kBT
or
mT 2898μm K
Wien’s displacement law
proposed by Wien in 1893
In 1869 Wien proposed a formula empirically from experimental data:
u( ,T )d ~ 3e T d ~ e T 2d.
photoelectrons photoelectric current ~ I
Tmax eV0 ?~ I incident
stopping potential
Experiments show Tmax~ C below it, no ... 10 – 9s after irradiation
Blackbody a complete black object that reflects none of the radiation that strikes it.
A cavity with a small hole Radiation from outside that strikes the hole gets lost inside the cavity.
V0
h
e
f
e
1916 Millikan
1923 Nobel prize was awarded to Millikan for his work on the elementary charge of electricity and on the photoelectric effect.
1889 Max Planck proposed a new formula
u( ,T )d
8 2
c3
h
eh
1
d
Or, equivalently
u(,T )
8π
4
hc 1
eβ
hcλ
dλ 1
.
u( ,T )d
8 2
c3
e
h
h
1
d
high limit
: u( ,T )d
8h
Wien’s formula
Rayleigh-Jeans law (1900-1905) Lord Rayleigh, Sir James Jeans
1. The cavity is filled with the electromagnetic standing wave.
2. The number of standing waves with frequencies
is just the energy current 1
2
3
density ju
ju
1 4
u
c.
see effusion §13.4
The experimental results
1. Stefan-Boltzmann law
ju
R( ,T )d
T 4.
0
5.67 108W m2 K 4.
The 1918 Nobel Prize was awarded to Planck for his discovery of energy quanta.
22.2 Photoelectric effect
ultraviolet light
+
In 1888, Hallwachs found photoelectric effect
This is against the second law of thermodynamics.
Therefore, in equilibrium, the energy density of the
radiation in a cavity is function of temperature alone.
quanta:
E nh.
nhenh
n
enh
h
e h
. 1
n
From
R( ,T )d T 4,
0
we can obtain
2 5kB4
15c2h3
,
and
h 6.6261034 Js.
The constant h has fundamental significance. which has no counterpart in classical physics.,
u u( ,T ) or u u(,T ).
If the energy density of the radiation depends on other properties so that
u( ,T ,x) u( ,T ,y),
a perpetual machine of second kind will become possible.
0
the radiated energy current
R( )d density of the radiation with
frequency in a range d
R( ) the radiant intensity
prism
The total radiant intensity
0 R( )d
between and +d is
N( )d
8V
c3
2
d
where V is the volume of the cavity.
3.Each individual standing wave contributes an
energy kBT to the radiation in the cavity. Then, the energy density is
British physicist Lord Kelvin (W. Thomson)
“In the remote part of sunny sky of physics there are two small puzzling dark clouds.”
Michelson Morley experiment blackbody radiation
Example 22.1
~m
~W
power P0 ~ W; intensity is P0 / 4r2 absorbed power is
P
~
I
a2
P0
a
2
~
W
Å
m
2
4 r
To escape, the electron has to accumulate an amount of
energy about eV in a time interval t
Planck announced the result in 1900. There were no shock waves. Planck himself believed that he had just found a ad hoc explanation.
It was not until after 1911 that Planck fully appreciated the absolutely fundamental nature of quantization
u u( ,T ), [u u(,T )].
the energy density of the radiation in a cavity per unit range of frequency[wavelength].
the energy density of the radiation
u(T ) u( ,T )d
Part IV Fundamental Modern Physics
Chapter 22 Energy Quantization
discreteness the existence of fundamental unit
g
G c3
1.6
1035 m
e 1.602177331019C
At the end of 19th century, most physicists thought that the mansion of classical physics was basically established, the work left for the physicists would be just mending.
Critical frequency C
h f Tmax
0
f
h
C
Example 22.2 Critical wavelength and frequency
for Na and Pt
green-yellow visible
C (Na)
hc
f
1240eV nm 2.28eV
543 nm
C (Na)
22.1 Blackbody radiation
Thermal radiation (infrared-visible-ultraviolet) emitted by ordinary objects depends not only on the temperature, but also on other properties such as • shape • surface properties • material of which it is constructed • whether or not it reflects the radiation the falls on from its surroundings
u( )d
8 2
c3
d
8 2
c3
kBTd .