Module 1 : Atomic Structure and Periodic Table

Lecture 4 : The Schrödinger Wave Equation for hydrogen atom

 

The dependence of ψ on r , θ , and Φ can not be shown directly with equation (xxi). Because, it would require a four dimensional graph. However, the equation in this form can be express as follows,

(xxii)

Therefore, equation (xxii) can be express as,

This splits wave function into two parts which can be solved separately,

Radial part of wave functions, R :

The radial function R has no meaning. R 2 gives the probability of finding the electron in a small volume d v near the point at which R is measured.

Figure 1.6. Showing volume difference

For a given value of r the total volume will be,

We may consider that an atom is composed of thin layers of thickness d r . The volume d v for between r and r +d r will be then (Figure 1F),

The probability of finding the electron in that volume will be,

Figure 1.7. Radial probability functions for n = 1, 2,3 for the hydrogen atom. The radial density is along y axis.