Problem 75 - A Complete Resource Book in Chemistry for JEE Main

Question

If the nitrogen atom has electronic configuration \(1 \mathrm{~s}^{7}\), it would have energy lower than that of the normal ground state configuration \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{3}\), because the electrons would be closer to the nucleus. Yet \(1 \mathrm{~s}^{7}\) is not observed because it violates (a) Heisenberg uncertainty principle (b) Hund's rule (c) Pauli's exclusion principle (d) Bohr postulates of stationary orbits

Step-by-Step Solution

Answer

The configuration \(1\,\text{s}^7\) violates the Pauli exclusion principle.

Step 1: Understand the Problem Statement

We need to determine which principle or rule the electronic configuration \(1\,\text{s}^7\) violates. The configuration implies that seven electrons are filled into the 1s subshell, which can have only two distinct electron states according to known quantum mechanics principles.

Step 2: Recall Atomic Electron Configuration Rules

Electrons fill subshells according to certain rules: the Pauli exclusion principle, Hund's rule, the Aufbau principle, etc. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers, effectively limiting subshells to a set number of electrons.

Step 3: Identify the Pauli Exclusion Principle

The 1s subshell has only one orbital (which can have a maximum of 2 electrons). Assigning 7 electrons to this subshell (\(1\,\text{s}^7\)) means assigning more than two electrons to one orbital. This violates the Pauli exclusion principle, which allows only two electrons (with opposite spins) per orbital.

Step 4: Conclusion Based on Electron Filling Violations

Since the electronic configuration \(1\,\text{s}^7\) fills the 1s orbital with more than the permissible number of electrons, it violates the Pauli exclusion principle.

Key Concepts

Atomic Electron Configuration

Atomic electron configuration is how electrons are arranged around the nucleus of an atom. By understanding this arrangement, you can grasp how atoms interact with each other.
Electrons are arranged in different energy levels or shells, around the nucleus. These shells are assigned numbers, like 1, 2, 3, etc. Each shell can hold a specific maximum number of electrons determined by the formula \(2n^2\), where \(n\) is the shell number.
Within these shells, electrons further reside in subshells or orbitals (s, p, d, f), each with a certain shape and capacity for electrons. Typically:

• The 's' subshell can hold 2 electrons
• The 'p' subshell can hold 6 electrons
• The 'd' subshell can hold 10 electrons
• The 'f' subshell can hold 14 electrons

The electron configuration for a neutral atom is determined by filling the lowest energy levels first, following the Aufbau principle. This guides you and ensures that electrons are filled efficiently and according to natural laws.

Quantum Numbers

Quantum numbers are essential parts of understanding how electrons position themselves in atoms. Each electron in an atom has a unique set of four quantum numbers:

• Principal Quantum Number (n): Indicates the energy level of an electron and its distance from the nucleus. Values are positive integers like 1, 2, 3, etc.
• Angular Momentum Quantum Number (l): Defines the shape of an electron's orbital. It ranges from 0 to \(n-1\), where 0 refers to 's', 1 to 'p', 2 to 'd', and 3 to 'f'.
• Magnetic Quantum Number (m_l): Describes the orientation of the orbital in space, ranging from \(-l\) to \(+l\).
• Spin Quantum Number (m_s): Electrons can spin in two possible ways, represented as \(+\frac{1}{2}\) or \(-\frac{1}{2}\).

Knowing these quantum numbers allows you to understand why only two electrons with opposite spins can occupy any single orbital. This is a foundation of the Pauli exclusion principle, ensuring no two electrons in an atom have the same set of quantum numbers.

Electron Subshells

Electron subshells refer to the division within an atom's electron shell. These are crucial for understanding electron configuration and chemical properties of elements.
Each principal energy level holds different types of subshells, denoted by s, p, d, f.
Subshells vary in terms of their electron capacities and shapes. Here's a simple layout of how they differ:

• The s subshell is spherical and holds up to 2 electrons.
• The p subshell is dumbbell-shaped and can accommodate up to 6 electrons.
• The d subshell, with its more complex shape, can fit up to 10 electrons.
• The f subshell, even more intricate, has a capacity for 14 electrons.

Electrons fill these subshells in a specific order, starting from the lowest energy subshell moving upwards. This process respects the Pauli exclusion principle, ensuring that each electron has a unique set of quantum numbers and, hence, a unique place in the subshell structure. Understanding this order is critical for predicting electron behavior and the atom's reactivity.