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

Short answer

The configuration \(1s^7\) violates the Pauli exclusion principle.

Step-by-step solution

Understand the Given Electronic Configuration

The proposed electronic configuration for the nitrogen atom is \(1s^7\). This means that it suggests putting all seven electrons into the 1s orbital, which is unusual and potentially incorrect.

Current Ground State Configuration of Nitrogen

The ground state electronic configuration of nitrogen is \(1s^2 2s^2 2p^3\). In this configuration, the 1s orbital can hold only 2 electrons, and the remaining electrons are placed in the 2s and 2p orbitals.

Recognize Electron Orbital Capacity

The 1s orbital can hold a maximum of 2 electrons due to the Pauli exclusion principle, which states no more than two electrons can occupy a given orbital, and they must have opposite spins.

Identify the Violated Principle

The proposed \(1s^7\) configuration violates the Pauli exclusion principle since it suggests placing more than 2 electrons in the 1s orbital. This principle is a fundamental rule in quantum mechanics preventing more than 2 electrons in any singular orbital.

Key concepts

Pauli Exclusion Principle

The Pauli Exclusion Principle is a key idea in quantum mechanics that helps us understand how electrons are distributed in an atom. In simple terms, it states that no two electrons in the same atom can have identical quantum numbers. This means that each electron must have a unique set of quantum characteristics. Since an orbital is defined by its quantum numbers, only two electrons can "fit" into any given orbital. Moreover, these two electrons must have opposite spins.

For example, consider the nitrogen atom. In its ground state, the nitrogen atom's 1s orbital holds 2 electrons - one with spin-up and the other with spin-down. If we tried to place more electrons in this orbital, as suggested by the incorrect configuration of 1s^7, we would violate this principle.

• Ensures electrons are uniquely positioned and spinning.
• Prevents electron accumulation in a single orbital.

This principle assists in organizing elements in a way that contributes to their chemical properties, which is why it’s a fundamental concept in chemistry and physics.

Quantum Mechanics

Quantum mechanics is the branch of physics that explores the behavior of very small particles, like electrons in an atom. It provides the framework that describes how these particles behave, interact, and are arranged. In the world of quantum mechanics, particles don’t follow the ordinary laws of classical physics. Instead, they follow principles like wave-particle duality and uncertainty.

When we talk about electrons in atoms, quantum mechanics introduces us to quantum numbers, which describe the properties and positions of electrons.

• Principal quantum number (n): Indicates the energy level and size of the orbital.
• Azimuthal quantum number (l): Describes the shape of the orbital.
• Magnetic quantum number (m_l): Specifies which orbital the electron occupies within a subshell.
• Spin quantum number (m_s): Represents the electron's spin direction.

These numbers help define everything about an electron's position in an atom, ensuring that no two electrons in the same atom have the same set of quantum numbers, thanks to the Pauli Exclusion Principle.

Orbital Capacity

Orbital capacity refers to the maximum number of electrons that a given orbital can accommodate. This number is determined by the Pauli Exclusion Principle. For s orbitals, the capacity is 2 electrons; for p orbitals, it is 6; for d orbitals, it is 10; and for f orbitals, it is 14.

Each of these electrons must have opposite spins, maintaining the maximum stability and organization within an atom. Consider, for example, the nitrogen atom’s actual configuration: 1s^2 2s^2 2p^3. This configuration shows the proper filling of orbitals up to the given number of electrons, ensuring stability and adherence to quantum rules.

• The 1s orbital, in particular, may hold a maximum of 2 electrons.
• Going beyond this capacity leads to unstable or unknown chemical behavior.

Understanding orbital capacity is crucial since it dictates how atoms interact and form bonds.

Nitrogen Atom

The nitrogen atom, an essential element in the periodic table, has the atomic number 7. This means it contains 7 protons in its nucleus and, in a neutral state, 7 electrons. The electronic configuration of the nitrogen atom in its ground state is 1s^2 2s^2 2p^3, following the rules of orbital filling and quantum mechanics.

This configuration shows that the 1s and 2s orbitals are fully filled, and the p orbitals begin to fill next. This specific arrangement gives nitrogen its unique properties, as it can form three covalent bonds with other elements due to the three unpaired electrons in the 2p orbital.

• Allows formation of stable molecules like ammonia (NH₃).
• Participates in many biological processes, such as nucleic acid synthesis.

Understanding these details about nitrogen is key to studying its chemical interactions and role in nature.