Black-body Radiation & the Quantum Hypothesis

Physics 100

Chapt 20

Max Planck

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

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

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