Physics 214Physics 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•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

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 explanationheat causes accelerated charges (Maxwell like distribution of accelerations) that emit

radiation of various frequencies

Incandescent Spectra produced from Thermal Radiation

frequency

intensity

Wiens Displacement Law

maxT2.898 mK

Rayleigh-Jeans Law

I(,T)2ckT4

Intensity of radiation of wavelength at temp T

However this only agrees with experiment at long

Lim 0

I(,T) Ultraviolet Catastrophe

( total energy density)

Planck ' s Function

I ,T 2hc2

5 ehckT 1

h 6.626 10 34 Js Planck 's Constant

Planck’s Assumptions

Oscillating molecules that emit the radiation only have discrete energies

En = nhn = quantum number

En = energy of quantum state n of molecule

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

E1

h

E2

E2E1

h

The Photoelectric Effect

LightElectron

VG

A

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

V

I

-V0

plate A has negative potential Stopping Potential

high intensity light

low intensity light

•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

1. No electrons ejected if c (cut off frequency )

2. If c

the number of photo electrons light intensity

3. Kmax is independent of light intensity

4. Kmax

as

5. Electrons are emitted instantaneously even at low

light intensities

Observed Properties

Wave theory of light does not predict such properties

Einstein explained this by the hypothesis

that light is quantized in

energy packets = QUANTA with energy E = h

he called such quanta PHOTONS .

The intensity of the light is proportional to the number

of such quanta i .e.

I nh

In order for electrons to be emitted they must pass through

surface . use amount of energy to overcome surface

barrier Ionization Potential Work Function

Kmax

h - = h h c

1 . Kmax

h - ; so Kmax

depends on

2 . h ; for emission of electrons

3 . h - only depends on not on intensity

4. Kmax

as

5 . single electrons are excited by light

(not many gradually) instantaneous emission

Einsteins Theory Predicts

Kmax

c

slope = h

Kmax = h

Compton Effect

scattered photon

scattered electron

More Evidence that light is composed of particles

Observed scattering intensity I

I = I , ;

incident 0 scattered - this contradicts classical theory

= - 0

Compton (1923 ) suggested treating photon as particle

E = h =hc

The Special Theory of Relativity gives E = pc

p is the magnitude of the momentum of the photon

pc =hc

p =

h

Etot

= ptot

= 0

=hm

ec

1 cos

; ; Ephoton

during collision

Compton Wavelength of electron =h

mec

What is Light?

What is Light?

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

Atomic Spectra

gas

gas

Absorption Spectra

Emission Spectra

http://www.unm.edu/~astro1/101lab/lab5/lab5_D.html

1R

H

1n

1

2 1n

2

2

; n

2n

11,n

12,

RH1.097373210

m-1 Rydberg Constant

n11 Lyman

n12 Balmer

n13 Paschen

n14 Brackett

Bohr Model

1. Electron moves in circular orbit about nucleus

2. Electron can only exist in specific orbits determined by

L mev r I nh

2 n; n1,2,

Imr 2 ; vr

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

=Eh E

l

h

Angular Momentum Quantization

U r kq1q

2

r ke

2

rkcoulombs constant

E r K U12mev 2 ke

2

r

If electrons speed is constant

Fcm

eacmev 2

rke2

r2m

ev2 k

e2

r

12mev2 1

2ke2

r

E r 12ke2

r

r

+

-

Quantization of Angular Momentum

r n m e v

v =n me r

mev2

n2 2

mer 2

ke 2

r

r n 2 2

me ke2 ; n 1 , 2 ,

r rn i . e . r depends on n

Bohr radius is defined as r0

2

m e ke 2

so that rn

n2 r0

using these values for rn in the expression

for the energy we obtain

En

mek2e 4

2 2

1n2

; n 1, 2 ,

13 . 6 eV1

n 2

thus the frequencies of emitted photons are

21E2 E 1

hmek 2e 4

2h 2

1n

12 1n

22

1

cmek 2e 4

2h 2c

1

n12

1

n22

Theoretical expression for Rydberg constant

RHm ek 2e 4

2h 2cwhich is in good agreement with experimental value