Electron Orbitals Cartoon courtesy of lab-initio.com Quantum Mechanical Model of the Atom Mathematical laws can identify the regions outside of the nucleus where electrons are most likely to be found. These laws are beyond the scope of this class Heisenberg Uncertainty Principle One cannot simultaneously determine both the position and momentum of an electron. Werner Heisenberg The more certain you are about where the electron is, the less certain you can
be about where it is going. The more certain you are about where the electron is going, the less certain you can be about where it is. Quantum Numbers Each electron in an atom has a unique set of 4 quantum numbers which describe it. Principal quantum number Angular momentum quantum number Magnetic quantum number Spin quantum number Electron Energy Level (Shell) Generally symbolized by n, it denotes the probable distance of the electron from the nucleus. n is also known as the Principle
Quantum Number ofnumber electrons that can 2 fit in 2n a shell: Electron Orbitals An orbital is a region within an energy level where there is a probability of finding an electron. Orbital shapes are defined as the surface that contains 90% of the total electron probability. The angular momentum quantum number, generally symbolized by l, denotes the orbital (subshell) in which the electron is located. s Orbital shape The s orbital (l = 0) has a spherical shape centered around
the origin of the three axes in space. p orbital shape There are three dumbbell-shaped p orbitals (l = 1) in each energy level above n = 1, each assigned to its own axis (x, y and z) in space. d orbital shapes Things get a bit more complicated with the five d orbitals (l = 2) that are found in the d sublevels beginning with n = 3. To remember the shapes, think of and a dumbell double dumbells with a donut!
Shape of f (l = 3) orbitals Energy Levels, Sublevels, Electrons Energy Level (n) Sublevels in main energy level (n sublevels) Number of orbitals per sublevel Number of Electrons per sublevel Number of electrons per main energy
level (2n2) 1 s 1 2 2 2 s p 1 3 2 6 8 3
s p d 1 3 5 2 6 10 18 4 s p d f 1 3 5 7 2
6 10 14 32 Magnetic Quantum Number The magnetic quantum number, generally symbolized by m, denotes the orientation of the electrons orbital with respect to the three axes in space. Orbital filling table Electron Spin The Spin Quantum Number describes the behavior (direction of spin) of an electron within a magnetic field. Possibilities for electron spin: 1 2 1
2 Pauli Exclusion Principle Two electrons occupying the same orbital must have opposite spins Wolfgang Pauli Element Lithium Configuration notation Orbital notation 1s22s1 [He]2s1 ____ 1s Beryllium
Oxygen ____ 2s ____ ____ 2p ____ ____ 2s ____ ____ 2p ____ 1s22s2p2 [He]2s2p2 ____ 2s
____ ____ 2p ____ 1s22s2p3 [He]2s2p3 ____ ____ 1s 2s ____ ____ ____ 2p
1s22s2p4 [He]2s2p4 ____ 2s ____ ____ 2p ____ 1s22s2p5 [He]2s2p5 ____ 1s Neon ____ [He]2s2p1 ____ 1s
Fluorine ____ 2p 1s22s2p1 ____ 1s Nitrogen ____ [He]2s2 ____ 1s Carbon ____ 2s 1s22s2 ____ 1s Boron
Noble gas notation ____ 2s ____ ____ 2p ____ 1s22s2p6 [He]2s2p6 ____ 1s ____ 2s ____ ____ 2p
____ Exclusion Warning! Assigning quantum numbers to electrons has been exluded and will not be tested! The following slides are purely for your entertainment Assigning the Numbers The three quantum numbers (n, l, and m) are integers. The principal quantum number (n) cannot be zero. n must be 1, 2, 3, etc. The angular momentum quantum number (l ) can be any integer between 0 and n - 1. For n = 3, l can be either 0, 1, or 2. The magnetic quantum number (ml) can be any integer between -l and +l. For l = 2, m can be either -2, -1, 0, +1, +2. Quantum numbers for the first four levels of orbitals in the hydrogen atom n
l Orbital designation ml # of orbitals 1 0 1s 0 1 2 0 2s
0 1 1 2p -1, 0, 1 3 0 3s 0 1 1 3p -1, 0, 1 3
2 3d -2, -1, 0, 1, 2 5 0 4s 0 1 1 4p -1, 0, 1 3 2
4d -2, -1, 0, 1, 2 5 3 4f -3, -2, -1, 0, 1, 2, 3 7 3 4