Problem 93 - A Complete Resource Book in Chemistry for JEE Main

Question

The orbital diagram in which Aufbau principle is violated is (a) \(\uparrow \downarrow \quad \uparrow \downarrow \uparrow\) (b) \(\uparrow\) (c) \(\uparrow \downarrow \quad \uparrow|\uparrow| \uparrow \mid\) (d) \(\uparrow \downarrow\)

Step-by-Step Solution

Answer

Option (c) violates the Aufbau principle.

Step 1: Understanding the Aufbau Principle

The Aufbau principle states that electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. This helps to determine the electron configurations of atoms. Electrons are added one by one to an atom’s orbitals in a specific order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, and so on.

Step 2: Analyzing Option (a)

Option (a) is \(\uparrow \downarrow \quad \uparrow \downarrow \uparrow\). This diagram indicates two orbitals: the first is fully filled with one spin-up and one spin-down electron, and the second orbital partially filled with two spin-up electrons. This doesn't violate the Aufbau principle itself, although it seems more relevant to Hund's rule which states that every orbital in a subshell is singly occupied before any orbital is doubly occupied.

Step 3: Analyzing Option (b)

Option (b) is \(\uparrow\). This shows a single spin-up electron occupying a single orbital, implying the lowest energy level is occupied first. Therefore, this does not violate the Aufbau principle.

Step 4: Analyzing Option (c)

Option (c) is \(\uparrow \downarrow \quad \uparrow||\uparrow| \uparrow \mid\). Here, we see both paired and unpaired electrons. However, the key issue is the way electrons are distributed across orbitals in a manner that violates normal Aufbau or Hund's usage, as multiple orbitals are occupied unevenly, suggesting possible filling out of energy order.

Step 5: Analyzing Option (d)

Option (d) is \(\uparrow \downarrow\). This indicates a fully filled orbital with one spin-up and one spin-down electron, starting from the lowest energy level. It adheres to the Aufbau principle.

Step 6: Determine the Option that Violates the Principle

By checking each option, option (c) shows electrons distributed in an irregular manner, potentially violating either Aufbau or related princi, especially if energy levels are improperly filled.

Key Concepts

Electron Configurations

Electron configurations describe how electrons are distributed among the different atomic orbitals in an atom. The configuration is written using numbers and letters, where the numbers indicate energy levels, and the letters (s, p, d, f) represent the type of orbital. For instance, in the electron configuration 1s² 2s² 2p⁶, the numbers and letters specify:

• 1s²: Two electrons in the s orbital of the first energy level.
• 2s²: Two electrons in the s orbital of the second energy level.
• 2p⁶: Six electrons in the p orbital of the second energy level.

Each electron occupies an orbital according to rules such as the Aufbau principle and Hund's rule. Following these rules ensures that atoms have lower energy and stay stable. If electron configurations incorrectly depict this distribution, it might lead to configurations that do not adhere to these rules.

Atomic Orbitals

Atomic orbitals are regions in an atom where there is a high probability of finding electrons. These orbitals are denoted as s, p, d, and f:

• s orbitals: Spherical in shape and can hold up to two electrons.
• p orbitals: Dumbbell-shaped and can hold up to six electrons across three sub-levels.
• d orbitals: Complex shapes and hold up to ten electrons in five sub-levels.
• f orbitals: Even more complex, holding up to 14 electrons.

The arrangement of electrons in these orbitals determines how atoms interact with each other. Understanding atomic orbitals is crucial as they define the chemical properties of elements. For instance, knowing which orbitals are filled gives insight into chemical reactivity and bonding.

Hund's Rule

Hund's Rule states that every orbital in a subshell is singly occupied before any orbital is doubly occupied. This means electrons prefer to spread out within a subshell. By doing this, electrons stay as far away from each other as possible, minimizing repulsion and decreasing energy within the atom. If there's more than one unoccupied orbital in a subshell, electrons with parallel spins occupy these orbitals before pairing begins. This principle impacts the electronic structure of atoms significantly. For example, in the 2p subshell, an atom will fill each of the three p orbitals with one electron each before any of them receives a second electron. This spreading is what leads to more stable, lower energy configurations.