Quantum mechanics is based on Schrödinger’s wave equation and its solution. The solution of the wave equation brings the idea of shells, sub-shells and orbitals. The probability of finding an electron at a point within an atom is proportional to the |ψ|2 at that point, where ψ represents the wave-function of that electron.
Application of Schrödinger’s equation to multi-electron atoms present’s some difficulty: Schrödinger’s wave equation cannot be solved exactly for a multi-electron atom. This difficulty was overcome by using approximate methods.
The application of Schrödinger wave equation in determining the structure of an atom led to the formation of the quantum mechanical model of an atom.
Features of quantum mechanical model:
- The energy of an electron is quantized i.e. an electron can only have certain specific values of energy.
- The quantized energy of an electron is the allowed solution of the Schrödinger wave equation and it is the result of wave like properties of electron.
- As per Heisenberg’s Uncertainty principle, the exact position and momentum of an electron cannot be determined. So the only probability of finding an electron at a position can be determined and it is |ψ|2 at that point where ψ represents the wave-function of that electron.
- An atomic orbital is the wave-function (ψ) of an electron in an atom. Whenever an electron is described by a wave-function, it occupies atomic orbital. As an electron can have many wave-functions, there are many atomic orbitals for electron. Every wave-function or atomic orbital have some shape and energy associated with it. All the information about the electron in an atom is stored in its orbital wave function ψ and quantum mechanics makes it possible to extract this information out of ψ.
- The probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function i.e., | ψ |2 at that point. | ψ |2 is known as probability density and is always positive.
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