equipment
2,Photoelectric Effect,Einstein’s Photon Theory
(光电效应、爱因斯坦光子理论 )
R
K1
K2
E
G
V
les,called photons,
Einstein assumed that the
energy in a light beam travels
through space in concentrated
bund
pi The energy E of a single
photon is given by
E = hv,
Applying the photon
concept to the photoelectric
effect,Einstein wrote
SI
Si
光电管
K
A
)10(21 02m a x ?Amvh ???
Equation above says that a photon
carries an energy hv into the sur-
face,Part of this energy A0 is used
in causing the electron to pass
through the metal surface,The
excess energy (hv-A0) is given to
the electron in the form of kinetic
energy,
In 1916,Milikan,experiments
verified Einstein’s ideas in
every detail,
Einstein succeed in explaining
the photoelectric effect,
h?
-
-
金
属
electron
-
- - A v?
The dual nature of light,particle and wave
光的波粒二象性
particle wave
（ energy） （ frequency）
（ momentum） （ wavelength）
?E
??P
?h
These two natures are connected by h,
)1(??? hE ?
)2(/ ?
?
?
??
h
C
hCEP ???
22
0
2 )( cPEE ??
3,The Compton effect (康普顿效应 )
Compelling confirmation of the
concept of the photon as a concen-
trated bundle of energy was provided
in 1923 by A.H.Compton who earned
a Noble prize for this work in 1927,
Compton allowed a beam of X-rays
of sharply defined wavelengthλto fall
on a graphite block,He measured,
for various angles of scattering,
the intensity of the scattered X-rays
as a function of their wavelength,
1) Equipment
Compton allowed a beam of X-rays of sharply
defined wavelengthλto fall on a graphite block,
He measured,for various angles of scattering,the
intensity of the scattered X-rays as a function of
their wavelength,
0?
?
?
X光
光
栏 石墨
0.70?
X射线分析仪
1) Equipment
0?
?
2) Experimental results,
?
X光
光
栏 石墨
0.70?
X射线分析仪
2
3
4
1 ?=00
?=450
?=900
?=1350
0.70 0.75 ?(?)
强
度
?The scattered X-rays have intensity
peaks at two wavelengths,one of
the them is the same as the incident
wavelength,?0,the other,?,being
larger by an amount △ ?,
2
3
4
1 ?=00
?=450
?=900
?=1350
0.70 0.75 ?(?)
强
度
?
?This so-called Compton
shift △ ? varies with the
angle at which the
scattered X-rays are
observed,
?Compton shift △ ? for
collisions with tightly
bound electrons is
immeasurably small,
3) Explain Compton Effect 对康普顿效应的解释
Compton was able to explain his experimental
results by postulation that the incoming X-ray
beam was not a wave but an assembly of photons
of energy E (= hv) and that these photons expe-
rienced billiard-ball-like collisions with the free
electrons in the scattering block,
h?0
0?n
m0
e X
Before After
h?0
0?n
e m
V
h?
X
Analyze quantitatively
m0
e
h?0
0?n
2
0Cm
m0
e
n?
Before After
Before After
Electron Photon Electron Photon
energy
momentum
2mC
0?h ?h
0
0
0 ?n
C
h? n
C
h ??Vm ?
Let us assume this is an elastic scattering collision,
= + +
= +
h?0
0?n
m
V
h?
Analyze quantitatively
Before After
)1(2200 ?mChCmh ??? ??
)2(?? 00 ?
?
n
C
hVmn
C
h ?? ??
)4(c o s2)()()( 02202 ??????
C
h
C
h
C
h
C
hmV ???
{
?
?
n
C
h ??
Vm ?
0
0 ?n
C
h?
From（ 1） )3()( 2
00
2 ?CmhmC ??? ??
From the low of cosine
X
m0
e
h?0
0?n
m0
e n?
h?0
0?n
m
V
h?
Analyze quantitatively
)4(c o s2)()()( 02202 ??????
