6/28/2015 One Point Quiz  One quiz per table, list everyone’s name  Agree on an answer  You have two minutes

6/28/2015 Descriptive Chemistry  Besides assigned readings on orbital shapes and electron probability, there are readings on descriptive chemistry.  This week Group III (Boron family) Group IV (Carbon family)

Orbital Shapes Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology

6/28/2015 Orbitals  The region around a nucleus in which an electron has a probability of being located is called an orbital.  Orbitals can vary in distance from the nucleus (radial function) direction (angular function)

6/28/2015 Wave Function (  2  x 2  2  y 2  2  z 2  + V   2 m E  = h2h2 The shape of the orbital and the energy of the electron is related to the wave function (  ). The electron is mathematically described by the wave function, the Schrödinger Equation is used to calculate the energy of that electron. The wave function is composed of radial and angular functions (in three dimensions).

6/28/2015 Spherical Coordinates z x y r r = distance of electron from nucleus   = angle of declination (angle from z-axis)   = angle of rotation (angle from x-axis in xy plane) coordinates (r, ,  )

6/28/2015 Orbital Shapes  The shape of the orbital is determined by the wave function.  The shape of the orbital can be determined from the nodes of the wave function.  a o = Bohr radius (0.529 Å)  Z = nuclear charge

6/28/2015 Orbital Wave Functions Wave Function Radial Nodes Angular Nodes  1s = 3/2 1        Z aoao e        Zr aoao no radial nodes no angular dependence  2s =    3/            Z aoao 2 Zr aoao e        aoao when Zr/a o =2 no angular dependence

6/28/2015 Orbitals With No Angular Dependence 1s 2s s orbitals have a spherical shape isotropic orbitals

6/28/2015 Orbital Wave Functions  2p z =    3/           Z aoao Zr aoao e        2a o cos  no radial nodes  = 90° z x y Radial Nodes Angular Nodes Wave Function  

6/28/2015 Orbital Wave Functions z x y Radial Nodes Angular Nodes Wave Function  2p x =    3/           Z aoao Zr aoao e        2a o (sin  cos  no radial nodes   = 0° or  = 90° 

6/28/2015 Orbital Wave Functions z x y Radial Nodes Angular Nodes Wave Function    2p y =    3/           Z aoao Zr aoao e        2a o (sin  sin   = 0° or  = 0° no radial nodes

6/28/2015 Orbitals With Angular Dependence p orbitals have a propeller shape 2p x x y z x y z 2p y x y z 2p z How can you distinguish p x from p y or p z ? Anisotropic orbitals the angular probability function is not the same in all directions

6/28/2015 Higher Energy Orbitals  Higher energy levels correspond to higher wave functions including 3s, 3p x, 3p y, 3p z and d orbitals.

6/28/2015 d Orbitals x y z 3d xy x y z 3d yz x y z 3d xz x y z 3d x 2 -y 2 3d z 2 x y z

6/28/2015 Orbital Sets  Other orbitals are anisotropic, however when they are combined as a set the result is "spherically symmetric" (i.e., isotropic).  s orbitals are spherical in shape and therefore spherically symmetric.

6/28/2015 Orbital Sets ++ = no angular dependence  spherically symmetric  isotropic p orbitals are individually anisotropic, but as a set are isotropic. pxpx pypy pzpz

6/28/2015 Orbital Sets = d orbitals are individually anisotropic, but as a d xy, d xz, d yz, d x 2 -y 2, d z 2 set are isotropic. electrons in spherically symmetric orbitals are slightly more stable

6/28/2015 Quantum Numbers  Each electron in the orbital of the atom can be described by an unique combination of values known as quantum numbers.  There are four different quantum numbers n, , m, m s

6/28/2015 Principal Quantum Number n=1 n=2 n=3 n=4 n=5 n=6 n=7 principal quantum number Larger values of n refer to higher energy orbitals (further from the nucleus) range: n = 1, 2, 3, …,  The principal quantum number is related to the rows of the periodic table.

Angular Quantum Number = 0 s orbital (no angular dependence) = 1 p orbital = 2 d orbital = 3 f orbital range: = 0, …, n-1 Is it possible to have a 2f orbital? Is it possible to have a 3p orbital? This is the principal quantum number

6/28/2015 Magnetic Quantum Number What would be the names of these orbitals? m = - , …, 0, …, + Differentiates between orbitals with the same n and  quantum numbers In a magnetic field aligned along the z-axis, an electron in the 2p z orbital will behave differently than an electron in the 2p x or 2p y orbitals. p-1p-1 p0p0 p+1p+1 How many f-orbitals are there in an f-orbital set?

6/28/2015 Spin Quantum Number m s = -1/2, +1/2 Each orbital can contain up to two electrons one aligned with an external field one aligned against an external field Which electron has lower energy?

6/28/2015 Quantum Numbers and the Periodic Table Identify the regions of the periodic table that correspond to the s, p, d and f orbitals s p d f

6/28/2015 Four Quantum Numbers  Each electron in an atom can be described uniquely by the four quantum numbers.  Three rules involving quantum numbers Pauli Exclusion Principle Aufbau Principle Hund's Rule

6/28/2015 Pauli Exclusion Principle  Only one electron in an atom may have the same four quantum numbers. it’s like a house address /2

6/28/2015 Aufbau Principle  In the ground state, electrons fill in the lowest available energy state (orbital) first it’s like the best available seat in the house

6/28/2015 Hund's Rule  If more than one electron occupies a degenerate set of orbitals (orbitals of the same energy), then the electrons will fill in such a way as to maximize the number of orbitals filled. each electron would prefer to be single rather than be doubled up  It is more stable for the spin of the electrons to be aligned in the same direction.

6/28/2015

Laboratory  Special extra lab period today periods 7-9

6/28/2015 Problem Set  Electron Filling PS due Thursday  Four Ions PS to be done (but not submitted) by Exam 2