Chemistry Week 7

Chemistry Week 7 - (3 Orbitals and Quantum Numbers Another...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
(3) Orbitals and Quantum Numbers Another table showing alternative representations… l = 0 l = 1 l = 2 n = 1 Ψ 1 s ( r ) r 0 nodes n = 2 Ψ 2 s ( r ) Node r 1 node (spherical node) Ψ 2 p ( r ) r x y z 1 node (planar node) n = 3 Ψ 3 s ( r ) r r Ψ 3 p ( r ) r Ψ 3 d ( r )
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 nodes (2 spherical nodes) 2 nodes (1 spherical node; 1 planar node) x y x y z x z y z x y 2 nodes (2 planar or conical nodes) Two important aspects of atomic orbitals are their nodes and lobes . Consider the 3 2 p atomic orbitals: 2 p z 2 p y 2 p x Nodes are surfaces where () ,, 0 nlm r θϕ Ψ= . For these orbitals, the nodes are simply planes. The lobes are regions where the orbital takes a nonzero value (either positive or negative). These 2 p orbitals show their lobes pointing along the directions of the label. z y x 1 NODE ( yz -Plane) LOBES (along x ) y z x 1 NODE ( xz -Plane) LOBES (along y ) z y x 1 NODE ( xy -Plane) LOBES (along z )
Background image of page 2
Another set of examples come from the n = 3 shell: the 3 p atomic orbitals (illustrated by just the 3 p z orbital) and two of the 3 d atomic orbitals (the 3 d z 2 and 3 d yz orbitals): 3 p z 3 d z 2 3 d yz From the previous two tables, we see that the 2 p orbitals have 1 node (a plane), and the 3 p /3 d orbitals have 2 nodes . Furthermore, there are 3 different kinds of nodes: (a) spherical nodes ( r = constant); (b) conical nodes ( θ = constant; if = 90 ° ); (c) planar nodes ( ϕ = constant; these planes are parallel with the z -axis). In general, the quantum numbers n , l , and m are node counters : | m | = # of planar nodes; l | m | = # of conical nodes; therefore, l = # of conical nodes + # of planar nodes; n l 1 = # of spherical nodes (we are not counting the node as r ). Orbital Size : In the Bohr model, each orbit has a specific energy E n and radius r n . The wave- particle dual nature of the electron prohibits a specific localization of electron and electronic wavefunctions in space, but we can identify the most probable distance for an electron from the nucleus, depending upon the atomic orbital wavefunction. In the one-electron Schrödinger equation for the H atom, the most probable r n is related to n 2 , but r n n 2 a 0 ( a 0 = 0.529 Å). Here is a graph of the ns atomic orbital distributions for n = 1, 2, 3, and 4: at the very least, the most probable distance does increase with the value of n . z y 2 Planar Nodes ( xz -plane) z x y 2 Conical Nodes θ = 54.74 ° θ = 125.26 ° Planar Node ( xy -plane) Spherical Node x y z z y x z y x
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
r 4 π 2 R ns ( r ) 1 s 2 s 3 s 4 s Electron Spin : An electron has an intrinsic characteristic called spin , but this feature has no classical origin ; it is entirely a quantum mechanical phenomenon. Electron spin is identified by a quantum number ( s = 1/2), and it takes two possible values, m s = +1/2 (“spin up”) or 1/2 (“spin down”). We can see the effect of spin by exposing matter to a magnetic field, but we can only see the effect of the sum of spins of all electrons in the substance being examined. Here is a way that spin is represented on an orbital energy diagram: For a one-electron atom or ion, the state of the electron will be completely described by four quantum numbers, ( n , l , m , m s
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/27/2008 for the course CHEM 201 taught by Professor Miller during the Fall '07 term at Iowa State.

Page1 / 20

Chemistry Week 7 - (3 Orbitals and Quantum Numbers Another...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online