Can anyone plz solve all these problems? Chemistry 328-Physical Chemistry II Rec
ID: 3164301 • Letter: C
Question
Can anyone plz solve all these problems? Chemistry 328-Physical Chemistry II Recitation Solutions 9 Hydrogen Atom Wave Functions and Orbitals The eigenfunctions of the Hamiltonian operator H for the H atom are given by where the Y (6. are spherical harmonics, the RS() are Laguerre polynomials, and the allowed values of the quantum numbers are n 1,2,3,. i 0. 1. ....n-1, mu -1 ,0. ....+l The eigenfunctions throughn 3 are given on the last page of these exercises. sin cos 1. a. Show that y,, (r,6. sin sin and that va, (r,6.0) b. Show that v2, is normalized.Explanation / Answer
3. (a) for 3s
In 3s orbit, on the right is sliced in half to show that there are two spherical nodes in the 3s orbital.
(b) for 3pz
Each 3p orbital has four lobes. There is a planar node normal to the axis of the orbital (so the 3p_orbital has a xy nodal plane, for instance).
(c) for 3dz2
The 3dz2 orbital is different and has two conical nodes.
(d) for 3dyz
There are two planar node normal to the axis of the orbital (so the 3dyz orbital has xy and xz nodal planes, for instance).
(e) for 3dx2-y2
dx2-y2 orbital has four lobes. There are two planar node normal to the axis of the orbital.
2. At node, R = 0. Therefore, at node, (3– Zr/a0) = 0.
Therefore, 3 = Zr/a0, which means that 3a0 = Zr, and r = 3a0/Z.
For H atom, Z = 1, and a0 = 52.9, so the node occurs at r = 158.7 pm.