UnderstandingUnderstanding Atoms Atoms

Chapter 42Chapter 42

The Bohr Model – good but not perfect!The Bohr Model – good but not perfect!

For Hydrogen and “Hydrogenic” For Hydrogen and “Hydrogenic” atoms predicts the Rydberg formula atoms predicts the Rydberg formula

R is the Rydberg constant for the element, Z is the atomic number R is the Rydberg constant for the element, Z is the atomic number (nuclear charge) and n & m are integers(nuclear charge) and n & m are integers

Bohr Model fails hopelessly for Bohr Model fails hopelessly for Helium and most heavier atoms!Helium and most heavier atoms!

2

2 2

1 1 1RZ

n m

go to spreadsheet

Fine StructureFine Structure High resolution High resolution

spectroscopy shows spectroscopy shows that the Balmer lines that the Balmer lines are multiplets!are multiplets!

Key Concepts…Key Concepts…

Energy solutions for SE can Energy solutions for SE can consist of combinations of consist of combinations of radial and angular termsradial and angular terms

Conservation Laws help Conservation Laws help “set” the selection rules for “set” the selection rules for atomic transitionsatomic transitions

““Forbidden” transitions still Forbidden” transitions still occur but with very low occur but with very low probability. probability.

Will that be one hump or two?Will that be one hump or two?

Bohr model “n” Bohr model “n” (principal quantum (principal quantum number) number) represents energy represents energy levellevel

QM “n” represents QM “n” represents number of humps number of humps in the radial in the radial wavefunctionwavefunction

The radial – angular selection The radial – angular selection rules:rules:

n = energy level = maximum n = energy level = maximum number of humpsnumber of humps

l = orbital angular momentum ( l = l = orbital angular momentum ( l = 0,1,2, … n-1)0,1,2, … n-1)

m = z-component of angular m = z-component of angular momentum (-l, -(l-1)m, … (l-1),1)momentum (-l, -(l-1)m, … (l-1),1)

mmss = z-component of electron spin = z-component of electron spin

How to make atoms…How to make atoms…

The rules for n, nThe rules for n, nrr, l and m, l and mss tell us tell us how many different energy how many different energy eigenfunctions exist for an atomeigenfunctions exist for an atom

Example 42.4Example 42.4

Stern and Gerlach (SG)Stern and Gerlach (SG)

Link to fascinating historical account of the SG experiment – how a cheap cigar changed physics!

Using the “rules”Using the “rules”n l ml ms # e

0,1,2,…,(n-1) l-1,..,0,..l1 0 0 +1/21 0 0 -1/2 22 0 0 +1/2 22 0 0 -1/22 1 -1 +1/2 62 1 -1 -1/22 1 0 +1/22 1 0 -1/22 1 1 +1/22 1 1 -1/23 0 0 +1/2 63 0 0 -1/23 1 -1 +1/2 63 1 -1 -1/23 1 0 +1/23 1 0 -1/23 1 1 +1/23 1 1 -1/23 2 -2 +1/2 103 2 -2 -1/23 2 -1 +1/23 2 -1 -1/23 2 0 +1/23 2 0 -1/23 2 1 +1/23 2 1 -1/23 2 2 +1/23 2 2 -1/2

Photons Spin?

Photons carry angular momentum – they are “spin-1 particles”

All photons carry the same angular momentum:

L = ±ћ Confirmed by

number of ingenious experiments in the 1930s

Photon spin and allowed Photon spin and allowed transitions…transitions…

Photon’s are spin=1 particles Photon’s are spin=1 particles (bosons)(bosons)

Electron transitions – to conserve Electron transitions – to conserve angular momentum - are “angular momentum - are “l = ±1” l = ±1” transitionstransitions

Transitions that violate the above Transitions that violate the above rule are not strictly prohibited – they rule are not strictly prohibited – they have a very low probability of have a very low probability of occurrenceoccurrence

Hydrogen and Multi-Electron Atoms

Hydrogen Sodium

Metastable states and Forbidden or Metastable states and Forbidden or Auroral TransitionsAuroral Transitions

Example questions…Example questions…

Practice with radial and angular parts Practice with radial and angular parts use this appletuse this applet