1. Black-body Radiation & the Quantum Hypothesis
Max Planck
Physics 100
Chapt 20

2. Black-body Radiation l peak = 2.9 x 10-3 m T(Kelvin) UV IR
Light intensity UV IR

3. lpeak vs Temperature T l peak = 3100K 58000K 2.9 x 10-3 m T(Kelvin)
(body temp)
2.9 x 10-3 m
3100
=9x10-6m
infrared light
58000K
(Sun’s surface)
visible light
2.9 x 10-3 m
58000
=0.5x10-6m

4. “Room temperature” radiation

5. Photo with an IR camera

6. IR Cat

7. IR house

8. Theory & experiment disagree wildly
the UV catastrophe
Theory & experiment disagree wildly
Pre-1900 theory

9. Planck’s solution h = 6.6 x 10-34 Js “Planck’s constant”
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 Js
“Planck’s constant”

10. Other “quantum” systems

11. The quantum of the US monetary system
We don’t worry about effects of quantization
Because the penny’s value is so small

12. Suppose the quantum were a $1000 bill
A quantum this large would have an
enormous effect on “normal” transactions

13. The quantum of the US Income tax system

14. US Income tax with a $1 quantum
Number of taxpayers

15. US Income tax with a $1000 quantum
Number of taxpayers
All these guys don’t
have to pay anything
Quantum effects
are negligible to
these taxpayers
Quantum effects are
huge to these guys

16. How quanta defeat the UV catastrophe
Without
the quantum
With the quantum
Low frequency,
small quantum,
Negligible effects
high frequency,
large quantum,
huge effects

17. Planck’s quantum is small for “ordinary-sized” objects but large for atoms etc
pendulum
f = 1 Hz
Hydrogen atom
f  2x1014 Hz
about the same as
the electron’s KE
Equant= hf
=(6.6x10-34Js)x(2x1014Hz)
Equant= hf
=6.6x10-34Jsx1Hz
=(6.6 x 2) x J
very tiny
=6.6x10-34J
=1.3 x 10-19J

18. Typical energies in “ordinary” life
Typical energy of
a tot on a swing:
Etot = mghmax
= 20kgx10m/s2x1m
= 20kgx10m/s2x
= 20kgx
hmax
= 200 kgm2/s2
= 200 J
much, much larger than
Equant=6.6x10-34J

19. Typical electron KE in an atom
Energy gained by an
electron crossing a 1V
voltage difference
1 “electron Volt”
Energy = q V - - -
1eV = 1.6x10-19C x 1V 1V
= 1.6x10-19 Joules
similar
Equant = 1.3 x 10-19J
for f  2x1014 Hz

20. Classical vs Quantum world
At atomic & subatomic scales,
quantum effects
are dominant & must be considered
In everyday life,
quantum effects
can be safely
ignored
Laws of nature
developed without
consideration of
quantum effects do not work for atoms
This is because
Planck’s constant is so small