chapter 04 structure of the atom general bibliography 1) various wikipedia, as specified 2)...

Chapter 04Structure of the Atom

General Bibliography1) Various wikipedia, as specified

2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated

Outline

• 4.1 Atomic Models of Thomson & Rutherford• 4.2 Rutherford Scattering• 4.3 Classical Atomic Model• 4.4 Bohr Model• 4.5 Failures of the Bohr Model• 4.6 Characteristic X-Ray Spectra• 4.7 Atomic Excitations

4.1 Plum Pudding Model

J.J. Thomson

Positive pudding with negative ‘raisins’

Electrons oscillate about their equilibrium position when heated and produce EM radiation

If made oscillations about ~10-10 m, could produce visible wavelengths, but never line spectra.

4.1 Geiger-Marsden-Rutherford

http://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment

http://www.kutl.kyushu-u.ac.jp/seminar/MicroWorld1_E/Part2_E/P23_E/Geiger_Marsden_E.jpg

4.2 Geiger-Marsden-Rutherford

2sin

1~

4

2221

KE

eZZratecount

Derivation on pages 131-137

Assume massive positive objectsCoulomb force

4.2 Geiger-Marsden-Rutherford

Example 4.4 & 4.5: Estimate distance of closest approach for an alpha particle striking

an aluminum nucleusKE = 7.7 MeV

s

4.3 Classical Atomic Model

r

v

Using Newtonian Mechanics & JJThomson’s anticipated sizes:

1. Estimate the speed of the orbiting electron

2. Total Energy of the system

4.3 Classical Atomic Model

Failures of the classical model:

1.

2.

4.4 Bohr’s Postulates

• A countable number of “stationary states” exist. (electrons in a selection of allowed orbit radii)

• EM radiation emitted when electron jumps/transitions between states

• Classical rules apply to stationary states, but not during transitions between states.

• …Angular momentum occurs in integer multiples of h/2.

n=1

n=2 n=3

4.4 Bohr Model

2

24

mea oo

on anr 2

)(6.13

8 22

2

eVinnna

eE

oon

on

e

nv

41 2

1371

4

21

c

e

c

v

o

4.4 Bohr Model

4.5 Successes & Failures of Bohr Model

rseparationCoulomb

rrradiusorbit e

Reduced Mass Correction

ee

e

Mm

Mmmfixmagic

4.5 Successes & Failures of Bohr Model

• + Rydberg Eqn predicts many lines of He (except for a few extra lines)

• Higher resolution diffraction gratings in advanced spectrographs indicated some transitions were multiple (fine structure)

• Bohr’s “n” quantum number is only partially associated with angular momentum (1s, 2s, 3s,… states do not have angular momentum)

• Worked best for single-electron atoms– H+, He+, Li+

4.6 Characteristic X-Ray Spectra

4.7 Atomic Excitation