Module 1 : Atomic Structure
Lecture 5 : Wave Functions and Charge Densities.
 

The square of the function is shown in the adjoining figure. This function is positive throughout . The next function is R 21 (r ) which is the radial part of the 2p orbital. This function has the form e - / 2. The function rises from 0, reaches a maximum value and then asymptotically goes to zero as . This function goes to zero more slowly than e - / 2 because of the multiplying factor 2. Using the arguments given so far in this section, adjoining plots of Rnl ( r ) and R 2nl (r) can be rationalized .

 

The 3s function has a quadratic function multiplying an exponential. The function crosses zero twice. The two crossing points are the roots of the quadratic equation 6 – 6 + 2 . For higher values n, there will be polynomials of higher order multiplying the exponential part and the function will cross the axis as many times as the zeros of the polynomial multiplying the exponential. The sketches of a few other radial parts are also shown in fig 5.1.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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