bohr model of the hydrogen atom

8/3/2019 Bohr Model of the Hydrogen Atom

1/27

Bohr model of the Hydrogen Atom

Duality of matter led tothe hypothesis thatelectrons behave aswaves.

Bohr model assumed Only circular orbits

around the nucleus andthat the angular momentum

around the atom must bequantized.

Stable orbital whereconstructive interferenceoccurs.

Destructive interferenceprevents observation oforbits with mismatch ofwaves


2/27

Bohrs Model of the

Hydrogen Atom Bohr concluded:

the energy of the electron in an orbit of hydrogen is

quantized

the energy difference between two orbits must also be

quantized

The frequency of a line in the spectrum corresponds to the

energy difference between two orbits;

Note that this is slightly different than the Einstein equation

for the energy of photons:

E= h

E= h E= h

E= h


3/27

Bohrs Model of the

Hydrogen Atom

The energy of a Bohr orbit(and an

electron in it) is given by

whereRHis theRydberg constant = 2.179 x 10-18 J

En = -RH1

2n


4/27

Hydrogen atom spectra

Visible lines in H atom

spectrum are called the

BALMER series.

Energy

Ultra Violet

Lyman

Infrared

Paschen

Visible

Balmer

En = -2.179x10-18 J

n2

65

3

2

1

4

n


5/27

De Broglie Wave Nature of Matter

E = mc2 Particle behavior E = h Wave behavior Wave and particle behavior

Duality of matter expressed by replacing thespeed of light with the speed of the particle to get called the de Broglie wavelength of any moving

form of matter

mv

h=

mc

h

mc

hc

c

mch

2

2

=

=

==


6/27

De Brogilie WavelengthsParticle or Object Mass (kg) Speed (m/s) de Broglie Wavelength (nm)

Electron 9.109 x 10-31 1.00 x 106 7.27 x 10-1

Proton 1.673 x 10-27 1.00 x 106 3.96 x 10-4

Neutron 1.675 x 10-27 1.00 x 103 3.96 x 10-1

Bullet 1.000 x 10-2 8.00 x 102 8.28 x 10-26

Tennis Ball 5.68 x 10-2 5.00 x 101 2.33 x 10-25

________________________________________________


7/27

Matter - Particles or Waves?

short de Broglie wave

fits within containment

particle properties

observed

long de Broglie wave

exceeds confinement

wave properties

observed

Ugh, this is

outrageous.

Not even one of

us fits in here.

Lets rebel andact like waves

Wow, this is a

great place, lots

of us will fit in

here comfortably.

Lets behave welland act like

particles


8/27

Davisson G.P. Thomson

Davisson, C. J.,

"Are Electrons

Waves?," Franklin

Institute Journal205, 597 (1928)

The Davisson-Germer experiment:

scattering a beam of electrons from

a Ni crystal. Davisson got the 1937

Nobel prize.

At fixed accelerating voltage (fixed

electron energy) find a pattern of sharp

reflected beams from the crystal

At fixed angle, find sharp peaks in

intensity as a function of electron energy

G.P. Thomson performed similar interference

experiments with thin-film samples

i

i

ELECTRON DIFFRACTIONELECTRON DIFFRACTION

The DavissonThe Davisson--GermerGermer experiment (1927)experiment (1927)


9/27

ELECTRON WAVE PROPERTIESELECTRON WAVE PROPERTIES


10/27

X-RAYS AND ELECTRONS WITH THE SAME

WAVELENGTH SHOW IDENTICAL DIFFRACTIONPATTERNS

X-RAYS AND ELECTRONS WITH THE SAME

WAVELENGTH SHOW IDENTICAL DIFFRACTIONPATTERNS

X-Rays Diffracted Electrons Diffracted

LightNo Light

Electrons

No Electrons


11/27

ELECTRON MICROSCOPE


12/27

Electron Micrographs of HIV Virus


13/27

Co

O

Li

The Lithium Ion

Battery Anode

Cobalt Oxide with

Li+

Ions


14/27

Electron Microscopy of LiCoO2

Lithium Ion Rechargeable Batteries

Electron

Micrograph

Computer Simulation

Of LiCoO2 Structure

*Li is the smallest atom

seen in Electron

Microscopy so far


15/27

Inventors of the Scanning Tunneling Microscope

Gerd

BinnigHeinrich

Rohrer

1986 Nobel Prize in Physics for their design of the

scanning tunneling microscope


16/27


17/27

Electron Waves in STM

Thick Barrier

Thin Barrier

Tunneling


18/27

The Picture is a kanji symbolthat translates literally asoriginal child. It is used to

represent the atom inscientific translation.