C
h
C
h
C
h
C
hmV ???
)3()( 2002 ?CmhmC ??? ??
)5()c o s1(2 022202222 ?????? ???? hhhCVm
（ 3） 2-（ 5）
Before After
?
?
n
C
h ??
Vm ?
0
0 ?n
C
h?
X
m0
e
h?0
0?n
m0
e n?
h?0
0?n
m
V
h?
)6()(2 020 ??? ?? hCm
)c o s1(2)1( 024202
2
42 ??? ???? hCm
C
VCm
)3()( 2002 ?CmhmC ??? ??
)5()c o s1(2 022202222 ?????? ???? hhhCVm
（ 3） 2-（ 5）,
)c o s1(2 02420420 ??? ??? hCmCm
?
?
nCh ??
Vm?
0
0 ?n
C
h?
)7()(2 020 ??? ?? hCm
)8()c o s1(
)(
00
0 ??
??
??
??
?
Cm
hC
or
or
2
2
0
1
C
V
m
m
?
?
)9()c o s1(
00
??
??
???
Cm
hCC
)c os1(
0
???
Cm
h
0??? ???
2
s in
2 2
0
?
Cm
h
? （ m）
m
Cm
h 12
0
1043.2 ????
2
s in0 2 4 3.02 20 ???? ????? （ ?）
….(10)
….(11)
?
?
nCh ??
Vm?
0
0 ?n
C
h?
)8()c o s1()(
00
0 ??
??
?? ???
Cm
hC
Compton wavelength
2
s in0 2 4 3.02 20 ???? ????? （ ?）
)c os1(
0
???
Cm
h
0??? ???
2
s in
2 2
0
?
Cm
h
? （ m）
….(10)
….(11)
Discuss,
?Equation (11) predicts
within experimental
error the experimentally
observed Compton shifts,
? The peak for ?0 can be
understood as resulting
?
?
nCh ??
Vm ?
0
0 ?n
C
h?
Discuss,
? The peak for ?0 can be
understood as resulting
from a collision between a
photon and electrons bound
in an ionic core,The
electron’s effective mass
is much greater,
ionic core铅球
Photon
乒乓球
?The Compton effect for longer
wavelength is hardly observed,
quantum results reduces to
classical results,
For example,?0 = 10 cm,△ ?/ ?0 = 2.43× 10-11,
the Compton effect is hardly observed,
?
?
nCh ??
Vm ?
0
0 ?n
C
h?
4） Significance
A） Compelling confirmation
of the concept of the photon as
a concentrated bundle of energy
was provided,The photon has
mass,energy and momentum,
B) In microscopic field,the law of conservation of
momentum and the law of conservation of energy
are still strictly observed,
Exp,An X-ray with E = 0.60MeV are scattered from
a carbon block,Its wavelength changed 20%
in the collision,What kinetic energy is
imparted to the recoiling electron?
?
?
nCh ??
Vm ?
0
0 ?n
C
h?
例：能量为 0.60MeV的 X射线在碳块上散射后，波
长变化了 20%，求反冲电子动能。
Known,E0=h?0=0.6MeV,??=0.2?0,
Find,Ee=?
Solve,
0
00 ??
ChhE ??
)(1048.22.12.0 12000 m?????? ????
)(1007.2
1060.11060.0
1031063.6/ 12
196
834
00 mEhC
?
?
?
??
???
??????
kinetic energy of the recoiling electron,
??? hhEEE e ???? 00
eE
m0
e
n?h?0
0?n
m
V
h?
)(1048.22.12.0 12000 m?????? ????
kinetic energy of the recoiling electron,
??? hhEEE e ???? 00
0
0
0 ??
??
??
???? hCChCh
0
12
0834
1048.2
2.01031063.6
?
?
?
?
?
????
)(1060.1 14 J???
M e VE e 10.0?
The kinetic energy 0.10Mev imparted to the
recoiling electron,
eE
n?h?0
0?n
e m
V
h?