Download Black-body Radiation & the Quantum Hypothesis

Black-body Radiation & the
Quantum Hypothesis
Max Planck
Physics 100
Chapt 20
Black-body Radiation
Light intensity
l peak
UV
IR
2.9 x 10-3 m
=
T(Kelvin)
lpeak vs Temperature
T
3100K
(body temp)
58000K
(Sun’s surface)
l peak
2.9 x 10-3 m
=
T(Kelvin)
2.9 x 10-3 m
-6m
=9x10
3100
infrared light
10-3
visible light
2.9 x
m
-6m
=0.5x10
58000
“Room temperature” radiation
Photo with an IR camera
IR Cat
IR house
the UV catastrophe
Theory & experiment disagree wildly
Pre-1900 theory
Planck’s solution
EM energy cannot be radiated or absorbed
in any arbitrary amounts, but only in discrete
“quantum” amounts.
The energy of a “quantum” depends on frequency
as
Equantum = h f
h = 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 quantization
Because the penny’s value is so small
Suppose the quantum were a
$1000 bill
A quantum this large would have an
enormous effect on “normal” transactions
The quantum of the US Income tax
system
Number of taxpayers
US Income tax with a $1 quantum
Number of taxpayers
US Income tax with a $1000
quantum
Quantum effects are
huge to these guys
All these guys don’t
have to pay anything
Quantum effects
are negligible to
these taxpayers
How quanta defeat the UV
catastrophe
Without
the quantum
With the quantum
high frequency,
large quantum,
huge effects
Low frequency,
small quantum,
Negligible effects
Planck’s quantum is small for “ordinarysized” objects but large for atoms etc
“ordinary”
pendulum
f = 1 Hz
Hydrogen atom
f  2x1014 Hz
Equant= hf
Equant= hf
=6.6x10-34Jsx1Hz
=6.6x10-34J
=(6.6x10-34Js)x(2x1014Hz)
=(6.6 x 2) x 10-34+14J
=1.3 x 10-19J
Typical energies in “ordinary” life
Typical energy of
a tot on a swing:
Etot = mghmax
22x1m
20kgx
===20kgx10m/s
20kgx10m/s
x
= 200 kgm2/s2
= 200 J
hmax
much, much larger than
Equant=6.6x10-34J
Typical electron KE in an atom
1 “electron Volt”
- - 1V
Energy gained by an
electron crossing a 1V
voltage difference
Energy = q V
1eV = 1.6x10-19C x 1V
= 1.6x10-19 Joules
similar
Equant = 1.3 x 10-19J
for f  2x1014 Hz
Classical vs Quantum world
In everyday life,
quantum effects
can be safely
ignored
This is because
Planck’s constant
is so small
At atomic &
subatomic scales,
quantum effects
are dominant &
must be considered
Laws of nature
developed without
consideration of
quantum effects do
not work for atoms