Black-body Radiation & the Quantum Hypothesis Physics 100 Chapt 20 Max Planck
Mar 26, 2015
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