Structure of Atom
Subatomic Particles : Discovery and Characteristics

Macroscopic objects have particle character, so their motion can be described in terms of classical mechanics, based on Newton’s laws of motion.

Microscopic objects, such as electrons, have both wavelike and particlelike behaviour, so they cannot be described in terms of classical mechanics. To do so, a new branch of science called quantum mechanics was developed.

Quantum mechanics was developed independently by Werner Heisenberg and Erwin Schrodinger in 1926.

Quantum mechanics takes into account the dual nature (particle and wave) of matter.

On the basis of quantum mechanics, a new model known as quantum mechanical model was developed.

In the quantum mechanical model, the behaviour of microscopic particles (electrons) in a system (atom) is described by an equation known as Schrodinger equation, which is given below:
Where,
= Mathematical operator known as Hamiltonian operator
ψ = Wave function (amplitude of the electron wave)
E = Total energy of the system (includes all subatomic particles such as electrons, nuclei)

The solutions of Schrodinger equation are called wave functions.
Hydrogen atom and Schrodinger equation

After solving Schrodinger equation for hydrogen atom, certain solutions are obtained which are permissible.

Each permitted solution corresponds to a definite energy state, and each definite energy state is called an orbital. In the case of an atom, it is called atomic orbital, and in the case of a molecule, it is called a molecular orbital.

Each orbital is characterised by a set of the following three quantum numbers:

Principal quantum number (n)

Azimuthal quantum number (l)

Magnetic quantum number (m_{l})

For a multielectron atom, Schrodinger equation cannot be solved exactly.
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