University:
Brigham Young University
Course:
CHEM 102 | Concepts of Chemistry
Academic year:

2023
Views:

438

Pages:

5
Author:

InterstellarInsight

Radial and Angular wave Function:- Schrodinger cartesian wave equation is for H-atom in co-ondinate (x,y,z) is - d24 +++ (+)=0. dy2 By putting the value of polar co-ordinate (n.@.q) in place of cartesian. co-ordinate (x,y,z); x=rsine cos d' y= = Rsina sing Schrodinger wave equation in spherical polar co-ordinate GR, &, $) can be represented ou, 2 Sing [media] + ne de [Since 'dea] 2 da Et 1 da doa 8 =0. Ψ)) = Roy. Q). Φα) Rn ↳ Rive) is a function that depends on distance From nucleus i.e. quantum no. 2 and 1. It gives the energy and size of shell. 4Qcce) is a function that depends on quantum no. mand L. It gives shape of orbital. 4) is a Function that depends on It also gives shape of orbital. quantum no. m only. Ria) is known as radial wave function where as Q(a) and called argular wave Feenction. 4(RQ)=RL). @milla). Φm(4). Let us consider that the space around the nucleus is divided in to concentric shall of thickness dr. Let, de Thickness of space in between concentric shell dv: Volume of space betiveen concentric shell. 4 Radial probablity is the total prabablity of Finding e- in a radial shell between sphere of radius 'n' and ret dr Mathematically, Radial probability Where, dv - 4dr is Probablity density x volume of radial shell. = ψαχαν = 4x4nradr. the volume of radial shell between sphere of roolis and refdr. Volume of radial shell (dv) = (retdr) = r²dr. dr and dre are neglected as 'dr' is very small. The radial probablity distribution means the Probablity of Finding of thickness drive R e with in a small radial space = 47. RAL. Thus, the radial probablity distribution curve of e can be obtained by plotting 47. Ral and n. such "charge density curve". a graph between graph is also called