What is the quantum mechanical model of the atom? Give its important features.

(N/A) Quantum Mechanical Model of Atom: This model of the atom is the picture of the structure of the atom,which emerges from the application of the Schrodinger equation to atoms.
Important features of the quantum mechanical model of the atom:
$(i)$. The energy of electrons in atoms is quantized (i.e.,can only have certain specific values),for example,when electrons are bound to the nucleus in atoms.
$(ii)$. The existence of quantized electronic energy levels is a direct result of the wave-like properties of electrons and are allowed solutions of the Schrodinger wave equation.
$(iii)$. Both the exact position and exact velocity of an electron in an atom cannot be determined simultaneously (Heisenberg uncertainty principle). The path of an electron in an atom,therefore,can never be determined or known accurately.
$(iv)$. An atomic orbital is the wave function $\psi$ for an electron in an atom.
- Whenever an electron is described by a wave function,we say that the electron occupies that orbital. Since many such wave functions are possible for an electron,there are many atomic orbitals in an atom.
- These "one-electron orbital wave functions" or orbitals form the basis of the electronic structure of atoms.
- In each orbital,the electron has a definite energy. An orbital cannot contain more than two electrons.
- In a multi-electron atom,the electrons are filled in various orbitals in the order of increasing energy.
- All the information about the electron in an atom is stored in its orbital wave function $\Psi$,and quantum mechanics makes it possible to extract this information out of $\Psi$.
$(v)$. Finding of electron probability $|\Psi|^{2}$:
- The probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function,i.e.,$|\Psi|^{2}$ at that point. $|\Psi|^{2}$ is known as probability density and is always positive.
- From the value of $|\Psi|^{2}$ at different points within an atom,it is possible to predict the region around the nucleus where the electron will most probably be found.