Question

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enen #6. (Quantum numbers: 15 pts) (a) Explain about the quantum numbers determining the probability density function of the What is the selection rule in the transition of the electron?, and (c) Draw the wave function in electron in hydrogen atom, y(r,0,) sin0 cosø w(r,0,6)=cos0, and as follows: the hydrogen atom given

Answer 1

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R21 (2) 2- a Rio(n) o6 o.3 20 alnar 1 Ry D 20 Pinctioos fnl few radiol wo above H-atom The he We See Can Bohs Yadius unita Df isin Radial tength that R C has Cn-l-) noder Fo example Note μολ exam ple (3-1-1) node = 1node .+tence are R3, thene point of is 'a Fin ding that the e at porobabil nao wil shouw the voriDus be havioun bf Next, we Anqula part few of Co,p) them drawn Pant i.e, y ? aYe no te It belbw impont quanlam Pίnipal auaniu that ant which is infach Controlled numbers de termined by no n. Since the Por a cen tain n, there. are b,,2 --n, nD. of l and

torres pondingly there CaltU no of m xample, esc - 2 -1,0,1,2 -1, D, L-O,, for m Por for o oablity Now angular distri bution given belau y node m ma, tonly Coniy bne node) b ne node) m o, l 2

c) Answer.:

Using matlab, we can draw the wavefunctions, matlab code for plotting these 3D wavefunctions are given below:

theta-linspace(0,2 pi); phi- linspace (-pi/2,pi/2); [theta,phi]-neshgrid(theta , phi); »rho-cos(theta); [x,y,z]-sph2cart (theta, phi, rho) »surf(x,y,z); » alpha 0.5 » rho-cos (theta)sin (phi); »[x,y,z]-sph2cart(theta,phi,rho); surf(x,y,z); » alpha 1 » surf(x,y,z)

Plot for (r, 0,)= cos(0) is given below

0.8 0.6 0.4 0.2 0- -0.2 -0.4 0.6 -0.8- 0.5 09 0.4 0.8 0.3 0.7 0.2 0.6 0.1 0.5 0.4 0.1 0.2 0.3 0.2 4 0.1 -0.5 0

Plot for P(r, 0, ) = cos(0)sin() is given below

14 10 8 6 Д 2 О- А Б А 15 х 10 А 15 х 10 -6 я