Quantum Mechanical Model of Atom
Quantum Mechanics is the branch of physics that deals with the motion and kinematics of microscopic objects. Since atoms are of below microscopic size and the limitations of Bohr’s Atomic Model motivated the scientists to give a more general and accurate atomic model based on Quantum Theory. The Quantum Mechanical Model of the Atom basically uses two following theories to explain the structure of the atom:
- Dual Behaviour of Matter
- Heisenberg Uncertainty Principle
Dual Behaviour of Matter
Dual Behaviour of Matter was proposed by French physicist de-Broglie. He stated that every matter irrespective of its size exhibits both wave-like properties and particle-like properties. He meant to say that just like a photon has both wavelength and momentum similarly an electron will have both wavelength(λ) and momentum(p). He called these waves Matter Waves. The relation between wavelength and momentum is given by
λ = h/p
where,
- λ is Wavelength
- p is Momentum
- h is Planck’s Constant
Heisenberg Uncertainty Principle
Heisenberg’s Uncertainty Principle states that when a microscopic particle is in motion it is impossible to find the exact position and momentum of the particle simultaneously. He meant that at a time we can find either position or momentum i.e. if the exact position is known then momentum is uncertain and vice-versa. It is represented as
Δx.Δp ≥ h/4π
where,
- Δx is Uncertainty in Position
- Δp is Uncertainty in Momentum
- h is Planck’s Constant
From the formula, it means that if Δ for the position is very small i.e. if the position is known exactly then Δp will be very large hence, physically we will have a blurred image of the measurement. Hence, it talks about probability which is the basis of the Quantum Mechanical Model of Atom.
Although the above two concepts are important for understanding of Quantum Mechanical Model of Atom, it is equally important to know the Schrodinger Wave Equation which was the most fundamental equation of Quantum Mechanics related to the energy of the system.
Schrodinger Wave Equation
Schrodinger Wave Equation gives the equation for the total energy of the system (an atom or a molecule) whose energy doesn’t change with time i.e. there is no loss or gain of energy. Mathematically, Schrodinger Wave Equation is represented as
Hψ = Eψ
where
- H is Hamiltonian Operator in Mathematics
- E is the Total Energy of the System
- ψ is a Wave function
The solution of the Schrodinger Wave Equation gives the value of E and ψ.
Postulates of Quantum Mechanical Model of Atom
Quantum Mechanical Model states the following about structure of the atom
- The energy of electrons in atoms is quantized i.e. energy level of an electron is an integral multiple of the smallest energy quantity.
- Quantized Energy levels exist due to Wave like Properties of electrons and their solution can be given by Schrodinger Wave Equation.
- Since it is impossible to find the position and momentum of an electron simultaneously therefore we talk about the probability of different physical points related to the electron.
- Atomic Orbital of an atom is represented by wave function ψ. Each orbital can be occupied by two electrons at maximum. When an electron occupies an orbital it is represented by ψ.
- Quantum Model states that there is an electron cloud around the nucleus inside an atom. The probability to find an electron inside an atom is given by |ψ|2, which is called Probability Distribution Function.
Atomic Structure
Atomic structure is the structure of an atom that consists of a nucleus at the center containing neutrons and protons, while electrons revolve around the nucleus. Atoms are made up of a very tiny, positively charged nucleus that is surrounded by a cloud of negatively charged electrons.
The earliest concept of atoms was given by Indian philosopher Maharshi Kanad who proposed that matter is made up of microscopic indestructible particles called ‘Parmanu’. A Greek philosopher named Democritus also initially claimed that matter is formed of atoms, and is credited with developing the concepts of atomic structure and quantum mechanics. Later in the 1800s, John Dalton a British Scientist put out the first atomic structure scientific theory.
This article explores the concept of atomic structure in detail, including the atomic models, and the concept of quantum theory.
Table of Content
- What is Atomic Structure?
- Atomic Models
- Dalton’s Atomic Theory
- Postulates of Dalton’s Atomic Theory
- Demerits of Dalton’s Atomic Theory
- Thomson’s Atomic Model
- Cathode Ray Experiment
- Observations of Cathode Ray Experiment
- Discovery of Electron
- Plum Pudding Model
- Drawbacks of Thomson’s Atomic Model
- Rutherford Atomic Model
- Alpha Ray Scattering Experiment
- Observation of Alpha Ray Scattering Experiment
- Conclusion of Rutherford’s model
- Discovery of Nucleus
- Limitations of Rutherford Atomic Model
- Bohr’s Atomic Model
- Postulates of Bohr’s Atomic Theory
- Limitations of Bohr’s Atomic Theory
- Quantum Mechanical Model of Atom
- Dual Behaviour of Matter
- Heisenberg Uncertainty Principle
- Schrodinger Wave Equation
- Postulates of Quantum Mechanical Model of Atom
- Quantum Number
- Principal Quantum Number(n)
- Azimuthal Quantum Number(l)
- Magnetic Quantum Number(ml)
- Spin Quantum Number(ms)
- Subatomic Particles
- Isotopes
- Atomic Structure of Isotopes
- Electronic Configuration of Elements
- Aufbau Principle
- Hund’s Rule
- Pauli Exclusion Principle
- Atomic Structure Class 11
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