University:
Carleton University
Course:
CHEM 1001 | General Chemistry I
Academic year:

2024
Views:

65

Pages:

3
Author:

ali

QUANTUM NUMBERS LECTURES: Shapes of p and d orbitals UNDER HEADS: Drumheads can also generate asymmetric standing waves of various kinds. In the simplest kind of harmonic, the membrane is halved, making a nodal line. In 3D, we will observe a planar node. The 3D lobes represent the angular dependence of the associated wavefunctions. They're separated by a planar node. 3p orbitals: a linear node can be combined with a circular node. 2p: 1 circular node + 1 linear node 3d: 1 spherical + 2 planar nodes Adding spherical nodes will increase n, but the general shape will be unchanged, hence 3p, 4p, 5p, etc. More planar nodes also leads to shorter n's and thus higher angular momentum. Two planar nodes give rise to d orbitals. When n = 3, l can be 0, 1, or 2. l = 0 (one 3s orbital) l = 1 (three 3p orbitals) l = 2 (d orbitals), 3d orbitals have more lobes than 2p orbitals, and their shape is obviously different. For d orbitals, m can take on 5 values: -2, -1, 0, 1, 2. Most 3d orbitals have 2 planar + 0 spherical nodes. Electrons have angular momentum which is quantized. It can be described by an additional quantum number. ANGULAR MOMENTUM QUANTUM NUMBER Spherically symmetric (s) orbitals have 0 angular momentum. Other shapes of orbitals have angular momentum, which is an integral multiple of h/2π. This integer is the orbital angular momentum quantum number, l. l may take any value between 0 and n-1 For n=1, l=0 (only s orbital possible) For n=2, l=0 (s orbital) or 1 (p orbital) The number of orbitals with a given angular momentum quantum number is determined by their shape. For eg for p orbitals we have 3 different orientations: Px, Py, Pz. This is characterized by the magnetic quantum number, m or mℓ. m can take any integer value between -l and +l, and describes the orientation of the orbital. For l=0, m=0 (one s orbital) For l=1, m=-1, 0, +1 (three p orbitals) For a given l, there are always 2l+1 orbitals Quantum states or wavefunctions of equal energy are referred to as degenerate. The 2px, 2py, 2pz orbitals are degenerate (equal in the H-atom). In H-like atoms, the energy of the orbital depends only on the principal quantum number, n. When n=3, l can be 0 (one 3s orbital), 3s orbitals can have two spherical nodes. When n=3, l=1 (three 3p orbitals), 3p orbitals (3px, 3py, 3pz).