.g., two paired in one $2p$ orbital, and one unpaired in each of the other two $2p$ orbitals, following Hund's rule).

This configuration follows the Pauli exclusion principle.

2. $1s^2,2s^2,2p^4,3s^2$:

This configuration is similar to option 1, with an additional $3s^2$ subshell.

The $3s$ orbital has 2 electrons (spin-paired).

All subshells are filled according to the Pauli exclusion principle.

This configuration follows the Pauli exclusion principle.

3. $1s^2,2p^4$:

The $1s$ orbital has 2 electrons.

The $2p$ subshell has 4 electrons.

While this configuration might violate the Aufbau principle (as $2s$ is skipped), it does not violate the Pauli exclusion principle itself, as no orbital contains more than two electrons with the same spin. Each orbital within the $2p$ subshell can hold up to two electrons.

This configuration follows the Pauli exclusion principle.

4. $1s^2,2s^{2}2p^6,3s^3$:

The $1s$ orbital has 2 electrons.

The $2s$ orbital has 2 electrons.

The $2p$ subshell has 6 electrons (fully filled).

The $3s$ orbital has 3 electrons. This violates the Pauli exclusion principle because an $s$ orbital can only hold a maximum of two electrons. Having three electrons in the $3s$ orbital means at least two electrons would have the same set of four quantum numbers, which is forbidden.

Therefore, the electronic configuration $1s^2,2s^{2}2p^6,3s^3$ does not follow the Pauli exclusion principle.

The final answer is D.