Question

The plot below shows the radial distribution function of the 3s and 3p orbitals of the hydrogen atom. Identify each curve (a & b) as 3s or 3p and explain in terms of penetrating power how you came to this decision.

Radial distribution Function > Radius- >

Answer 1

Radial distribution function rading → In general there are (n-1-1) radial nodes (ignoring the nodal point al Gradius) =o) in the radial distribution functions, and consequently there are [ (n-1) +17 maxima in the radial distribution function for the orbitats. for as orbital, no of radial nodes n r for 35 og bital (n--1) n=3 -lo 1 - 3-0 -1 2 sadial modos So for 3s orbital there are two radial modes for ap orbital, no of radial nodes = (n-l- l for 3 Porbitul n=3 l T = 3- 1-1 So for 3 p orbital there is only one radial node Hence, in the graph, the curve à is for 3p orbital and the curve t' is for. 38 orbital. Penetrating Power of orbitals :- It is evident that the "max for the largest maximum probability region lies in the sequence Imax (35)> (3p), but for 35 and a 3p orbitals, there are two and one additional intranodal maxima (Smaller, at the lower distance towards the nucleus respectively. By considering these additional Smaller

( peaks at the lower distance, it is found that as orbital election spends a larger fraction of its time closer to the smelrus Compared to 3p electron - By Considering the combined effect of all the maxima of a particular orbital, we should consider the average naax value in. (&max>. It runs (Smax (35)) < (Simax (3P) This is why the 3s electrons are most tightly bound to the neelacz followed by ap electrong. This the energy Segmence becomes as op 35/3p. This is why for a given value of n, the ionisation energy sung in the Sequence asynpynd. In other words, we can say that the penetrating power of an orbital measured by the probability of locating the Corresponding electron at the closer distance towards the nudeus lies in the Seanence nsynpynd. Here it is worth mentioning that in Sommerfeld's model the penetrating power of an orbital was explained interms of its ellipficity, but in wave mechanics the concept of radial distribution function can nicely trekk the problem .