Problem 13 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Wave functions of electrons in atoms and molecules are called

Step-by-Step Solution

Answer

Wave functions of electrons in atoms and molecules are called orbitals.

Step 1: Understanding the Context

In the context of quantum mechanics and atomic physics, electrons in atoms and molecules are described by mathematical functions. These functions are crucial for predicting the behavior and properties of electrons within atoms and molecules.

Step 2: Introducing Wave Functions

Wave functions are solutions to the Schrödinger equation, which is a fundamental equation in quantum mechanics. They provide information about the probability distribution of an electron's position and momentum in an atom or molecule.

Step 3: Defining the Term

The specific term used to describe the wave functions of electrons in atoms and molecules is "orbitals". Orbitals are regions in space where there is a high probability of finding an electron.

Step 4: Clarifying Orbital Types

There are different types of orbitals (s, p, d, and f) that have specific shapes and energy levels. These shapes and energy levels determine the chemical properties and reactivity of atoms and molecules.

Key Concepts

Schrödinger Equation

The Schrödinger equation is a cornerstone of quantum mechanics. It was formulated by the physicist Erwin Schrödinger in 1925. This equation helps us understand how quantum particles, like electrons, behave. At its core, the equation is a way to describe how the quantum state of a system changes over time.
In layman's terms, you can think of it as a rulebook for how particles move and exist in the quantum world. Solving the Schrödinger equation for a specific system, such as an atom or molecule, gives us the system's wave function, which contains all the information about the system's state. This is crucial for predicting anything about the particle, such as its energy or how it might interact with other particles.
The mathematical form of the equation involves derivatives and complex numbers, which are used to describe the wave-like properties of particles. It can be written as:\[ - \frac{\hbar^2}{2m} abla^2 \Psi + V \Psi = E \Psi \]Where:

• \(\hbar\) is the reduced Planck's constant.
• \(m\) is the particle's mass.
• \(abla^2\) is the Laplacian operator, representing the kinetic energy.
• \(V\) is the potential energy.
• \(E\) is the total energy.
• \(\Psi\) is the wave function.

This form shows how kinetic and potential energy are related to total energy in a quantum system.

Orbitals

Orbitals are regions around an atom where electrons are most likely to be found. They are the 'shapes' formed by the solution to the Schrödinger equation for electrons in atoms. These wave functions give rise to different types of orbitals, like the s, p, d, and f orbitals.
Each type of orbital has a distinct shape and energy level, influencing the chemical behavior of atoms. For example:

• s orbitals are spherical.
• p orbitals have dumbbell shapes.
• d orbitals can be more complex, often shaped like clovers.
• f orbitals are even more complex, with convoluted shapes.

These shapes affect how atoms bond and interact with each other. Understanding orbitals is crucial for predicting how chemical reactions occur and how atoms form molecules.

Quantum Mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties at the microscopic scale, such as atoms and subatomic particles. Unlike classical physics, which deals with macroscopic objects, quantum mechanics reveals a world where things can exist in multiple states at once, known as superposition, and particles can be in multiple places at once, known as entanglement.
Every particle or even atom is described by a wave function. This wave function encodes all the probabilistic information about the particle's state. This probabilistic nature is a key difference from classical mechanics, where the future behavior of particles can be calculated with certainty given their initial positions and velocities.
Some key principles of quantum mechanics include:

• Uncertainty Principle: Proposed by Heisenberg, it suggests that you cannot simultaneously know both the position and momentum of a particle with absolute precision.
• Wave-Particle Duality: This concept, championed by Einstein and others, states that particles like electrons exhibit both wave-like and particle-like properties.
• Quantum Tunneling: This is the phenomenon where particles pass through potential barriers, which is impossible in classical physics.

These principles help us understand and leverage the strange and counterintuitive properties of quantum systems.

Probability Distribution

In quantum mechanics, the concept of probability distribution is crucial. It tells us the likelihood of finding a particle, like an electron, in a particular location around an atom. Instead of moving in predictable paths like planets around the sun, electrons exist in regions described by probability clouds.
This idea is intimately tied to the wave function (\(\Psi\)), a fundamental solution of the Schrödinger equation. The probability of finding an electron in a specific location is given by the square of the absolute value of the wave function, \(|\Psi|^2\).
This results in what is often visualized as a "cloud" around the nucleus of an atom, showing where electrons are likely to be found. Remember, this is not telling us exactly where the electron will be but gives a map of where it might be:

• High probability regions are depicted with denser areas in the cloud and indicate a higher likelihood of finding the electron there.
• Low probability regions suggest that the electron is less likely to be found.

Understanding these distributions enables scientists to predict the behavior of atoms and molecules much more accurately than possible with classical physics, allowing for technologies like lasers, semiconductors, and MRI machines.