Problem 30 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Any \(p\)-orbital can accommodate upto (a) four electrons (b) six electrons (c) two electrons with parallel spins (d) two electrons with opposite spins

Step-by-Step Solution

Answer

d) Two electrons with opposite spins.

Step 1: Understanding the p-Orbital

A p-orbital is one of the types of orbitals that electrons can occupy in an atom. In quantum chemistry, the p orbital is characterized by its 'dumbbell' shape and is found in sets of three (px, py, pz). Each p orbital can hold electrons, but with specific rules regarding their quantity and spin characteristics.

Step 2: Pauli Exclusion Principle

According to the Pauli Exclusion Principle, an atomic orbital can hold a maximum of two electrons, and these electrons must have opposite spins. This means that no two electrons can have the same set of quantum numbers within an atom.

Step 3: Identify Maximum Electron Capacity

Given the rules from the Pauli Exclusion Principle, a single p-orbital can accommodate, at most, two electrons. Each of these electrons must have opposite spins, which means they will pair up within the p orbital.

Step 4: Conclusion on Options

The choices given refer to the number and characteristics of electrons that can occupy a p-orbital. Option (a) is incorrect because only one p orbital can hold up to two electrons, not four. Option (b) refers to the capacity of all three p orbitals combined in a given energy level, but we focus here on a single p-orbital. Option (c) suggests parallel spins, which is incorrect as both cannot have parallel spins in the same orbital. Option (d) provides the correct interpretation of the Pauli Exclusion Principle.

Key Concepts

Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental rule in quantum mechanics, discovered by physicist Wolfgang Pauli. It dictates that no two electrons in an atom can have the same set of four quantum numbers. This principle is crucial in understanding the behavior of electrons in atoms and their corresponding atomic orbitals. Each electron in an atom is described by a set of quantum numbers that define its energy, angular momentum, magnetic orientation, and spin direction. For electrons to coexist in the same orbital, they must differ in at least one of these quantum characteristics.
For a single orbital, such as a p-orbital, this principle means that:

• It can hold a maximum of two electrons.
• The two electrons must have opposite spins, typically represented as 'spin-up' and 'spin-down'.

This pairing of opposite spins ensures an efficient and stable distribution of electrons. By prohibiting similar quantum numbers in a given atom, the Pauli Exclusion Principle is essential in determining the electron arrangements across different energy levels and orbitals.

Quantum Chemistry

Quantum chemistry involves the study of chemical systems using the principles of quantum mechanics. It deals with the mathematical description of the wave-like behaviors of particles at the atomic and subatomic levels. Quantum chemistry is essential for understanding the complex interactions and properties of atoms and molecules.
In the context of orbitals, quantum chemistry helps us understand how electrons are arranged around an atom's nucleus. Orbitals are derived from quantum mechanical models and can be envisioned as regions of space where electrons have a high probability of being found. Each type of orbital (s, p, d, f) has distinct shapes and orientations.
The significance of quantum chemistry lies in:

• Predicting the arrangement and behavior of electrons in atoms and molecules.
• Understanding the energy levels and bonding characteristics.
• The ability to explain phenomena such as electron configuration and chemical bonding using quantum mechanical concepts.

Quantum chemistry thus provides a framework for modern chemistry, guiding everything from the design of new materials to the understanding of biological processes.

Electron Spin

Electron spin is a fundamental property intrinsic to electrons, akin to an angular momentum. It is represented by quantum numbers that can take one of two possible values: +1/2 or -1/2. These values are often referred to as 'spin-up' and 'spin-down'.
Electron spin is crucial in quantum chemistry because it affects how electrons fill up orbitals. According to the Pauli Exclusion Principle, electrons sharing the same orbital must have opposite spins. This balance reduces electron repulsion, allowing the electrons to coexist in close proximity with minimal energy.

• The concept of spin explains why two electrons in the same p-orbital must be paired with opposite spins.
• Spin is a key factor in determining the magnetic properties of materials. Unpaired spins lead to magnetism, while paired spins contribute to non-magnetic properties.

Understanding electron spin is vital for grasping complex chemical phenomena. It affects everything from the arrangement of electrons in atoms to the way in which atoms bond to form compounds.