CHEM 112 Chapter Notes - Chapter 8.7-8.12 and 9.1=9.7: Unpaired Electron, Pauli Exclusion Principle, Electron Configuration
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Interpreting and representing the orbitals of the hydrogen atom. The square of the wave function relates to the probability density of three dimensional shapes. The angular part of the wave functions for an s-orbital =(cid:4672)(cid:2869)4(cid:4673)(cid:2869)/(cid:2870) is always the same regardless of the principal quantum number. The term is equal to (cid:2870)(cid:3027)(cid:3045)(cid:3041)(cid:3028)0 the quantity (cid:2868) is equal to the bohr radius, the value of which can be related to other constants in the schr dinger equation. Thus all the orbitals of a given type (s,p,d,f) have the same angular behavior (cid:2868)= (cid:2868) (cid:2870) (cid:1865)(cid:1857)(cid:2870)=5. (cid:884)9(cid:883)77(cid:883)(cid:882) (cid:2869)(cid:2869)(cid:1865) To obtain the wave function of a particular state, we must multiply the angular part by the radial part. The radial functions: determines how the probability density for a particular state changes with distance from the nucleus. Each radial function decays exponentially with increasing radius of an orbital and sometimes cross the horizontal axis before settling at 0.
