Question

4. An orbital of atomic hydrogen is described by the wave function, ¥(,0,4) = (20 - 4) ze zo cos e (a) Consider the radial part, R(r), of this orbital. By considering the values of r for which R(r) = 0 identify the number of radial nodes (points where the R(r) = 0 when r IS NOT equal to 0 or oo). [3 marks)

Answer 1

a) When R(r)=0 then

(r/2a-4)=0 since r=/=0 and $\alpha$ so, r=8a

Number of radial node = 1

b) Now for angular node Y($\Theta, \Phi$)=0

so cos$\Theta$=0

so, $\Theta$ =$\Pi$/2

So number of angular node=1 .i.e l=1 .i.e p orbital

C) Now we know total number of nodes=n-1

Hence n-1=2 .i.e n=3

So it is a 3p orbital,

Now $L^$ *Y($\Theta, \Phi$)=mh/2$\Pi$(Y($\Theta, \Phi$)

So the eigen value is m.

Now -i*h/2$\Pi$*d/d$\Phi$(cos$\Theta$)=0

So m=0 hence it is a 3pz orbital