Wave Mechanical Model of Atom (Schrodinger wave equation)
Erwin Schrodinger in 1926 developed the model which is based on the particle and wave nature of the electron is known as wave mechanical model of the atom. The equation determines the behaviour of the wave function that describes the wavelike properties of a subatomic system. It relates kinetic energy and potential energy to the total energy, and it is solved to find the different energy levels of the system. Schrödinger applied the equation to the hydrogen atom and predicted many of its properties with remarkable accuracy. The differential equation is:
Where x is the coordinates m is the mass of the electron and E is the total energy of the electron. V= potential energy of the electron; h= Planck’s constant and
wave function of electron.
Schrödinger's equation results in a series of so called wave functions, represented by the letter (psi). Although has no actual physical meaning, the value of 2 describes the probability distribution of an electron.
The sum of the probabilities over all values of V must be 1 and is called the normalization condition:
For one particle (such as an electron) of mass (m) in one-dimension, the Schrödinger Equation is:
Significance of ??When we solve the Schrödinger equation it is observed that for some regions of space the value of is positive and for other it is negative. But the probability must be positive so it is proper to use ψ2 in place of .
Significance of 2 :- It is the probability factor. It describes the probability of finding an electron within a space. we can compute energy of electron with a given
The important point of the solution of this equation is that it provides a set of numbers called quantum numbers. These numbers describe the energies of the electrons in atoms, information about shapes and orientations is also known with the help of these numbers.
For hydrogen wave function,
Number of radial nodes = n-l-1.