Physics 214
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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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Physics 214

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Physics 214

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


Physics 214

  • 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


Physics 214

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


Physics 214

Incandescent Spectra produced from Thermal Radiation

intensity

Animation

frequency


Physics 214

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

)


Physics 214

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


Physics 214

E2

hn

hn=E

E1

E = E2-E1


Physics 214

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


Physics 214

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


Physics 214

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


Physics 214

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


Physics 214

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


Physics 214

Compton Effect

scattered photon

q

f

scattered electron

More Evidence that light is composed of particles


Physics 214

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


Physics 214

What is Light?


Physics 214

  • 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


Physics 214

Atomic Spectra


Physics 214

Absorption Spectra

gas

gas

Emission Spectra


Physics 214

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


Physics 214

Bohr Model


Physics 214

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


Physics 214

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


Physics 214

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


Physics 214

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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