Scanning Tunneling Microscopy

The Symbol is Composed

of About 100 Individual

Iron Atoms on Copper. The

atoms were assembled by

scientists at IBM using a

method known as

Scanning TunnelingMicroscopy (STM).

What does the kanji symbol mean?

What are the red dots that form

the symbol?


19/27

President Clinton today used this tiny map of

the Western Hemisphere created by IBMResearch as a backdrop for hisannouncement of the $497-million NationalNanotechnology Init iative during a speech atthe California Institute of Technology today.Only one-hundredth the diameter of a humanhair, this map was made by a scanningtunneling microscope that deposited smallclusters of gold atoms to form each dot.Nanotechnology is the science of controllingmatter at the atomic scale.

San Jose, Calif. (January 21, 2000) --


20/27

Uncertainty PrincipleUncertainty PrincipleUncertainty PrincipleProblem of defining nature of

electrons in atoms solved by W.

Heisenberg.Cannot simultaneously define the

position and momentum (= mv)

of an electron.x p = h

At best we can describe the

position and velocity of anelectron by a

PROBABILITY DISTRIBUTION

W. Heisenberg

1901-1976


21/27

Uncertainty Principle

24

h

px

h

=

m2vx h

p=mv

Position, x and

momentum, p

Position, xand

Velocity, v

p= mv, m is constant


22/27

Trying to measure the pathway of

an electronElectron

Velocity

Photon

Y

X

h

h

h

h

h


23/27

Where is the electron in an atom?Where is the electron in an atom?

v = 1 x 106 m/s

h

v = 106 0.29 x 106 m/sx = 0.1 nm

Calculate the

uncertainty

in the position of the

electron after a time

period of 1 ms (10-3s) after the initial

measurement

The Heisenberg Viewpoint

x = vt

x = vt

x = (.58 x 106 m/s)(10-3 s)

x = 580 m

The de Broglie Viewpoint

( )( )nm727.0m10x27.7

s/m10x1kg10x109.9

sJ10x626.6

mv

h

10

631

34

=

=

?

. .Where will I be in

one millisecond ?

Electron confined to region <

will act like a wave The uncertainty inposition rapidly increases


24/27

Schrodinger applied idea of e-

behaving as a wave to the problemof electrons in atoms.

Solution to WAVE EQUATION givesset of mathematical expressions

called

WAVE FUNCTIONS,Each describes an allowed energy

state of an e-

Quantization introduced naturally.

E.E. SchrodingerSchrodinger

18871887--19611961

Wave MechanicsWave MechanicsWave Mechanics


25/27

WAVE FUNCTIONS, WAVE FUNCTIONS,WAVE FUNCTIONS, is a function of distance and twois a function of distance and two

angles.angles.

For 1 electron,For 1 electron, corresponds to ancorresponds to anORBITALORBITAL the region of spacethe region of spacewithin which an electron is found.within which an electron is found.

does NOT describe the exactdoes NOT describe the exactlocation of the electron.location of the electron.

22 is proportional to the probabilityis proportional to the probabilityof finding an eof finding an e-- at a given point.at a given point.


26/27

Quantum Numbers (QN)Quantum Numbers (QN)- Application of wave mechanics or the Schrdingerequation yielded energies for the electrons that

agreed well with the experimental data.

- The Schrdinger equation yields three quantumnumbers (QN) which define electron energies betterthan did the Bohr theory.

- Quantum mechanics does not allow us to describethe e- in an atom as moving in an orbit, but it doesallow us to make statistical statements about e-

density.

- We need to know these QN and how they define theorbital.


27/27

Orbital energies of the hydrogen atom.

Schrdinger Result Bohr Result22

42en

n2

eZmEh

=

(Note Scale Break Here)

bohr model of the hydrogen atom

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