Question

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

Answer 1

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R10() 2 yyao la R31l R20) O4 O3 20 rIna R32 D21 D 2 Yna radial funcHens Png() few is in uniis see Thea Aom abere for we Can Bohr adius The Radial leng tn H-atom. n-1-1) has nodes fun 2 a = N01 That Rn C) nace 1node. henc is 3ero uez 3-1-) e at That point ex ample, fwr R3Thu the are finding PAobability behovicur Angular Next We will sh ow The various are dham Y (e paot few of Them part i- e CD, is gt is impantant to nate That belaw. b m, aMantum numbers Tue puinaipal quontum numbes, n, since 込 inface which COntudl d dutermined b far 212ッn no.9l and a centain There auL n, 4)no. coHrespandingly There m.

far cxample, far n 2 m- 2,-o, , 2 far 2 far Na Puobability far angular distuibutian is given below Pncbability 1 finding here is ro noce nedi teTocw C enly Inad) Conly 1 nee meo,2 Yo 2 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 is given below:

p(r, 0, cos(0)

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 is given below:

(r,0, cos(0)sin(

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