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Name principal
Symbol Permitted Values Property n positive integers(1,2,3,…)^ orbital energy (size) angular momentum l integers from 0 to n-1 orbital shape (The^ l^ values 0, 1, 2, and 3 correspond to s, p, d, and f orbitals, respectively.) magnetic (^) m l integers from - l to 0 to + l orbital orientation in space spin (^) m s +1/2 or -1/2 direction of e
Hydrogen atoms shot through a strong magnet are split into two and only two groups of atoms on a collection plate. Electron spins must be quantized as if they were not one would expect a rectangular patch extending dot to dot. The Stern-Gerlach Experiment----1922. Classical result had it not been quantized
PLAN: Determining Quantum Numbers for an Energy Level PROBLEM: What values of the angular momentum ( l ) and magnetic (m l ) quantum numbers are allowed for a principal quantum number (n) of 3? How many orbitals are allowed for n = 3? remember l values can be integers from 0 to n-1; m l can be integers from - l through 0 to + l.
n-Quantum Number = Orbital Energies
Electrons will fill lowest energy levels first!
How many 2p orbitals are there in an atom? 2p n= l = 1 If l = 1, then m l = -1, 0, or + 3 orbitals How many electrons can be placed in the 3d subshell? 3d n= l = 2 If l = 2, then m l = -2, -1, 0, +1, or + 5 orbitals which can hold a total of 10 e
PROBLEM: Give the orbital name, possible magnetic quantum numbers, and number of orbitals for each sublevel with the following quantum numbers: (a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l = 1 (d) n = 4, l = 3 SOLUTION: n l Orbital name possible m l values^ # of orbitals (a) (b) (c) (d) 3 2 5 4 2 0 1 3 3d 2s 5p 4f -2, -1, 0, 1, 2 0 -1, 0, 1 -3, -2, -1, 0, 1, 2, 3 5 1 3 7
The Shapes of Atomic Orbital The shape of an orbital is VERY IMPORTANT IN UNDERSTANDING BONDING..............this means Chapter 8/9/ and ultimately your final grade! Here is the riff: each angular momentum quantum number l there is a unique “probability density” that represent the volume where the electron is likely to be found. l = 1 = s orbital l = 2 = p orbital l = 3 = d orbital l = 4 = f orbital
Where Is the Electron? Boundary Surface Plot Probability at points in space Probability of points added up in a circular strip.
The Shapes of Orbitals 1s 2s 3s Radial Probability Distribution Plots
The p Orbitals ( l = 1)
The 3-p Boundary Surface Plots (Orbitals) Three p-orbitals superimposed 2 px 2 py 2 pz
One of the seven possible 4f orbitals. 1of 7 f-orbitals superimposed
Use The Aufbau Process To Construct Electron Configurations The Aufbau Process. ---Build up elements electron by electron for “ ground state (lowest energy) electronic configuration of elements ”. ---Lower energy (n-quantum number) orbitals fill first followed by higher energy --Each orbital holds two electrons of opposite spin. No two electrons can have same 4-quantum numbers! --- Hund’s Rule - degenerate orbitals are occupied singly first and fill last (don’t pair electrons until each orbital has one electron).
