Chemistry 141 Friday, November 3, 2017 Lecture 25 H Atom Orbitals Chemistry 11 - Lecture 11 9/30/2009 Chemistry 141 Friday, November 3, 2017 Lecture 25 H Atom Orbitals

Matter Waves Scientists at IBM accidentally observed standing waves from the interference of electrons on a copper surface with defect sites They then decided to intentionally create electron standing waves by arranging iron atoms in a ring, thereby confining the space the electrons can roam in, and forming standing waves Images from: http://www.almaden.ibm.com/vis/stm/atomo.html

A very deep question: Waves do not have a location. If a small particle (i.e. an electron) behaves like a wave, can we specify its location?

Heisenberg’s Uncertainty Principle The Uncertainty Principle (Heisenberg, 1927) states: There is an inherent uncertainty in our ability to specify an electron’s exact location there is a fundamental limit to our ability to describe the properties of particles that are very small Instead of certainty, we must rely on probabilities to tell us the likely location of these small particles

When does the uncertainty principle matter? What is the uncertainty in the position of an electron (mass = 9.11x10-31 kg) moving with a speed of 5x106 m/s? Assume the uncertainty in the speed is 1%.

When does the uncertainty principle matter? What is the uncertainty in the position of a baseball (mass = 0.145 kg) moving with a speed of 18 m/s? Assume the uncertainty in the speed is 1%.

The Founders of Quantum Mechanics on Their Creation Anyone who is not shocked by quantum theory has not understood it. -- Neils Bohr I don’t like it, and I’m sorry I ever had anything to do with it. -- Erwin Schrödinger [I] think I can safely say that nobody understands quantum mechanics. -- Richard Feynman Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. -- Albert Einstein God does not play dice with the universe -- Albert Einstein

Wave Functions Wave function () A mathematical description of the electron accounting for dual wave/particle nature – an ORBITAL  can have positive or negative values; the sign of  is called the phase The points at which =0 are called nodes  has no direct physical interpretation, but the square of the wave function gives us the electron density, or probability of finding the electron at a given location http://www.falstad.com/qmatom/

H-atom quantum numbers For each wavefunction () or orbital there are three quantum numbers that characterize that wavefunction The principal quantum number, n quantization of energy can take on integer values (n = 1, 2, 3, …) determines the energy associated with the wavefunction determines the size of the orbital (smaller n means smaller size) determines the total number of nodes (# total nodes = n – 1)

H-atom quantum numbers The angular momentum quantum number, l quantization of angular momentum can have integer values from 0 to n – 1 n = 4 determines the number of angular nodes (# angular nodes = l) and therefore shape l = 0: spherically symmetric l = 1: 1 planar node dumb-bell orbital higher l: 2 or more planar nodes more complex shapes From rules for n and l, # radial nodes = n – l - 1 each value of l is assigned a letter: for H atoms, energy does not depend on l l = 0, 1, 2, 3

H-atom quantum numbers The magnetic quantum number, ml quantization of the z-component of the angular momentum can have values from –l to +l l = 2 Therefore, for each l, there are 2l + 1 values of ml 1 s, 3 p’s, 5 d’s, etc. determines the orientation of an orbital ml = 0: orbital is oriented along the z axis energy does not depend on ml ml = -2, -1, 0, +1, +2

H-atom quantum numbers Each set of three quantum numbers (n, l, ml) defines a unique wavefunction or orbital n = 1, 2, 3, … l = 0, 1, 2, …, n – 1 ml = -l, … -1, 0, 1, … +l nodes n l ml name energy total angular radial 1 1s E1=-2.18×10-18 J 2 2s E2=¼ E1 2pz +1 -1 3 3s E3=1/9 E1 0, ±1 3px,y,z E3 0, ±1, ±2 3d n2 = 1 n2 = 4 2px, 2py n2 = 9

Hydrogen atom energy levels The energy is determined only by the principle quantum number, n For each energy (each n), there are n2 wave functions (orbitals) excited states all orbitals with the same n have the same energy ground state

What is an orbital? http://www.falstad.com/qmatom/ http://resource.isvr.soton.ac.uk/spcg/tutorial/tutorial/Tutorial_files/Web-standing-membrane.htm

s Orbitals (l = 0)

s Orbitals (l = 0) # nodes = n -1 # “bumps” = n most probable distance from nucleus increases 

p Orbitals (l = 1) two lobes divided by a planar node n = 3 and higher p orbitals also have radial nodes

d Orbitals (l = 2) four lobes divided by 2 planar nodes

Energies of Orbitals Hydrogen Atom Multi-electron Atom

Spin Quantum Number, ms An electron has a “spin” – either “up” or “down”, which describes its magnetic field Indicated by the spin quantum number, ms, which has only two allowed values, +½ and –½. Pauli Exclusion Principle No two electrons in the same atom can have the same 4 quantum numbers.

Electron Configurations 1s2 2s1

Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”