Structure of Atom
12.0 Quantum Mechanical Model of Atom
12.0 Quantum Mechanical Model of Atom
The branch of science that takes into account the dual behaviour of matter is called quantum mechanics.
- Quantum mechanics is a theoretical science that deals with the study of the motions of the microscopic objects that have both observable wave like and particle like properties. It specifies the laws of motion that these objects obey. When quantum mechanics is applied to macroscopic objects, the results are the same as those from the classical mechanics.
- In the realm of quantum mechanics, the state of a system is described by a wave function. Schrödinger based his theory on the idea that the total energy of a system, Eb could be estimated by solving an equation. Since this equation has some similarity with the equation expressing a wave in classical physics, it was called Schrödinger’s wave equation.
- Schrödinger’s wave equation is
$$\frac{{{\partial ^2}\psi }}{{\partial {x^2}}} + \frac{{{\partial ^2}\psi }}{{\partial {y^2}}} + \frac{{{\partial ^2}\psi }}{{\partial {z^2}}} + \frac{{8{\pi ^2}m}}{{{h^2}}}(E - U)\psi = 0$$
where x,y,z = cartesian coordinates
m=mass of electron, h= Planck's constant
U=potential energy of electron, E=total energy of electron
$\psi $=wave function which gives the amplitude of wave
${\psi ^2}$ =probability function
- By solving the Schrödinger equation (H$\psi $ = E$\psi $), we obtain a set of mathematical equations, called wave functions ($\psi $), which describe the probability of finding electrons at certain energy levels within an atom.
- H is the total energy operator, called Hamiltonian.
- A wave function for an electron in an atom is called an atomic orbital.
- This atomic orbital describes a region of space in which there is a high probability of finding the electron. Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy (usually accompanied by the absorption or emission of a photon of light).
