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Physics 214. 4: Introduction to Quantum Physics. Blackbody Radiation and Planck’s Hypothesis The Photoelectric Effect Compton Effect Atomic Spectra The Bohr Quantum Model of the Atom. Classical Physics Material objects obey Newtons Laws of Motion

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slide1
Physics 214

4: Introduction to Quantum Physics

  • Blackbody Radiation and Planck’s Hypothesis
  • The Photoelectric Effect
  • Compton Effect
  • Atomic Spectra
  • The Bohr Quantum Model of the Atom
slide2
Classical Physics
    • Material objects obey Newtons Laws of Motion
    • Electricity and Magnetism obey Maxwells Equations
    • Position and momentum are defined at all times
    • Initial Position and momentum plus knowledge of all forces acting on system predict with certainty the position and momentum at all later times.
  • Could not explain
    • Black Body Radiation
    • Photo Electric Effect
    • Discrete Spectral Lines
slide3
Blackbody Radiation and Planck’s Hypothesis

Any object with a temperature T>0 K radiates away thermal energy through the emission of electromagnetic radiation

Classical explanation

heat causes accelerated charges (Maxwell like distribution of accelerations) that emit radiation of various frequencies

slide5
Wiens Displacement Law

mK

l

T

=

2

.

898

max

Rayleigh

-

Jeans Law

2

p

ckT

I

(

l

,

T

)

=

4

l

Intensity of radiation of wavelength

l

at temp

T

However this only agrees with experiment at long

l

Lim

I

(

l

,

T

)

=

¥

Ultraviolet Catastrophe

l

¯

0

(

Þ

¥

total energy density

)

slide7
Planck’s Assumptions

Oscillating molecules that emit the radiation only have discrete energies

En = nhn

n = quantum number

En = energy of quantum state n of molecule

Molecules emit or absorb energy in discrete units of light called QUANTA

slide8
E2

hn

hn=E

E1

E = E2-E1

slide9
The Photoelectric Effect

Light

A

Electron

  • A is maintained at a positive potential by battery.
  • IG = 0 until monochromatic light of certain l is incident

G

V

Animation

slide10
high intensity light

I

low intensity light

-V0

V

plate A has negative potential

Stopping Potential

  • When A is negative only electrons having K.E. > eV0 will reach A, independent of light intensity
  • Maximum K.E. of ejected electrons Kmax= eV0
slide11
Observed Properties

1

.

No electrons ejected if

n

£

n

(cut off frequency

)

c

2

.

If

n

³

n

the number of photo electrons

µ

light intensity

c

3

.

K

is independent of light intensity

max

4.

K

­

as

n

­

max

5

.

Electrons are emitted instantaneously even at low

light intensities

Wave theory of light does not predict such properties

slide12
Einstein explained this by the hypothesis

that light is quantized in

energy packets

=

QUANTA with energy E

=

h

n

he called such quanta PHOTONS

.

The intensity of the light is proportional to the number

of such quanta i

.

e

.

I

µ

nh

n

In order for electrons to be emitted they must pass through

surface

.

\

use

f

amount of energy to overcome surface

barrier

º

Ionization Potential

º

Work Function

K

=

h

n

-

f

=

h

n

-

h

n

max

c

slide13
Einsteins Theory Predicts

1

.

K

=

h

n

-

f

;

so K

depends on

n

max

max

2

.

h

n

³

f

;

for emission of electrons

3

.

h

n

-

f

only depends on

n

not on intensity

4.

