3313 Andrew Brandt 1

Physics 3313 - Lecture 9

2/23/2009

Monday February 23, 2009Dr. Andrew Brandt

1. The Electron2. Rutherford Scattering3. Bohr Model of Atom

2Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt

Evolution of Atomic Models

• 1803: Dalton’s billiard ball model

• 1897: J.J. Thompson Discovered electrons– Used cathode ray tubes– Called corpuscles– Made a bold claim that these

make up atoms– Measured charge/mass ratio

• 1904: J.J. Thompson Proposed a “plum pudding” model of atoms – Negatively charged electrons

embedded in a uniformly distributed positive charge

Cathode ray tube

Personally I prefer chocolate chip cookie model

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Millikan’s Oil Drop Experiment

• Millikan (and Fletcher) in 1909 measured charge of electron, showed that free electric charge is in multiples of the basic charge of an electron

• By varying electric field to balance gravitational field, could determine charge of electron

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4Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt

Rutherford Experiment

• 1911: Geiger and Marsden with Rutherford performed a scattering experiment firing alpha particles at a thin gold foil

Rutherford Scattering

• The actual result was very different—although most events had small angle scattering, many wide angle scatters were observed

• “It was almost as incredible as if you fired a 15 inch shell at a piece of tissue paper and it came back at you”

• Implied the existence of the nucleus. • We perform similar experiments at

Fermilab and CERN to look for fundamental structure

4 2

( )sin

2

KN

KE

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Rutherford Example

• On blackboard demonstrate size of radius from distance of closest approach

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7Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt

Ruherford Atom

• 1912: Rutherford’s planetary model, an atomic model with a positively charged heavy core surrounded by circling electrons

• But many questions:

a) Z=A/2, Z=atomic number (number of electrons or protons) what is the other half of the atomic weight ?

b)what holds the nucleus together?

c)how do electrons move around the nucleus and does their motion explain observed atomic properties?

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Electron Orbit• Electrons must be in motion or would get sucked into nucleus by Coulomb

Force• “Assume a spherical orbit” : this implies that the centripetal force must be

balanced by the Coulomb force• so

• Energy of electron is kinetic energy plus potential energy

(where potential energy is defined to be 0 at infinity and negative at closer radius since you have to input work to keep electron and proton apart)

• Can thus determine radius of Hydrogen atom given Binding Energy (-13.6 eV)

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2 2

20

1

4

mv e

r r

22

0

1

2 4

eE mv

r

2 2 2

0 0 08 4 8

e e eE

r r r

219 2 9

2 211

190

(1.6 10 ) 9 105.3 10

8 2( 13.6 1.6 10 / )

N mCe CR m

E eV J eV

04

ev

mr

This is knownas Bohr Radius

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Quantum Effects• Classically an accelerating charge revolving with a

frequency would radiate at the same frequency. As it radiates, it loses energy, and radius decreases and frequency increases (death spiral)

• Law of physics in macro-world do not always apply in micro-world

• Quantum phenomena enter the picture• Evidence for quantum nature of atoms: discrete

line spectra emitted by low pressure gas when excited (by electric current)—only certain wavelengths emitted

• A gas absorbs light at some wavelengths of emission spectra, with the number intensity and wavelength of absorption lines depending on temperature, pressure, and motion of the source. This can be used to determine elements of a star and relative motion

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Spectral Lines

• For Hydrogen Atom (experimental observation):

• where nf and ni are final and initial quantum states

• R=Rydberg Constant

• Balmer Series nf = 2 and ni=3,4,5 visible wavelengths in Hydrogen spectrum 656.3, 486.3,…364.6 (limit as n)

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2 2

1 1 1( )

f i

Rn n

7 1 11.097 10 0.01097m nm

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Spectral Lines

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Bohr Atom• Assumptions

1) The electron moves in circular orbits under influence of Coulomb force

2) Only certain stable orbits at which electron does not radiate

3) Radiates when “jumps” from a more energetic initial state to a lower energy final state

• Introduced quantum number of orbit, can describe using de Broglie language (he didn’t, since it didn’t exist yet)

• Allowed orbits are integer number of de Broglie wavelengths

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i fE E hv

2 nn r

non-integernumber of wavelengths is discontinuous, so not physical

3313 Andrew Brandt 132/23/2009

h

mv 04 rh

e m

34

19

6.63 10 sec

1.6 10

J

C

11

29 31

2

5.3 10

9 10 9.1 10

m

N mkg

C

20

1 2

hr

me

2 2

02n

n hr

me

2 2 2 24 nn r

Bohr Atom Derivation

04

ev

mr

1133 10 2m r

• Consider n=1, the circular orbit case: for this to be self-consistent implies that

• with yields

• so finally

• Generally so with

so and

2 nn r 12 r

21nr n r 11

1 0 5.3 10r a m

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h

mv 04 rh

e m

34

19

6.63 10 sec

1.6 10

J

C

11

29 31

2

5.3 10

9 10 9.1 10

m

N mkg

C

20

1 2

hr

me

2 2

02n

n hr

me

2 2 2 24 nn r

Bohr Atom Derivation

04

ev

mr

1133 10 2m r

2 nn r 12 r

21nr n r 11

1 0 5.3 10r a m

• Consider n=1, the circular orbit case: for this to be self-consistent implies that

• with yields

• so finally

• Generally so with

so and