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rosepanda302Lv1
6 Nov 2019
Given the sp3 hybridized orbital . The angular parts of these wave functions are: . Consider four such orbitals (a,b,c,d): (1,1,1,1); (l,l,-l,-l); (1,-1,1,-1); and (1,-1 ,-1,1) emanating from the center of a unit cube. The coordinates system is oriented such that the Cartesian axes cut the centers of the faces of the cube. The angles given are spherical polar coordinates where 0 is the angle between a radial line and the z axis and 9 is the angle between the projection of a radial line in an x,y plane and the x axis. Calculate the amplitude of the angular part of each of the four orbitals at each of the six vertices of the cube. Show graphically that a tetrahedron can be inscribed in a cube with the vertices coincident Show that these four sp3 hybridized orbitals together have tetrahedral symmetry. Show transcribed image text
Given the sp3 hybridized orbital . The angular parts of these wave functions are: . Consider four such orbitals (a,b,c,d): (1,1,1,1); (l,l,-l,-l); (1,-1,1,-1); and (1,-1 ,-1,1) emanating from the center of a unit cube. The coordinates system is oriented such that the Cartesian axes cut the centers of the faces of the cube. The angles given are spherical polar coordinates where 0 is the angle between a radial line and the z axis and 9 is the angle between the projection of a radial line in an x,y plane and the x axis. Calculate the amplitude of the angular part of each of the four orbitals at each of the six vertices of the cube. Show graphically that a tetrahedron can be inscribed in a cube with the vertices coincident Show that these four sp3 hybridized orbitals together have tetrahedral symmetry.
Show transcribed image text