black-body radiation & the quantum hypothesis physics 100 chapt 20 max planck
TRANSCRIPT
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Black-body Radiation & the Quantum Hypothesis
Physics 100
Chapt 20
Max Planck
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Black-body Radiation
peak = 2.9 x 10-3 m
T(Kelvin)
Lig
ht
inte
nsit
y
UV
IR
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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
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“Room temperature” radiation
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Photo with an IR camera
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IR Cat
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IR house
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the UV catastrophe
Pre-1900 theory
Theory & experiment disagree wildly
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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”
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Other “quantum” systems
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The quantum of the US monetary system
We don’t worry about effects of quantizationBecause the penny’s value is so small
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Suppose the quantum were a $1000 bill
A quantum this large would have anenormous effect on “normal” transactions
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The quantum of the US Income tax system
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US Income tax with a $1 quantum
Nu
mb
er
of
taxp
ayers
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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
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How quanta defeat the UV catastrophe
Low frequency,small quantum,
Negligible effects
high frequency,large quantum,
huge effects
Withoutthe quantum
With the quantum
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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
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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
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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
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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