Quantum Mechanical Model
Bohr's Cencept of well defined circualr orbits was discarded after the wave character of electron (De Broglie) and heisenberg's uncertainty Principle was established.Then came the concept of Quantum Mecahnics or wave mechanics which described the behaviour the electrons around the nucleus .
Quantum Mechanics is the theoretical science that deals with the study of motion of microscopic objects that have both particle and wave nature.
Quantum mechanics is based on a fundamental equation which is called Schrodinger equation.
Schrodinger’s equation: For a system (such as an atom or a molecule whose energy does not change with time) the Schrödinger equation is written
Here
is a mathematical operator called Hamiltonian.
Schrodinger gave a recipe of constructing this operator from the expression for the total energy of the system. The total energy of the system takes into account the kinetic energies of all the sub atomic particles (electrons, nuclei), attractive potential between the electrons and nuclei and repulsive potential among the electrons and nuclei individually. Solution of this equation gives E and ψ.
Features of Quantum Mechanical Model

The energy of electrons in an atom is quantized i.e. it can have only certain specific energy values.

The existence of quantized electronic energy level is direct reset of wave properties of electron.

Both exact position and exact velocity of electron cannot be determined simultaneously.The path of an electron in an atom therefore, can never
be determined or known accurately

IMPORTANT: An atomic orbital is the wave function ψ for an electron in an atom. There are many orbital’s in an atom. Electrons occupy an orbital which has definite energy. An orbital can have more than two electrons the orbital are filled in increasing order of energy. All the information about an electron is stored in orbital wave function

The probability of finding an electron in a point within an atom is proportional to ψ^{2} it is known as probability density and it is always positive from the value of ψ^{2 }at different points. It is possible to predict the region around the nucleus where the electrons are most probability found.
Atomic orbital can be specified by giving their corresponding energies & angular momentum which are quantaised & expressed in terms of quantum numbers.
 The concept of orbit was discarded in favour of orbital i.e the most probable region of space around nucleus for the electron to be present
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