Black-body Radiation & the Quantum Hypothesis

Black-body Radiation & the Quantum Hypothesis

Micro-world Macro-world

Lect 13

Max Planck

Thermal atomic motion

Heat energy= KE and PE associated with the random thermal motion of atoms

Air solid

Temperature avg KE

Temperature scales

Fahrenheit 212 F

32 F

- 459 F

room temp 27o C 300oK 80 F

Black-body Radiation

peak = 2.9 x 10-3 m

T(Kelvin)

Lig

ht

inte

nsit

y

UV

IR

peak vs Temperature

peak = 2.9 x 10-3 m

T(Kelvin)T

3100K(body temp)

2.9 x 10-3 m3100 =9x10-6m

58000K(Sun’s surface)

2.9 x 10-3 m58000 =0.5x10-6m

infrared light

visible light

“Room temperature” radiation

Photo with an IR camera

IR Cat

IR house

5800oK

=5x10

-7m

300oK

=1x10

-5m

Light absorbtion in the atmosphere

Vis

ible

lig

ht T=300o

Infraredlight

Back to Planck, etc…

the UV catastrophe

Pre-1900 theory

Theory & experiment disagree wildly

Planck’s solution

EM energy cannot be radiated or absorbedin any arbitrary amounts, but only in discrete“quantum” amounts.

The energy of a “quantum” depends on frequency as

Equantum = h fh = 6.6 x 10-34 Js

“Planck’s constant”

Other “quantum” systems

The quantum of the US monetary system

We don’t worry about effects of quantizationBecause the penny’s value is so small (~10와 )

Suppose the quantum were a $1000 bill

A quantum this large would have anenormous effect on “normal” transactions

The quantum of the US Income tax system

US Income tax with a $1 quantum

Nu

mb

er

of

taxp

ayers

US Income tax with a $1000 quantum

All these guys don’thave to pay anything

Nu

mb

er

of

taxp

ayers

Quantum effectsare negligible tothese taxpayers

Quantum effects arehuge to these guys

How quanta defeat the UV catastrophe

Low frequency,small quantum,

Negligible effects

high frequency,large quantum,

huge effects

Withoutthe quantum

With the quantum

Planck’s quantum is small for “ordinary-sized” objects but large for atoms etc

“ordinary”pendulumf = 1 Hz

Hydrogen atomf 2x1014 Hz

Equant= hf =6.6x10-34Jsx1Hz

=6.6x10-34J

Equant= hf

=(6.6x10-34Js)x(2x1014Hz)

=(6.6 x 2) x 10-34+14J

=1.3 x 10-19Jvery tiny

about the same

as

the electron’s KE

Typical energies in “ordinary” life

Typical energy ofa tot on a swing:

Etot = mghmax

hma

x

= 20kgx

= 200 kgm2/s2

= 200 Jmuch, much larger than

Equant=6.6x10-34J

= 20kgx10m/s2x= 20kgx10m/s2x1m

Typical electron KE in an atom

1 “electron Volt”Energy gained by anelectron crossing a 1Vvoltage difference

1V

- - -Energy = q V

1eV = 1.6x10-19C x 1V

= 1.6x10-19 Joules

Equant = 1.3 x 10-19J

similar

for f 2x1014 Hz

Classical vs Quantum world

In everyday life,

quantum effects

can be safelyignored

At atomic & subatomic

scales,quantum effectsare dominant &

must be considered

This is because Planck’s

constant is so small

Laws of naturedeveloped

withoutconsideration ofquantum effects do not work for

atoms

photons

“Quantum Jump”

Photoelectric effect

Vacuumtube

Experimental results

Electron KE (electron Volts)

f0

For light freq below f0,no electrons leave the cathode

Even if the light Is very intense

0 0.5 1.0 1.5

Experimental results

Electron KE (electron Volts)

f0

For light freq above f0,the KE of electrons that leave the cathode increases with increasing freq

But does not changeWith light intensity

0 0.5 1.0 1.5

What does Maxwell’s theory say?