K

­

as

n

­

max

5

.

single electrons are excited by light

(not many gradually)

Þ

instantaneous emission

Kmax = hn-f

slope = h

Kmax

nc

slide14
Compton Effect

scattered photon

q

f

scattered electron

More Evidence that light is composed of particles

slide15
Observed scattering intensity I

(

)

I

=

I

l

,

q

;

incident

l

¹

scattered

l

-

this contradicts classical theory

0

D

l

=

l

-

l

0

Compton

(

1923

) suggested treating photon as particle

hc

E

=

h

n

=

l

The Special Theory of Relativity gives E

=

pc

[

]

p is the magnitude of the momentum of the photon

hc

h

\

pc

=

Þ

p

=

l

l

D

E

=

D

p

=

0

tot

tot

h

(

)

Þ

D

l

=

1

-

cos

q

m

c

e

Þ

l

­

;

n

;

E

during collision

¯

¯

photon

h

Compton Wavelength of electron

=

m

c

e

slide17
Youngs Double Slit Experiment
    • Light is composed of waves
  • Photo Electric Effect
    • Light is composed of particles
  • Compton Effect
    • Light is composed of particles
  • Paradox?
  • Wave Particle Duality
slide19
Absorption Spectra

gas

gas

Emission Spectra

slide22
æ

ö

1

1

1

ç

÷

=

R

-

;

n

=

n

+

1

,

n

+

2

,

K

l

n

n

2

2

è

ø

H

2

1

1

1

2

7

R

=

1

.

0973732

´

10

º

Rydberg Constant

m-1

H

n

=

1

Û

Lyman

1

n

=

2

Û

Balmer

1

n

=

3

Û

Paschen

1

n

=

4

Û

Brackett

1

slide24
1

.

Electron moves in circular orbit about nucleus

2

.

Electron can only exist in specific orbits determined by

Angular Momentum Quantization

h

n

L

=

m

v

r

=

I

w

=

n

=

;

n

=

1

,

2

,

K

h

e

2

p

v

é

ù

I

=

mr

;

w

=

2

ë

r

û

3

.

Electrons in such orbits DO

NOT

radiate energy

although they are accelerating.

Such orbits are thus called STATIONARY

STATES

4.

Atoms radiate only when electron jumps from higher

energy

(large radius

) to lower energy

(smaller radius

)

orbits

.

The frequency of light they radiate is given by

E

-

E

Animation

n

=

h

l

h

slide25
kq

q

e

2

(

)

U

r

=

=

-

k

1

2

r

r

k

=

coulombs constant

-

1

e

2

(

)

r

E

r

=

K

+

U

=

m

v

-

k

2

2

r

e

+

If electrons speed is constant

m

v

e

e

2

2

2

F

=

m

a

=

=

k

Þ

m

v

=

k

e

2

c

e

c

r

r

e

r

2

1

1

e

2

\

m

v

=

k

2

2

2

r

e

1

e

2

(

)

Þ

E

r

=

-

k

2

r

slide26
Quantization of Angular Momentum

ß

n

n

h

h

r

=

Û

v

=

m

v

m

r

e

e

n

ke

h

2

2

2

\

m

v

=

=

2

m

r

r

e

2

e

n

h

2

2

Þ

r

=

;

n

=

1

,

2

,

K

2

m

ke

e

\

r

=

r

i

.

e

.

r

depends on

n

n

h

2

Bohr radius is defined as

r

=

m

ke

0

2

e

so that

r

=

n

r

2

n

0

slide27
using these values for

r

in the expression

n

for the energy we obtain

2

4

m

k

e

1

æ

ö

e

E

=

-

;

n

=

1

,

2

,

K

è

ø

2

n

n

h

2

2

1

æ

ö

=

-

13

.

6

eV

è

ø

n

2

thus the frequencies of emitted photons are

æ

E

-

E

m

k

e

ö

1

1

2

4

ç

÷

2

1

e

n

=

=

-

h

2h

n

n

21

è

ø

h

2

2

2

1

2

æ

1

n

m

k

e

1

1

ö

2

4

ç

÷

=

=

-

e

l

c

n

n

è

ø

h

2

2

2

2h

c

1

2

Theoretical expression for Rydberg constant

m

k

e

2

4

e

R

=

H

2

2h

h

c

which is in good agreement with experimental value

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