Schroinger wave equation

(1) The Schrodinger wave equation was given by Erwin Schrödinger in the year 1926 and based on dual nature of an electron.

(2) In it electron it is described as a three dimensional  wave in the electric field of the positively charged nucleus.

(3) The probability of getting the electron at any point around the nucleus can be determined by the help of Schrodinger wave equation which is given as follows,

         Here x, y and z are the 3 space co-ordinates,
m = mass of an electron,
h = Planck's constant,
E = Total energy,
V  = potential energy of electron,
 =  the amplitude of wave also known as wave function,
∂   = for an infinitesimal change.

(4) The Schrodinger equation of the wave can also be written as,

      Here   = laplacian operator.

(5) Physical significance of    and 

         (i)  The wave function    represents amplitude of the electron wave. The amplitude    is therefore a function of space co-ordinates and time that is

         (ii) For the single particle, a square of the wave function    at any point of time is proportional to the probability of finding the particle at that point.

         (iii) If  is maximum than probability of finding e- is maximum around nucleus and the place where probability of finding e- is maximum is called electron cloud electron density, or an atomic orbital. It is not similar from the Bohr's orbit.

         (iv)    The solution of this equation provides us a set of number known as quantum numbers which describe the specific or definite energy state of the electron in an atom and information about the shapes and orientations of the most possible distribution of the electrons around the nucleus.

        

Radial probability distribution curves : The radial probability can be given as   
 The plats of R distance from the nucleus are given as follows 

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