Quantum Mechanical Model of Atom

Quantum mechanical model of atom is the atomic model which is based on the particle and wave nature of the electron. This model is also known as wave mechanical model of atom and Erwin Schrodinger developed it in 1926. In this model, the behavior of an electron in an atom is considered as a three-dimensional wave in the electronic field of positively charged nucleus. Schrodinger derived a differential equation which describes the wave motion of an electron. The differential equation is as follows:

In the above Schrodinger wave equation,

• x, y and z are cartesian coordinates of the electron,
• m is the mass of the electron,
• E is the total energy of the electron,
• V is the potential energy of the electron,
• h is Planck’s constant,
• ψ (Greek letter psi, pronounced as si) is a wave function which represents the amplitude of the electron wave at various points surrounding the nucleus. 

Key Features of Quantum Mechanical Model of Atom

The key features of the quantum mechanical model of atom is as follows:

1. Energy Quantization:

• In the quantum mechanical model of atom, the energy of electrons is quantized, meaning that electrons can only occupy specific discrete energy levels within the atom.
• These energy levels are determined by quantum numbers, especially the principal quantum number (n).
• Electrons can transition between these energy levels by absorbing or emitting discrete amounts of energy, referred to as quanta.

2. Wave-Particle Duality:

• The quantum mechanical model of atom considers the wave-like properties of electrons. This concept was proposed by Louis de Broglie.
• He proposed that electrons exhibit wave-particle duality, meaning that they have both particle-like and wave-like characteristics.
• De Broglie expressed this idea mathematically through his equation: λ = h/mv, where λ is the wavelength, h is Planck’s constant, m is the mass of the particle, and v is its velocity.

3. Uncertainty Principle:

• The quantum mechanical model emphasizes that the exact path of an electron within an atom can never be known accurately.

4. Atomic Orbitals:

• An atomic orbital is a region in 3D space where the probability of finding an electron is high. It is represented by a wave function (ψ), which is a mathematical solution to the Schrödinger equation for the electron.
• The square of the wave function (ψ²) represents the probability density of finding an electron in a specific region of 3D space. Each atomic orbital cannot have more than two electrons and electrons in each orbital have a definite energy.

5. Electron Configuration:

• In a multi-electron atom, electrons are filled in various orbitals in the order of increasing energy.

6. Probability Density:

• The quantum mechanical model of atom considers that the probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function (ψ²) at that point. The ψ² is known as probability density.
• The value of ψ² at different points within an atom allows prediction of the region around the nucleus, where an electron is most likely found.