E

E

E

Electrons incathode areaccelerated bythe E-field ofthe light wave

More intense light hasbigger E-fields

EE

E

And, thereforeLarger acceleration

Electron KE should depend on E-field strength light intensity

Electron’s motion

Not what is

observed

But that’s not what is observed

Electron KE (electron Volts)

f0

0 0.5 1.0 1.5

Above f0,the KE onlydepends on freq, & not on the light’s intensity

Below f0, no electrons jump out of the cathode no matter what the light’s intensity is

Einstein’s explanation

KEelectron = hf -

Light is comprised of particle-like

quanta each with energy Equant = hf

The quanta collide with electrons &Transfer all their energy to them

Each electron needs a minimum energy to escape the cathode. This is called

If Equant is less than , the electron can’t escape

If Equant is greater than , the electron escapes & the quantum energy in excess of becomes electron KE

Light quanta “photons”

Einstein’s light quantawere given the name“photons” by Arthur Compton

Photon Energy for red light

Red light: f = 4.0x1014 Hz

Ephoton = hf

= (6.6x10-34 Js) x (4.0x1014 Hz)

= 2.6 x 10-19 J

1eV 1.6 x 10-19 J

x

=

2.6 1.6

eV

=1.6 eV

(Hz = 1/s)

Photon Energies for visible light

color: freq Equant = hf

Red 4.0x1014 Hz 2.6x10-19J 1.6 eV

Yellow 5.0x1014Hz 3.3x10-19J 2.1 eV Green 6.0x1014

Hz 4.0x10-19J 2.5 eVBlue 6.7x1014Hz 4.4x10-19J 2.8 eVViolet 7.5x1014

Hz 5.0x10-19J 3.1 eV

Producing photoelectrons with photons

-

--

-2.1eV

-Not enough

energy to getover the barrierRed photon-

Clears the barrier with energy to

spare

KE=0.7eV

Blue photon

Surfac

e

barr

ier

1.6eV

2.8eV

inside the metal

outside ofthe metal

For E

Electron KE (electron Volts)

red

0 0.5 1.0 1.5

yellow

blue

violet

KEKE

Photons are weird particles

v=c (always)

11 – v2/c2

(always)

11 – c2/c2

11 – 1

What is the photon’s rest mass?

E=mc2 m= Ec2

m = m0 m0 = m =

m

= 0

m0 = 0 Rest mass = 0

Photon’s momentum

For any particle: p=mv

for a photon: m=Ec2 & v = c

p = cEc2

= Ec

Photon energy & momentum

E = hf

p = Ec =

hfc

Wavelength: = cf

= h

= fc

1

“particles” of light

E=hf

hp =

Two body collisions

conservationof momentum

Compton scattering

Scatter X-rays from electrons

Recoil electron &scattered photonconserve momentum

p=h/i

p=h/f

-

Compton’s expt proved the existence of photons

& won him the 1927 Nobel Prize (Physics)

Photon “spectrum”

Ult

ra-

vio

let

Infr

a-

red

X-

rays

- rays

mic

ro

wave

srad

io

wave

sTV

/FM

AM

4x10-3eV 4x10-11eV 4eV 4x103eV 4x106eV 4x10-7eV

visible light

1.6 – 3.1eV

Wave? Particles??

Maxwell

Light is a wave of oscillating E- and B-fields

James Clerk Maxwell

E

B

Einstein

Light is comprised of particle-like quanta

called photons

E=hf

hp =

Who’s right??

Waves explain diffraction & interference

Photons explain photoelectric effect & Compton scattering

Impossible to explain interference with particles

With 2 slits openno light goes here

Block off one slit

Now lightcan go here

Impossible to explain PE-effectand Compton scattering with waves

Electron KE (electron Volts)

red

0.5 1.0 1.5

yellow

blue

violet

Make an interferencepattern with low intensity light

One photon at a time goes through the two-slit apparatus

-Light behaves like a wave when it propagates through space-And as a particle when it interacts with matter

Photon photography